Deterministic reshaping and / or reordering of groups of atomic objects within an atomic object limiting device

Abstract

Various embodiments of the present invention provide a method, apparatus, system, or computer program product for deterministically reordering a set of atomic objects within an atomic object confinement device. The set of atomic objects includes object A, object B, object C, and object D, where object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The atomic object confinement device includes a plurality of potential energy generating elements that are controlled to form a time-dependent potential field within the atomic object confinement device. The time-dependent potential field experienced by the set of atomic objects causes object A, object B, object C, and object D to move along corresponding reordering trajectories such that the set of atomic objects is deterministically reshaped and / or reordered.

Description

Technical Field

[0001] Various embodiments relate to apparatuses, systems, and methods related to controlling atomic objects within an atomic object confinement device. For example, some exemplary embodiments relate to reordering ions within an ion trap. Background Art

[0002] An ion trap can use a combination of electric and magnetic fields to trap multiple ions in a potential well. The ions can be trapped for multiple purposes, which can include, for example, mass spectrometry, research, and / or control of quantum states. In various cases, it may be desirable to change the order of the group of ions within the ion trap. Current reordering schemes suffer from random reordering of the ions within the group of ions, which makes it difficult to use such reordering schemes when attempting to perform a deterministic process on the group of ions within the ion trap. Through the efforts, ingenuity, and innovation, many of the deficiencies of such prior ion traps have been solved by developing solutions constructed according to embodiments of the present invention, many examples of which are described in detail herein. Summary of the Invention

[0003] Exemplary embodiments provide methods, systems, apparatuses, computer program products, etc. for performing deterministic reshaping and / or reordering of a group of atomic objects within an atomic object confinement device. In various embodiments, the atomic object is an ion or an atom. In various embodiments, the atomic object confinement device is a trap or other confinement device configured to confine multiple atomic objects. For example, the multiple atomic objects can be multiple ions, and the atomic object confinement device can be an ion trap.

[0004] According to a first aspect, a method for deterministically reordering a set of atomic objects within an atomic object confinement device is provided. In an exemplary embodiment, the method includes providing a plurality of atomic objects in the atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy, the initial chain being in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C; a rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis by a rotation angle; and realignment of the set of atomic objects into a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, wherein object B and object C are in relative positions with respect to the initial chain. During a start portion of the rotation, the time-dependent potential energy includes a compression potential energy that compresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis. During an end portion of the rotation, the time-dependent potential energy includes a decompression potential energy that decompresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis.

[0005] In an exemplary embodiment, the rotation angle is approximately 180°. In an exemplary embodiment, the positions of object A and object D are the same in the initial chain and the final chain. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage drivers. In an exemplary embodiment, the corresponding voltage drivers are controlled by a controller of a quantum computer. In an exemplary embodiment, during an intermediate portion of the rotation, the set of atomic objects is not collinear, the intermediate portion being between an early portion and an end portion of the rotation.

[0006] According to another aspect, there is provided an apparatus and / or system for performing a deterministic reshaping and / or reordering function. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy, the initial chain being in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C; a rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis by a rotation angle; and the set of atomic objects being realigned into a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, where object B and object C are in a relative position with respect to the initial chain. During a start portion of the rotation, the time-dependent potential energy includes a compression potential energy that compresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis. During an end portion of the rotation, the time-dependent potential energy includes a decompression potential energy that decompresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis.

[0007] In an exemplary embodiment, the rotation angle is approximately 180°. In an exemplary embodiment, the positions of object A and object D are the same in the initial chain and the final chain. In an exemplary embodiment, the potential energy generating elements are controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage actuators. In an exemplary embodiment, the corresponding voltage actuators are controlled by a controller of a quantum computer. In an exemplary embodiment, during an intermediate portion of the rotation, the set of atomic objects is not collinear, the intermediate portion being between an early portion and an end portion of the rotation.

[0008] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more drivers to provide a sequence of driver actions to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, the initial chain being in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C; a rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis by a rotation angle; and the re-alignment of the set of atomic objects into a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, where object B and object C are in a relative position with respect to the initial chain. During a start portion of the rotation, the time-dependent potential energy includes a compression potential energy that compresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis. During an end portion of the rotation, the time-dependent potential energy includes a decompression potential energy that decompresses the set of atomic objects in a direction substantially aligned with the confinement potential energy axis.

[0009] In an exemplary embodiment, the rotation angle is approximately 180°. In an exemplary embodiment, the positions of object A and object D are the same in the initial chain and the final chain. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by a controller of a quantum computer. In an exemplary embodiment, during an intermediate portion of the rotation, the set of atomic objects is not collinear, the intermediate portion being between an early portion and an end portion of the rotation.

[0010] According to another aspect, a method for deterministically reordering a set of atomic objects within an atomic object confinement device is provided. In an exemplary embodiment, the method includes providing a plurality of atomic objects in the atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy. The initial chain is in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C. The reordering trajectories further include a rotation of object B and object C in a first direction caused by the rotational potential energy axis, the rotational potential energy axis being defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a first sequence of angles until the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis is a transition angle; and a compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis during a start portion of the rotation of the rotational potential energy axis through the first sequence of angles. The reordering trajectories further include, after the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis reaches the transition angle, a further compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis when the initial chain is in the first configuration, or a partial decompression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis when the initial chain is in the second configuration. The reordering trajectories further include a rotation of object B and object C in the first direction or a second direction caused by the rotational potential energy axis rotating in the first direction or a second direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a second sequence of angles; and a decompression of the set of atomic objects in a direction substantially aligned with the axis during an end portion of the rotation. When the rotational potential energy axis has rotated through the second sequence of angles, the set of atomic objects is arranged in a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis. When the initial chain is in the first configuration, the final chain is in the second configuration, and when the initial chain is in the second configuration, the final chain is in the first configuration.

[0011] In an exemplary embodiment, the rotational direction of the second sequence angle is determined based on the desired final position of object B or object C. In an exemplary embodiment, the transition angle is in the range of approximately 70° - 110°. In an exemplary embodiment, when object B and object C have rotated through the second sequence angle, the angle between the virtual line connecting object B and object C and the axis is the final second sequence angle, and the final second sequence angle is one of approximately 0° or approximately 180°. In an exemplary embodiment, when the angle between the virtual line connecting object B and object C and the axis reaches the transition angle, a set of atomic objects is not collinear. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving the Hamiltonian operator using a reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by a controller of a quantum computer.

[0012] According to another aspect, there is provided an apparatus and / or system for performing a deterministic reshaping and / or reordering function. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectory includes an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial chain is in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C. The reordering trajectory further includes a rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a first sequence of angles until an angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis is a transition angle; and a compression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis during a start portion of the rotation of the rotational potential energy axis through the first sequence of angles. The reordering trajectory further includes a further compression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis after the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis reaches the transition angle when the initial chain is in the first configuration, or a partial decompression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis when the initial chain is in the second configuration. The reordering trajectory further includes a rotation of object B and object C in a first direction or a second direction caused by a rotation of the rotational potential energy axis in the first direction or the second direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a second sequence of angles; and a decompression of a set of atomic objects in a direction substantially aligned with the axis during an end portion of the rotation. When the rotational potential energy axis has rotated through the second sequence of angles, a set of atomic objects is arranged in a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis. When the initial chain is in the first configuration, the final chain is in the second configuration, and when the initial chain is in the second configuration, the final chain is in the first configuration.

[0013] In an exemplary embodiment, the rotational direction of the second sequence angle is determined based on the desired final positions of object B or object C. In an exemplary embodiment, the transition angle is in the range of approximately 70° - 110°. In an exemplary embodiment, when object B and object C have rotated through the second sequence angle, the angle between the virtual line connecting object B and object C and the axis is the final second sequence angle, and the final second sequence angle is one of approximately 0° or approximately 180°. In an exemplary embodiment, when the angle between the virtual line connecting object B and object C and the axis reaches the transition angle, a group of atomic objects is not collinear. In an exemplary embodiment, the potential energy generating element is controlled according to the solution of the time-dependent potential field found by solving the Hamiltonian operator using the reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by the controller of the quantum computer.

[0014] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more actuators to provide an actuator action sequence to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial chain is in (1) a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D, or (2) a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C. The reordering trajectories further include a rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a first sequence of angles until the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis is a transition angle; and a compression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis during a start portion of the rotation of the rotational potential energy axis through the first sequence of angles. The reordering trajectories further include, after the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis reaches the transition angle, a further compression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis when the initial chain is in the first configuration, or a partial decompression of a set of atomic objects in a direction substantially aligned with the confinement potential energy axis when the initial chain is in the second configuration. The reordering trajectories further include a rotation of object B and object C in a first direction or a second direction caused by a rotation of the rotational potential energy axis in the first direction or the second direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a second sequence of angles; and a decompression of a set of atomic objects in a direction substantially aligned with the axis during an end portion of the rotation. When the rotational potential energy axis has rotated through the second sequence of angles, a set of atomic objects is arranged in a final chain. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis. When the initial chain is in the first configuration, the final chain is in the second configuration, and when the initial chain is in the second configuration, the final chain is in the first configuration.

[0015] In an exemplary embodiment, the rotational direction of the second sequence angle is determined based on the desired final positions of object B or object C. In an exemplary embodiment, the transition angle is in the range of approximately 70° - 110°. In an exemplary embodiment, when object B and object C have rotated through the second sequence angle, the angle between the virtual line connecting object B and object C and the axis is the final second sequence angle, and the final second sequence angle is one of approximately 0° or approximately 180°. In an exemplary embodiment, when the angle between the virtual line connecting object B and object C and the axis reaches the transition angle, a set of atomic objects is not collinear. In an exemplary embodiment, the potential energy generating element is controlled according to the solution of the time-dependent potential field found by solving the Hamiltonian operator using the reordered trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage to it by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by the controller of the quantum computer.

[0016] According to another aspect, a method for deterministically reordering atomic objects within an atomic object confinement device is provided. In an exemplary embodiment, the method includes providing a plurality of atomic objects in an atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial object chain is in a first configuration, where object B and object C are adjacent to each other and are disposed between object A and object D. The reordering trajectories further include a rotation of the initial chain caused by rotation of the rotational potential energy in a first direction to form a rotated initial chain such that a rotational potential energy axis defined by the rotational potential energy is rotated by a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain along a direction substantially parallel to the confinement potential energy axis such that object B is farther from the confinement potential energy axis than object A, and object C is farther from the confinement potential energy axis than object D, thereby forming a compressed configuration; a rotation of the compressed configuration in a second direction caused by rotation of the rotational potential energy in the second direction such that the rotational potential energy axis is rotated by a second angle relative to the confinement potential energy axis, the second angle being substantially equal to twice the first angle, and the second direction being opposite to the first direction, thereby providing a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis, thereby forming an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by rotation of the rotational potential energy axis by a third angle relative to the confinement potential energy axis in the first direction, thereby providing a final chain. The third angle is substantially equal to the first angle. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, where object B and object C are in relative positions with respect to the initial chain.

[0017] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying voltages thereto by corresponding voltage drivers. In an exemplary embodiment, the corresponding voltage drivers are controlled by a controller of a quantum computer.

[0018] According to another aspect, an apparatus and / or system for performing a deterministic reshaping and / or reordering function is provided. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial object chain is in a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D. The reordering trajectories further include a rotation of the initial chain caused by rotation of the rotational potential energy in a first direction to form a rotated initial chain such that a rotational potential energy axis defined by the rotational potential energy is rotated by a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain along a direction substantially parallel to the confinement potential energy axis such that object B is further from the confinement potential energy axis than object A and object C is further from the confinement potential energy axis than object D, thereby forming a compressed configuration; a rotation of the compressed configuration in a second direction caused by rotation of the rotational potential energy in the second direction such that the rotational potential energy axis is rotated by a second angle relative to the confinement potential energy axis, the second angle being substantially equal to twice the first angle and the second direction being opposite to the first direction, thereby providing a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis, thereby forming an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by rotation of the rotational potential energy axis by a third angle in the first direction relative to the confinement potential energy axis, thereby providing a final chain. The third angle is substantially equal to the first angle. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, wherein object B and object C are in relative positions with respect to the initial chain.

[0019] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating elements are controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage actuators. In an exemplary embodiment, the corresponding voltage actuators are controlled by a controller of a quantum computer.

[0020] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more drivers to provide a sequence of driver actions to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectory includes an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial object chain is in a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D. The reordering trajectory further includes a rotation of the initial chain caused by rotation of the rotational potential energy in a first direction to form a rotated initial chain such that a rotational potential energy axis defined by the rotational potential energy is rotated by a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain in a direction substantially parallel to the confinement potential energy axis such that object B is farther from the confinement potential energy axis than object A and object C is farther from the confinement potential energy axis than object D, thereby forming a compressed configuration; a rotation of the compressed configuration in a second direction caused by rotation of the rotational potential energy in the second direction such that the rotational potential energy axis is rotated by a second angle relative to the confinement potential energy axis, the second angle being substantially equal to twice the first angle, and the second direction being opposite to the first direction, thereby providing a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis, thereby forming an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by rotation of the rotational potential energy axis by a third angle in the first direction relative to the confinement potential energy axis, thereby providing a final chain. The third angle is substantially equal to the first angle. The final chain includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis, wherein object B and object C are in relative positions with respect to the initial chain.

[0021] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by a controller of a quantum computer.

[0022] According to another aspect, a method for deterministically reordering a set of atomic objects within an atomic object confinement device is provided. In an exemplary embodiment, the method includes providing a plurality of atomic objects in the atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial object chain is in a third configuration, wherein object B and object C are adjacent to each other, and object A and object D are adjacent to each other. The reordering trajectories further include rotation of the initial chain by controlling the potential energy generating element to rotate the rotational potential energy in a first direction to form a rotated initial chain such that a rotational potential energy axis defined by the rotational potential energy is rotated by a first angle relative to the confinement potential energy axis; compression of the rotated initial chain along a direction substantially parallel to the confinement potential energy axis to form a compressed configuration; rotation of the compressed configuration in a second direction by controlling the potential energy generating element to rotate the rotational potential energy in the second direction such that the rotational potential energy axis is rotated by a second angle relative to the confinement potential energy axis, the second angle being greater than twice the first angle, and the second direction being opposite to the first direction to provide a rotated configuration; decompression of the rotated configuration along the confinement potential energy axis to form an off-axis final chain; and rotation of the off-axis final chain in the first direction by controlling the potential energy generating element to rotate the rotational potential energy in the first direction such that the rotational potential energy axis is rotated by a third angle relative to the confinement potential energy axis to provide a final chain that is substantially aligned along the confinement potential energy axis. The final chain includes object A, object B, object C, and object D, wherein object A and object C are in relative positions with respect to the initial chain.

[0023] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving the Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage drivers. In an exemplary embodiment, the corresponding voltage drivers are controlled by a controller of a quantum computer.

[0024] According to another aspect, an apparatus and / or system for performing a deterministic reshaping and / or reordering function is provided. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement apparatus that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement apparatus, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential and a rotational potential. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential axis of the confinement potential. The initial object chain is in a third configuration where object B and object C are adjacent to each other, and object A and object D are adjacent to each other. The reordering trajectories further include a rotation of the initial chain achieved by controlling the potential energy generating elements to rotate the rotational potential in a first direction to form a rotated initial chain such that a rotational potential axis defined by the rotational potential is rotated by a first angle relative to the confinement potential axis; a compression of the rotated initial chain along a direction substantially parallel to the confinement potential axis to form a compressed configuration; a rotation of the compressed configuration in a second direction achieved by controlling the potential energy generating elements to rotate the rotational potential in the second direction such that the rotational potential axis is rotated by a second angle relative to the confinement potential axis, the second angle being greater than twice the first angle, and the second direction being opposite to the first direction to provide a rotated configuration; a decompression of the rotated configuration along the confinement potential axis to form an off-axis final chain; and a rotation of the off-axis final chain in the first direction achieved by controlling the potential energy generating elements to rotate the rotational potential in the first direction such that the rotational potential axis is rotated by a third angle relative to the confinement potential axis to provide a final chain that is substantially aligned along the confinement potential axis. The final chain includes object A, object B, object C, and object D, where object A and object C are in relative positions with respect to the initial chain.

[0025] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating elements are controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement apparatus is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage drivers. In an exemplary embodiment, the corresponding voltage drivers are controlled by a controller of a quantum computer.

[0026] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more drivers to provide a sequence of driver actions to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy. The initial object chain is in a third configuration in which object B and object C are adjacent to each other and object A and object D are adjacent to each other. The reordering trajectories further include a rotation of the initial chain achieved by controlling the potential energy generating element to rotate the rotational potential energy in a first direction to form a rotated initial chain such that a rotational potential energy axis defined by the rotational potential energy rotates by a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain in a direction substantially parallel to the confinement potential energy axis to form a compressed configuration; a rotation of the compressed configuration in a second direction achieved by controlling the potential energy generating element to rotate the rotational potential energy in a second direction such that the rotational potential energy axis rotates by a second angle relative to the confinement potential energy axis, the second angle being greater than twice the first angle and the second direction being opposite to the first direction to provide a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis to form an off-axis final chain; and a rotation of the off-axis final chain in the first direction achieved by controlling the potential energy generating element to rotate the rotational potential energy in the first direction such that the rotational potential energy axis rotates by a third angle relative to the confinement potential energy axis to provide a final chain that is substantially aligned along the confinement potential energy axis. The final chain includes object A, object B, object C, and object D, where object A and object C are in relative positions with respect to the initial chain.

[0027] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, the corresponding voltage driver is controlled by a controller of a quantum computer.

[0028] According to another aspect, a method for deterministically reordering a set of atomic objects within an atomic object confinement device is provided. In an exemplary embodiment, the method includes providing a plurality of atomic objects within the atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential energy, a rotational potential energy, and a radial push potential energy. The time evolution of the amplitude of the radial push potential energy includes monotonically increasing to a maximum value and then monotonically decreasing to a minimum value. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, the initial object chain being in a third configuration where object B and object C are adjacent to each other and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move further away from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in relative positions with respect to object A and object D that are opposite to those in the initial chain.

[0029] In an exemplary embodiment, object B and object C each have a greater mass than object A and object D. In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of the rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to the confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy.

[0030] According to another aspect, an apparatus and / or system for performing a deterministic reshaping and / or reordering function is provided. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy, a rotational potential energy, and a radial push potential energy. The time evolution of the amplitude of the radial push potential energy includes a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, the initial object chain being in a third configuration where object B and object C are adjacent to each other and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move further away from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in a relative position with respect to object A and object D that is opposite to their relative position in the initial chain.

[0031] In an exemplary embodiment, object B and object C each have a greater mass than object A and object D, respectively. In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of the rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to the confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy.

[0032] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more actuators to provide an actuator action sequence to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy, a rotational potential energy, and a radial push potential energy. The time evolution of the amplitude of the radial push potential energy includes a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. The reordering trajectories include: an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy, the initial object chain being in a third configuration in which object B and object C are adjacent to each other and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move further away from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in relative positions with respect to object A and object D that are opposite to their relative positions in the initial chain.

[0033] In an exemplary embodiment, each of object B and object C has a greater mass than each of object A and object D. In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of a rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to a confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy.

[0034] According to another aspect of the present invention, a method for deterministically reordering a set of atomic objects within an atomic object confinement device is provided. For example, the method can be applied to objects similar to Figure 4 , Figure 5 and / orFigure 6 Deterministically reorder a set of atomic objects within the atomic object confinement device of the illustrated example. In an exemplary embodiment, the method includes providing a plurality of atomic objects in an atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field includes a confinement potential and a rotational potential. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential axis of the confinement potential; a rotation of object B and object C in a first direction caused by a rotational potential axis that is defined by a rotational potential that rotates in the first direction such that the rotational potential axis rotates relative to the confinement potential axis by a rotation angle; and a realignment of the set of atomic objects into a final chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential axis and in a different order relative to the initial chain. During a start portion of the rotation, a confinement ratio of the time-dependent potential energy is adjusted to cause a compression of the set of atomic objects in a direction substantially aligned with the confinement potential axis. During an end portion of the rotation, the confinement ratio of the time-dependent potential energy is adjusted to cause a decompression of the set of atomic objects in a direction substantially aligned with the confinement potential axis.

[0035] In an exemplary embodiment, the rotation angle is approximately 180°. In an exemplary embodiment, two of the inner ones among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer ones among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer ones among objects A, B, C, and D in the initial chain are two of the inner ones in the final chain. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of a time-dependent potential field found by solving a Hamiltonian operator using a reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, during an intermediate portion of the rotation, a group of atomic objects is not collinear, the intermediate portion being between an early portion and an ending portion of the rotation. In an exemplary embodiment, after an angle between a rotation potential axis and a confinement potential axis reaches a transition angle, a confinement ratio of the time-dependent potential energy is adjusted to cause one of the following: (a) a further compression of a group of atomic objects in a direction substantially aligned with the confinement potential axis, or (b) a partial decompression of a group of atomic objects in a direction substantially aligned with the confinement potential axis. In an exemplary embodiment, (a) the rotation angle is the transition angle, and (b) after the rotation potential axis rotates through the rotation angle in a first direction, the rotation potential axis rotates in a second direction such that the rotation potential axis rotates through a second sequence of angles relative to the confinement potential axis, the second direction being opposite to the first direction. In an exemplary embodiment, the transition angle is in the range of approximately 70° - 110°.

[0036] According to another aspect, there is provided an apparatus and / or system for performing a deterministic reshaping and / or reordering function. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential and a rotational potential. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential axis of the confinement potential; a rotation of object B and object C in a first direction caused by a rotational potential axis defined by a rotational potential that rotates in the first direction such that the rotational potential axis rotates relative to the confinement potential axis by a rotation angle; and a re-alignment of a set of atomic objects into a final chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential axis and in a different order relative to the initial chain. During a start portion of the rotation, a confinement ratio of the time-dependent potential energy is adjusted to cause a compression of the set of atomic objects in a direction substantially aligned with the confinement potential axis. During an end portion of the rotation, the confinement ratio of the time-dependent potential energy is adjusted to cause a decompression of the set of atomic objects in a direction substantially aligned with the confinement potential axis.

[0037] In an exemplary embodiment, the rotation angle is approximately 180°. In an exemplary embodiment, two of the inner objects among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer objects among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer objects among objects A, B, C, and D in the initial chain are two of the inner objects in the final chain. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of a time-dependent potential field found by solving the Hamiltonian operator using a reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, during an intermediate portion of the rotation, a group of atomic objects is not collinear, the intermediate portion being between an early portion and an ending portion of the rotation. In an exemplary embodiment, after an angle between a rotational potential energy axis and a confinement potential energy axis reaches a transition angle, a confinement ratio of the time-dependent potential energy is adjusted to cause one of the following: (a) further compression of a group of atomic objects in a direction substantially aligned with the confinement potential energy axis, or (b) partial decompression of a group of atomic objects in a direction substantially aligned with the confinement potential energy axis. In an exemplary embodiment, (a) the rotation angle is the transition angle, and (b) after the rotational potential energy axis rotates through the rotation angle in a first direction, the rotational potential energy axis rotates in a second direction such that the rotational potential energy axis rotates through a second sequence of angles relative to the confinement potential energy axis, the second direction being opposite to the first direction. In an exemplary embodiment, the transition angle is in the range of approximately 70° - 110°.

[0038] According to yet another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more actuators to provide an actuator action sequence to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy; a rotation of object B and object C in a first direction caused by a rotational potential energy axis that is defined by a rotational potential energy that rotates in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis by a rotation angle; and a re-alignment of a set of atomic objects into a final chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis and in a different order relative to the initial chain. During a start portion of the rotation, a confinement ratio of the time-dependent potential energy is adjusted to cause a compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis. During an end portion of the rotation, the confinement ratio of the time-dependent potential energy is adjusted to cause a decompression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis.

[0039] In an exemplary embodiment, the rotation angle is about 180°. In an exemplary embodiment, two of the inner objects among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer objects among objects A, B, C, and D in the initial chain have switched positions in the final chain. In an exemplary embodiment, two of the outer objects among objects A, B, C, and D in the initial chain are two of the inner objects in the final chain. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving the Hamiltonian operator using a reordering trajectory. In an exemplary embodiment, the atomic object is an ion, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver. In an exemplary embodiment, during an intermediate portion of the rotation, a set of atomic objects is not collinear, the intermediate portion being between an early portion and an end portion of the rotation. In an exemplary embodiment, after the angle between the rotation potential axis and the confinement potential axis reaches a transition angle, the confinement ratio of the time-dependent potential energy is adjusted to cause one of the following: (a) further compression of a set of atomic objects in a direction substantially aligned with the confinement potential axis, or (b) partial decompression of a set of atomic objects in a direction substantially aligned with the confinement potential axis. In an exemplary embodiment, (a) the rotation angle is the transition angle, and (b) after the rotation potential axis rotates through the rotation angle in a first direction, the rotation potential axis rotates in a second direction such that the rotation potential axis rotates through a second sequence of angles relative to the confinement potential axis, the second direction being opposite to the first direction. In an exemplary embodiment, the transition angle is in the range of about 70°-110°.

[0040] According to yet another aspect, a method for deterministically reordering atomic objects within an atomic object confinement device is provided. For example, the method can be similar to Figure 3 and / or Figure 7A set of atomic objects within the atomic object confinement device of the illustrated example is deterministically reordered. In an exemplary embodiment, the method includes providing a plurality of atomic objects in an atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling the potential energy generating elements among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field is a superposition of a confinement potential energy and a rotational potential energy. The reordering trajectory includes an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy; a rotation of the initial chain caused by the rotational potential energy axis, the rotational potential energy axis being defined by a rotational potential energy that rotates in a first direction such that the rotational potential energy axis rotates a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain along a direction substantially parallel to the confinement potential energy axis to form a compressed configuration; a rotation of the compressed configuration in a second direction caused by a rotation of the rotational potential energy axis in the second direction such that the rotational potential energy axis rotates through a second angle relative to the confinement potential energy axis, the second angle being substantially equal to or greater than twice the first angle, and the second direction being opposite to the first direction, thereby providing a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis to form an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by a rotation of the rotational potential energy axis in the first direction such that the rotational potential energy axis rotates through a third angle to cause the rotational potential energy axis to be substantially parallel to the confinement potential energy axis and provide a final chain, wherein two of the inner ones of object A, object B, object C, and object D in the initial chain have switched positions in the final chain.

[0041] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the first angle is greater than 5° and less than 60°. In an exemplary embodiment, compression and decompression are caused by adjusting a confinement ratio of the time-dependent potential energy. In an exemplary embodiment, the potential energy generating elements are controlled according to a solution of the time-dependent potential field found by solving the Hamiltonian operator using the reordering trajectory. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage drivers.

[0042] According to another aspect, an apparatus and / or system for performing a deterministic reshaping and / or reordering function is provided. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential and a rotational potential. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential axis of the confinement potential; a rotation of the initial chain caused by a rotational potential axis defined by a rotational potential that rotates in a first direction such that the rotational potential axis rotates a first angle relative to the confinement potential axis; a compression of the rotated initial chain in a direction substantially parallel to the confinement potential axis to form a compressed configuration; a rotation of the compressed configuration in a second direction caused by a rotation of the rotational potential axis in the second direction such that the rotational potential axis rotates through a second angle relative to the confinement potential axis, the second angle being substantially equal to or greater than twice the first angle, and the second direction being opposite to the first direction, thereby providing a rotated configuration; a decompression of the rotated configuration along the confinement potential axis to form an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by a rotation of the rotational potential axis in the first direction such that the rotational potential axis rotates through a third angle to make the rotational potential axis substantially parallel to the confinement potential axis and provide a final chain, wherein two of the interior ones of object A, object B, object C, and object D in the initial chain have switched positions in the final chain.

[0043] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the first angle is greater than 5° and less than 60°. In an exemplary embodiment, compression and decompression are caused by adjusting a confinement ratio of the time-dependent potential energy. In an exemplary embodiment, the potential energy generating elements are controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating elements are electrodes, and the potential energy generating elements are controlled by applying a voltage thereto by corresponding voltage drivers.

[0044] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more drivers to provide a sequence of driver actions to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field includes a confinement potential energy and a rotational potential energy. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy; a rotation of the initial chain caused by a rotational potential energy axis defined by a rotational potential energy that rotates in a first direction such that the rotational potential energy axis rotates a first angle relative to the confinement potential energy axis; a compression of the rotated initial chain along a direction substantially parallel to the confinement potential energy axis to form a compressed configuration; a rotation of the compressed configuration in a second direction caused by a rotation of the rotational potential energy axis in the second direction such that the rotational potential energy axis rotates through a second angle relative to the confinement potential energy axis, the second angle being substantially equal to or greater than twice the first angle, and the second direction being opposite to the first direction to provide a rotated configuration; a decompression of the rotated configuration along the confinement potential energy axis to form an off-axis final chain; and a rotation of the off-axis final chain in the first direction caused by a rotation of the rotational potential energy axis in the first direction such that the rotational potential energy axis rotates through a third angle to make the rotational potential energy axis substantially parallel to the confinement potential energy axis and provide a final chain, wherein two of the inner ones of object A, object B, object C, and object D in the initial chain have switched positions in the final chain.

[0045] In an exemplary embodiment, the first angle is greater than 0° and less than 90°. In an exemplary embodiment, the first angle is greater than 5° and less than 60°. In an exemplary embodiment, compression and decompression are caused by adjusting a confinement ratio of the time-dependent potential energy. In an exemplary embodiment, the potential energy generating element is controlled according to a solution of the time-dependent potential field found by solving a Hamiltonian operator using the reordering trajectories. In an exemplary embodiment, the atomic objects are ions, the atomic object confinement device is an ion trap, the potential energy generating element is an electrode, and the potential energy generating element is controlled by applying a voltage thereto by a corresponding voltage driver.

[0046] In another aspect, a method for deterministically reordering a set of atomic objects within an object confinement device is provided. For example, the method can be similar to Figure 8Deterministically reorder a set of atomic objects within the atomic object confinement device of the illustrated example. In an exemplary embodiment, the method includes providing a plurality of atomic objects in the atomic object confinement device. The atomic object confinement device includes a plurality of potential energy generating elements. The plurality of atomic objects includes object A, object B, object C, and object D. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The method further includes controlling the potential energy generating elements among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories. The time-dependent potential field is a superposition of a confinement potential energy, a rotational potential energy, and a radial pushing potential energy. The time evolution of the amplitude of the radial pushing potential energy includes a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, where object B and object C are adjacent to each other, and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move further away from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in relative positions with respect to object A and object D relative to the initial chain.

[0047] In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of the rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to the confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction, and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy.

[0048] According to another aspect, an apparatus and / or system for performing a deterministic reshaping and / or reordering function is provided. In an exemplary embodiment, the apparatus and / or system includes an atomic object confinement device that includes a plurality of potential energy generating elements and one or more actuators configured to provide an actuator action sequence to the plurality of potential energy generating elements to control a potential field generated by the plurality of potential energy generating elements. The apparatus and / or system is configured to operate the one or more actuators to cause the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field is a superposition of a confinement potential energy, a rotational potential energy, and a radial push potential energy. The time evolution of the amplitude of the radial push potential energy includes a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, where object B and object C are adjacent to each other, and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move further away from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in a relative position with respect to object A and object D that is opposite to their relative position in the initial chain.

[0049] In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of the rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to the confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction, and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy.

[0050] According to another aspect, a computer program product is provided. In an exemplary embodiment, the computer program product includes a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more actuators to provide an actuator action sequence to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes object A, object B, object C, and object D to move along corresponding reordering trajectories. Object B and object C are of a first atomic type, and object A and object D are not of the first atomic type. The time-dependent potential field is a superposition of a confinement potential energy, a rotational potential energy, and a radial pushing potential energy. The time evolution of the amplitude of the radial pushing potential energy includes a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. The reordering trajectories include an initial chain that includes object A, object B, object C, and object D that are substantially aligned along a confinement potential energy axis of the confinement potential energy, where object B and object C are adjacent to each other and object A and object D are adjacent to each other; a movement of object A, object B, object C, and object D radially outward from the confinement potential energy axis, where object B and object C move farther from the confinement potential energy axis than object A and object D; a movement of object B and object C from a first side of object A and object D to a second opposite side of object A and object D; and a realignment of object A, object B, object C, and object D along the confinement potential energy axis in a final chain. The final chain includes object A, object B, object C, and object D, where object B and object C are in a relative position with respect to object A and object D that is opposite to their relative position in the initial chain.

[0051] In an exemplary embodiment, the time evolution of the rotational potential energy includes: a first rotation of a rotational potential energy axis of the rotational potential energy by a first angle in a first direction with respect to a confinement potential energy axis of the confinement potential energy; a second rotation of the rotational potential energy axis by a second angle in a second direction with respect to the confinement potential energy axis, where the second direction is opposite to the first direction and the second angle is substantially equal to twice the first angle; and a third rotation of the rotational potential energy axis by a third angle in the first direction with respect to the confinement potential energy axis, where the third angle is substantially equal to the first angle. In an exemplary embodiment, the time evolution of the rotational potential energy includes a rotation of the rotational potential energy axis of the rotational potential energy by an angle of approximately 180° in a first direction with respect to the confinement potential energy axis of the confinement potential energy. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Accordingly, the present invention has been generally described, and now reference will be made to the accompanying drawings, which are not necessarily drawn to scale, and in which:

[0053] Figure 1 A top view of an exemplary atomic object confinement device that can be used in an exemplary embodiment is provided.

[0054] Figure 2 is a flowchart of various processes, procedures, and / or operations according to an exemplary embodiment, which can be executed, for example, by a controller of an atomic object confinement device to perform deterministic reshaping and / or reordering on a set of atomic objects within the atomic object confinement device.

[0055] Figure 3 is a schematic diagram showing a set of atomic object trajectories of a set of atomic objects for reordering objects B and C when the initial and final states of the set of atomic objects are a first configuration in which objects B and C are adjacent to each other and are disposed between object A and object D according to an exemplary embodiment.

[0056] Figure 4 is a schematic diagram showing another set of atomic object trajectories of a set of atomic objects for reordering objects B and C when the initial and final states of the set of atomic objects are the first configuration according to an exemplary embodiment.

[0057] Figure 5 is a schematic diagram showing a set of atomic object trajectories of a set of atomic objects for reordering objects B and C when the initial and final states of the set of atomic objects are a second configuration in which objects A and D are adjacent to each other and are disposed between object B and object C according to an exemplary embodiment.

[0058] Figure 6 is a schematic diagram showing a set of atomic object trajectories of a set of atomic objects for reshaping a set of atomic objects from an initial state in one of the first configuration or the second configuration to a final state in the other of the first configuration and the second configuration according to an exemplary embodiment.

[0059] Figure 7 is a schematic diagram showing a set of atomic object trajectories of a set of atomic objects for reshaping a set of atomic objects from an initial state in one of the third configurations to a final state in the fourth configuration according to an exemplary embodiment.

[0060] Figure 8 is a schematic diagram showing a set of atomic object trajectories of a set of atomic objects for reordering a set of atomic objects from an initial state in one of the third configurations to a final state in a different third configuration according to an exemplary embodiment.

[0061] Figure 9 is a schematic diagram showing an exemplary quantum computing system configured to perform one or more deterministic reshaping and / or reordering functions according to various embodiments.

[0062] Figure 10A schematic diagram of an exemplary controller of a quantum computer configured to perform one or more deterministic reshaping and / or reordering functions according to various embodiments is provided.

[0063] Figure 11 A schematic diagram of an exemplary computing entity of a quantum computer system that can be used according to an exemplary embodiment is provided. Detailed Description

[0064] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments of the invention are shown. In fact, the invention can be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. Unless otherwise specified, the term "or" (also denoted as " / ") is used herein in an alternative and conjunctive sense. The terms "exemplary" and "exemplification" are used for examples without indication of a quality level. Unless otherwise specified, the terms "generally" and "about" refer to within engineering and / or manufacturing limits and / or within the user's measurement capabilities. Throughout the specification, like reference numerals refer to like elements.

[0065] In various embodiments, methods, apparatuses, systems, computer program products, etc. for performing various deterministic reshaping and / or reordering functions on a set of atomic objects are provided. In various embodiments, a set of atomic objects is at least a portion of a plurality of atomic objects confined within an atomic object confinement device (also referred to herein as a confinement device). In various embodiments, the atomic objects are ions or atoms. In various embodiments, the confinement device is a trap or other device configured to confine the atomic objects. For example, in an exemplary embodiment, the atomic objects are ions and the confinement device is an ion trap (e.g., a surface ion trap).

[0066] In various embodiments, a group of atomic objects includes object A, object B, object C and object D and / or is composed of object A, object B, object C and object D, wherein object A, object B, object C and object D are each atomic objects. In an exemplary embodiment, object B and object C are the first atomic object type. For example, object B and object C are ions of the same type. In an exemplary embodiment, object B and object C are singly ionized ytterbium ions, but in various embodiments, they can be various other types of atomic objects. In various embodiments, object A and object D are not the first atomic object type. For example, in an exemplary embodiment in which object B and object C are singly ionized ytterbium ions, object A and object D are not ytterbium ions. In an exemplary embodiment, object A and object D are singly ionized barium ions, but in various embodiments, they can be various other types of atomic objects. In another example, object B and object C are barium ions, and object A and object D are strontium ions. In various embodiments, object A and object D each have a smaller mass than object B and object C. In various embodiments, the ratio of the mass of object A to the mass of object D is in the range of about 1:0.8 to 1:1.2. In an exemplary embodiment, object B and object C are different atomic types, and the ratio of the mass of object B to the mass of object C is in the range of about 1:0.8 to 1:1.2. In an exemplary embodiment, object B and object C are both first atomic object types, and the ratio of the mass of object B to the mass of object C is about 1:1.

[0067] In various embodiments, an initial state of a group of atomic objects (e.g., before performing a reshaping and / or reordering function) is one of a first configuration or a second configuration. In various embodiments, a final state of a group of atomic objects (e.g., after performing a reshaping and / or reordering function) has an initial state that is in one of a first configuration or a second configuration. In an exemplary embodiment, when a group of atomic objects is in a first configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device) and in a chain (e.g., arranged in a row) aligned along an axis within the plane (in an exemplary embodiment, defined by a confinement device), wherein objects B and C are adjacent to each other and are disposed between objects A and D. As used herein, when a first atomic object and a second atomic object are adjacent to each other, the first atomic object and the second atomic object are adjacent to each other and / or close to each other, such that there are no atomic objects disposed between the first atomic object and the second atomic object. For example, as Figure 3 , Figure 4 and Figure 6As shown, illustrations 302, 312, 402, 414, and 602 respectively show a set of atomic objects in a first configuration. In an exemplary embodiment, when a set of atomic objects is in a second configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device) and in a chain aligned along an axis within the plane (in an exemplary embodiment, defined by a confinement device), where objects A and D are adjacent to each other and are disposed between objects B and C. For example, as Figure 5 and Figure 6 shown, illustrations 502, 514, 616R, and 616L respectively show a set of atomic objects in a second configuration. In various embodiments, the spacing of the atomic objects in the initial and final states is controlled by a force balance between the electrostatic forces that push the atomic objects apart and the confinement potential energy.

[0068] In various embodiments, the initial state of a set of atomic objects (e.g., before performing a reshaping and / or reordering function) is one of a third configuration or a fourth configuration. In an exemplary embodiment, when a set of atomic objects is in a third configuration, objects A, B, C, and D are in a plane (e.g., defined by a confinement device) and in a chain (e.g., arranged in a row) along an axis within the plane (e.g., defined by a confinement device), where objects B and C are adjacent to each other, and objects A and D are adjacent to each other. Figure 3 Illustration 702 shows a set of atomic objects in a third configuration. In an exemplary embodiment, when a set of atomic objects is in a fourth configuration, objects A, B, C, and D are in a plane (e.g., defined by a confinement device) and in a chain (e.g., arranged in a row) along an axis within the plane (e.g., defined by a confinement device), where objects B and C are not adjacent to each other, and objects A and D are not adjacent to each other. Figure 3 Illustration 712 shows a set of atomic objects in a fourth configuration. In various embodiments, the deterministic reshaping and / or reordering function results in a final state of a set of atomic objects, where the set of atomic objects is in a third configuration or a fourth configuration.

[0069] In various embodiments, a deterministic reshaping and / or reordering function can be executed to switch the positions of objects B and C while maintaining the set of atomic objects in the first configuration (see Figure 3 and Figure 4 ) or the second configuration (see Figure 5)。For example, in various embodiments, the initial and final states of the reshaping and / or reordering function are the same as the first or second configuration, but the positions of object B and object C are swapped. In various embodiments, a deterministic reshaping and / or reordering function can be performed to switch a set of atomic objects from a first configuration to a second configuration, or vice versa (see Figure 6 ).

[0070] In various embodiments, the confinement device includes a plurality of potential energy generating elements. For example, the potential energy generating elements can generate a time-dependent potential field experienced by a set of atomic objects (e.g., object A, object B, object C, and object D). The potential energy generating elements can be configured to generate a time-dependent potential field that causes each atomic object in the set of atomic objects to traverse a specific trajectory such that the desired deterministic reshaping and / or reordering function is performed. In an exemplary embodiment, the potential energy generating element is an electrode configured to generate a time-dependent electric potential experienced by each atomic object in a set of atomic objects (e.g., object A, object B, object C, and object D).

[0071] Exemplary atomic object limiting device

[0072] In an exemplary embodiment, the confinement device is an ion trap (e.g., a surface ion trap), the potential energy generating element is an electrode of the ion trap, and the atomic objects are ions. Figure 1 A top schematic view of an exemplary surface ion trap 100 is provided. In an exemplary embodiment, the surface ion trap 100 is fabricated as part of an ion trap chip and / or part of an ion trap device and / or package. In an exemplary embodiment, the surface ion trap 100 is at least partially defined by a plurality of radio frequency (RF) rails 112 (e.g., 112A, 112B). In various embodiments, the ion trap 100 is at least partially defined by a plurality of sequences 114 of capture and / or transport (TT) electrodes (e.g., 114A, 114B, 114C). In an exemplary embodiment, the ion trap 100 is a surface Paul trap with symmetric RF rails. In various embodiments, the potential energy generating elements of the confinement device include the TT electrodes 116 in the sequence 114 of TT electrodes and / or the RF rails 112. In various embodiments, the upper surface of the ion trap 100 has a planarized topology. For example, the upper surfaces of each of the plurality of RF rails 112 and the upper surfaces of each of the TT electrodes 116 in the plurality of sequences 114 of TT electrodes can be substantially coplanar.

[0073] In various embodiments, the ion trap 100 includes a plurality of RF rails 112 and / or is at least partially defined by the plurality of RF rails. The RF rails 112 are formed with substantially parallel longitudinal axes 111 (e.g., 111A, 111B) and have substantially coplanar upper surfaces. For example, the RF rails 112 are substantially parallel such that the distance between the RF rails 112 is substantially constant along the length of the RF rails 112 (e.g., the length of the RF rails 112 along the longitudinal axis 111 of the RF rails 112). For example, the upper surfaces of the RF rails 112 may be substantially flush with the upper surface of the ion trap 100. In an exemplary embodiment, the plurality of RF rails 112 includes two RF rails 112 (e.g., 112A, 112B). In various embodiments, the ion trap 100 may include a plurality of numbers of RF rails 112. For example, the ion trap 100 may be a two-dimensional ion trap including a plurality of numbers (e.g., pairs and / or groups) of RF rails 112, where each number (e.g., pair and / or group) of RF rails 112 has substantially parallel longitudinal axes 111. In an exemplary embodiment, a first number of RF rails 112 has longitudinal axes 111 that are substantially parallel to each other, a second number of RF rails 112 has longitudinal axes 111 that are substantially parallel to each other, and the longitudinal axis of the first number of RF rails is substantially non-parallel (e.g., transverse) to the longitudinal axis of the second number of RF rails. Figure 1 An exemplary one-dimensional ion trap 100 with two RF rails 112 is shown, but other embodiments may include additional RF rails in various configurations.

[0074] In various embodiments, two adjacent RF rails 112 may be separated (e.g., insulated) from each other by a longitudinal gap 105. For example, the longitudinal gap (in one or two dimensions) may define a confinement channel or region of the ion trap 100, where one or more atomic objects (e.g., ions in the case where the confinement device is the ion trap 100) may be trapped at various positions within the ion trap. In various embodiments, the longitudinal gap 105 defined thereby may extend substantially parallel to the longitudinal axes 111 of the adjacent RF rails 112. For example, the longitudinal gap 105 may extend substantially parallel to the y-axis. In an exemplary embodiment, the longitudinal gap 105 may be at least partially filled with an insulating material (e.g., a dielectric material). In various embodiments, the dielectric material may be silicon dioxide (e.g., formed by thermal oxidation) and / or other dielectric materials and / or insulating materials. In various embodiments, the height of the longitudinal gap 105 (e.g., in the x direction) is approximately between 40 μm and 500 μm. In various embodiments, one or more sequences 114 of TT electrodes (e.g., the second sequence 114B of TT electrodes) may be disposed and / or formed within the longitudinal gap 105.

[0075] In an exemplary embodiment, a lateral gap may exist between neighboring and / or adjacent electrodes 116 of one or more sequences 114 of electrodes. In an exemplary embodiment, the lateral gap may be an empty space and / or at least partially filled with a dielectric material to prevent electrical communication between neighboring and / or adjacent electrodes. In an exemplary embodiment, the lateral gap between neighboring and / or adjacent electrodes may be in the range of approximately 1 μm - 10 μm.

[0076] In an exemplary embodiment, a longitudinal gap exists between a sequence 114 of TT electrodes and neighboring and / or adjacent RF rails 112. In an exemplary embodiment, the longitudinal gap may be at least partially filled with a dielectric material and / or an insulating material to prevent electrical communication between the TT electrodes 116 in the sequence 114 of electrodes and the RF rails 112. In an exemplary embodiment, the longitudinal gap between neighboring and / or adjacent electrodes may be in the range of approximately 1 μm - 10 μm.

[0077] In various embodiments, the ion trap 100 may be at least partially defined by a plurality of sequences 114 of TT electrodes (e.g., a first sequence 114A of TT electrodes, a second sequence 114B of TT electrodes, a third sequence 114C of TT electrodes). Each sequence 114 of TT electrodes is formed to extend substantially parallel to a substantially parallel longitudinal axis 111 of the RF rails 112. For example, the plurality of sequences 114 of TT electrodes may extend substantially parallel to the y-axis, as Figure 1 shown. In various embodiments, the plurality of sequences 114 of TT electrodes includes two, three, four, and / or another number of sequences 114 of TT electrodes. In an exemplary embodiment, the ion trap 100 includes a plurality of sequences 114 of TT electrodes. For example, the illustrated ion trap 100 is a one-dimensional ion trap including three sequences 114 of TT electrodes. For example, the ion trap 100 may be a two-dimensional ion trap including a plurality of sequences 114 of TT electrodes, and each of the plurality of sequences of TT electrodes extends substantially parallel to a substantially parallel longitudinal axis of a corresponding number of RF rails 112. In an exemplary embodiment, a first number of sequences 114 of TT electrodes extends substantially parallel to a substantially parallel longitudinal axis 111 of a first number of RF rails 112, a second number of sequences 114 of TT electrodes extends substantially parallel to a substantially parallel longitudinal axis 111 of a second number of RF rails 112, and the longitudinal axis of the first number of RF rails is substantially non-parallel (e.g., transverse) to the longitudinal axis of the second number of RF rails. In some embodiments, each TT electrode 116 in the plurality of sequences 114 of TT electrodes may be formed with a substantially coplanar upper surface that is substantially coplanar with the upper surface of the RF rails 112.

[0078] In an exemplary embodiment (e.g., as Figures 3 to 5As shown, multiple (e.g., a pair of) RF rails 112 can be formed between a first sequence 114A of TT electrodes and a third sequence 114C of TT electrodes, where a second sequence 114B of TT electrodes extends along a longitudinal channel 105 between the RF rails 112. For example, each sequence 114 of TT electrodes can extend in a direction substantially parallel to the longitudinal axis 111 of the RF rails (e.g., in the y direction). In various embodiments, the upper surfaces of the sequences 114 of TT electrodes are substantially coplanar with the upper surfaces of the RF rails 112.

[0079] In various embodiments, an RF signal can be applied to the RF rails 112 to generate an electric field and / or a magnetic field for holding ions trapped within the ion trap 100 in a direction transverse to the longitudinal direction of the ion trap 100 (e.g., the x direction and the z direction). In various embodiments, a TT voltage can be applied to the TT electrodes 116 to generate a time-dependent potential field that causes objects in a group of objects to traverse corresponding trajectories to perform a deterministic reshaping and / or reordering function. In various embodiments, multiple sequences 114 of TT electrodes can be combined and biased with a TT voltage that helps a variable combination of electric fields and / or magnetic fields to trap at least one ion in a potential well above at least one of the upper surfaces of the sequences 114 of TT electrodes and / or the RF rails 112. In various embodiments, the potential energy experienced by the ions of the ion trap 100 can be a combination of a static potential energy and / or a non-rotational potential energy (e.g., in various embodiments, which defines a confinement potential energy axis 125 that can be substantially parallel and / or collinear with the trap axis 101) and a rotational potential energy (e.g., which defines a rotational potential energy axis 135). In an exemplary embodiment, the potential energy experienced by the ions of the ion trap 100 can further include a radial pushing potential energy. For example, an electric field and / or a magnetic field at least partially generated by a voltage applied to the TT electrodes in the sequence 114 of TT electrodes can trap at least one ion in a potential well above the upper surface of the second sequence 114B of TT electrodes and / or the longitudinal gap 105. Additionally, the TT voltage applied to the electrodes 116 can cause the ions trapped in the potential well above the upper surface of the second sequence 114B of TT electrodes and / or the longitudinal gap 105 to traverse the trajectory, such that a deterministic reordering and / or reshaping function is performed.

[0080] In various embodiments, the TT voltage applied to the TT electrodes 116 is generated by one or more connected devices (e.g., as Figure 9The controller 30 shown etc.) is controlled via leads. For example, depending on the positive or negative charge on at least one ion, the TT voltage near a particular ion at the TT electrode 116 can be increased or decreased to cause the particular ion to traverse a desired trajectory. For example, the controller 30 can control a voltage driver to cause the voltage driver to apply a TT voltage to the TT electrode to generate a time-dependent electric potential (e.g., an electric potential that evolves over time), which causes the ions of a set of atomic objects to traverse a desired trajectory to perform a deterministic reshaping and / or reordering function.

[0081] Depending on factors such as the charge on at least one ion and / or the shape and / or amplitude of a combined electric and / or magnetic field, the at least one ion can be stabilized at a particular distance (e.g., from about 20 μm to about 200 μm) above the upper surface of the ion trap 100 (e.g., the coplanar upper surface of the sequence of TT electrodes 114 and the RF rails 112). To further assist in controlling the transport of ions along a desired trajectory, in various embodiments, the ion trap 100 can be operated in a cryogenic chamber and / or a vacuum chamber capable of cooling the ion trap to a temperature below 124 Kelvin (e.g., below 100 Kelvin, below 50 Kelvin, below 10 Kelvin, below 5 Kelvin, etc.).

[0082] In various embodiments, the RF rails 112, the sequence of electrodes 114, and / or the confinement potential generated by the RF rails and / or the sequence of electrodes 114 define the confinement plane 103 of the ion trap. In various embodiments, the RF rails 112, the sequence of electrodes 114, and / or the confinement potential generated by the RF rails and / or the sequence of electrodes 114 define the axis 101 of the ion trap.

[0083] In various embodiments, atomic objects within the ion trap 100 experience a confinement potential generated by the RF rails 112 and a TT potential generated by the TT electrodes 116. In various embodiments, the confinement potential is generally used to align atomic objects within the ion trap 100 within the longitudinal gap 105 and / or along the ion trap axis 101. For example, in an exemplary embodiment, the confinement potential may be generally tubular and / or cigar-shaped to confine the atomic objects within the longitudinal gap 105. In various embodiments, the confinement potential may not change when performing reshaping and / or reordering functions. For example, during the performance of reshaping and / or reordering functions, the confinement potential may be generally constant with respect to time. The TT potential generated by applying a voltage sequence to the TT electrodes 116 is configured to move the atomic objects through a combined potential (e.g., the potential experienced by the atomic objects due to the superposition of the confinement potential and the TT potential) to perform reshaping and / or reordering functions. For example, a voltage sequence may be applied to the TT electrodes 116 to cause a minimum of the combined potential at a specific location at a specific time, such that the minimum of the combined potential guides the atomic objects through a trajectory corresponding to the reshaping and / or reordering function. In various embodiments, the non-rotating potential (e.g., which defines the confinement potential axis 125) includes the confinement potential and possibly a portion of the TT potential. In various embodiments, the rotating potential (e.g., which defines the rotating potential axis 135) includes at least a portion of the TT potential.

[0084] Exemplary method for performing reshaping and / or reordering functions

[0085] In various embodiments, the controller 30 may control one or more drivers to cause a plurality of potential generating elements of the confinement device to generate a time-dependent potential field (e.g., a potential field that evolves over time), which causes atomic objects within a set of atomic objects to traverse a desired trajectory, such that a deterministic reshaping and / or reordering function is performed. In various embodiments, the controller 30 may determine a sequence of driver actions (e.g., in an exemplary embodiment where the confinement device is the ion trap 100, the TT voltage to be applied to the electrodes 116). For example, the controller 30 may cause a quantum circuit and / or algorithm to be executed, and may determine the sequence of driver actions based on one or more steps, gates, etc. of the quantum circuit and / or algorithm to be executed. In various embodiments, another computing entity may determine the sequence of driver actions to be provided to the controller 30.

[0086] Figure 2 A flowchart is provided showing exemplary processes, programs, operations, etc. that may be executed by the controller 30 to cause a deterministic reshaping and / or reordering function to be performed. Starting at step / operation 202, a desired reshaping and / or reordering function may be defined. For example, the controller 30 (e.g., using Figure 10The processing device 1005) shown can read a quantum circuit and / or algorithm that defines and / or indicates that reshaping and / or reordering functions should be performed. For example, based on the quantum circuit and / or algorithm, an initial state and a final state (e.g., the order of atomic objects within the atomic object confinement device 100) can be determined. The controller 30 can, in response to reading the quantum circuit and / or algorithm, identify and / or define the reshaping and / or reordering functions to be performed as part of the execution of the quantum circuit and / or algorithm. In an exemplary embodiment, the controller 30 includes a memory 1010 (as Figure 10 shown), which stores a set of trajectories corresponding to various executable reshaping and / or reordering functions. Figure 3 , Figure 4 , Figure 5 and Figure 6 show some exemplary trajectories for performing some exemplary deterministic reshaping and / or reordering functions according to some exemplary embodiments.

[0087] At step / operation 204, the controller 30 (or another computing entity) can solve a Hamiltonian operator, etc., based on the trajectories and / or the initial and final states corresponding to the reshaping and / or reordering functions defined and / or identified (e.g., and accessed from the memory 1010) at step / operation 202. In various embodiments, the controller 30 (e.g., using the processing device 1005) solves a Hamiltonian operator, etc., based on the trajectories and / or the initial and final states corresponding to the reshaping and / or reordering functions defined and / or identified at step / operation 202 to determine a sequence of driver actions. In an exemplary embodiment (e.g., where the confinement device is an ion trap 100), the sequence of driver actions is a sequence of TT voltages to be applied to the electrodes 116. In an exemplary embodiment, rather than solving the Hamiltonian operator for a specific set of trajectories, a sequence of TT voltages can be solved such that one or more minima of the potential field (e.g., generated by the combination of the voltage applied to the electrodes 116 and the potential energy generated by the RF rails 112) move along the desired trajectory. For example, a time-dependent potential field can be solved for the Hamiltonian operator, etc., that includes a time-dependent confinement potential energy, a time-dependent rotational potential energy, and in some cases, a time-dependent radial push potential energy.

[0088] At step / operation 206, the controller 30 can control one or more drivers (e.g., using, for example, Figure 10 the drivers shown, the Figure 9The voltage driver 50 shown is configured to cause one or more drivers to perform a sequence of driver actions. For example, the controller 30 may cause the voltage driver to provide a sequence of driver actions (e.g., a sequence of TT voltages) to be applied to a potential energy generating element (e.g., electrode 116). In response to receiving the sequence of driver actions, the potential energy generating element may generate a time-dependent potential field experienced by the atomic objects in a set of atomic objects. The atomic objects in the set of atomic objects experiencing the time-dependent potential field causes each atomic object in the set of atomic objects to traverse a corresponding trajectory such that the deterministic reshaping and / or reordering function defined and / or identified in step / operation 202 is performed. For example, applying the sequence of driver actions to the potential energy generating element may generate a time-dependent potential field that causes a set of atomic objects (e.g., object A, object B, object C, and object D) to traverse a trajectory from an initial state to a final state. In various embodiments, the atomic objects move through a time-dependent potential field in a plane (e.g., a confinement plane parallel to the ion trap plane 103). In various embodiments, the trajectories traversed by the atomic objects include out-of-plane portions. For example, the atomic objects may have a velocity component transverse to the confinement plane and / or the ion trap plane 103 as they traverse the trajectory. For example, a first rotation direction and a second rotation direction are described herein as being in a plane (e.g., a confinement plane parallel to the ion trap plane 103). However, the rotations described herein may have a component transverse to the plane (e.g., the confinement plane).

[0089] Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 each illustrate an exemplary deterministic reshaping and / or reordering function. Figure 3 , Figure 4 , Figure 5 , Figure 6 , Figure 7 and Figure 8 Each of the figures includes an arrow indicating the flow of time through the illustrated sequence, which depicts a snapshot of the trajectories of the atomic objects during various steps of the exemplary deterministic reshaping and / or reordering function. It should be understood that each of the exemplary deterministic reshaping and / or reordering functions may be performed in the direction opposite to the time arrow to perform the reverse function of the illustrated function.

[0090] First exemplary deterministic reshaping and / or reordering function

[0091] Figure 3Shows an initial state of a set of atomic objects and multiple snapshots of the set of atomic objects when each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed, resulting in a final state of the set of atomic objects. In various embodiments, the atomic objects in the set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element.

[0092] Illustration 302 shows an initial state of a set of atomic objects. In the initial state, the set of atomic objects is in an initial chain in a first configuration. When the set of atomic objects is in the first configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device) and in a chain aligned along a confinement potential axis 125 within the plane (in an exemplary embodiment, defined by a confinement device), where objects B and C are adjacent to each other and are disposed between objects A and D. In an exemplary embodiment, the confinement potential axis 125 is substantially aligned with the ion trap axis 101. In an exemplary embodiment, the confinement potential axis 125 is an axis and / or line that is substantially parallel to the ion trap axis 101 and passes through a point equidistant between objects B and C. For example, the confinement potential axis 125 may be substantially parallel and / or collinear with the ion trap axis 101. In an exemplary embodiment, the rotational potential axis 135 rotates about a center point 140 of the set of atomic objects. For example, the center point 140 of the set of atomic objects may be the center of mass of the set of atomic objects or the average position of the atomic objects in the set of atomic objects (e.g., not mass-weighted). As described above, objects B and C are of a first atomic object type, and objects A and D are not of the first atomic object type. Objects B and C have a greater mass than objects A and D. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is an atomic object type different from the first atomic object type. In an exemplary embodiment, in the initial state of the set of atomic objects, the confinement potential dominates the potential experienced by the atomic objects within the confinement device. For example, when the set of atomic objects is in the initial state, the confinement ratio, i.e., the ratio of the confinement potential (e.g., generated by the voltage applied to the RF rails 112) to the intensity of the TT potential, is X:1, where X is greater than 1. For example, in an exemplary embodiment, X is such that the voltage applied to the RF rails 112 and the voltage applied to the TT electrodes 116 are within the stable region of the ion trap 100. Generally, the stable region of the ion trap 100 is defined based on the geometry of the ion trap 100. For example, the stable region may be a first stable region and may be a voltage region of the ion trap 100 where ions can be trapped in a stable manner within the ion trap 100. For example, X may be a value greater than one such that there is a preferred confinement direction (e.g., along and / or substantially parallel to the axis 101) within the ion trap 100 and such that trapping within the ion trap 100 is feasible.

[0093] In an exemplary embodiment, a potential energy generating element generates a potential field that causes an atomic object in a set of atomic objects to traverse a trajectory such that the atomic object moves through the positions shown in diagrams 304, 306, 308, 310 and reaches the final state shown in diagram 312. Although diagrams 304, 306, 308 and 310 are split to show different steps in the movement of the atomic object, in various embodiments, some of these steps may occur simultaneously. For example, in an exemplary embodiment, the steps shown in diagrams 304 and 306 occur simultaneously and / or the steps shown in diagrams 308 and 310 occur simultaneously.

[0094] Between diagram 302 and diagram 304, a time-dependent potential field causes an initial chain (e.g., including aligned atomic objects in a set of atomic objects) to rotate through a first angle θ in a first direction to form a rotated chain. In various embodiments, the initial chain rotates through a first angle θ about a center point 140 in a first direction to form a rotated chain. The first direction is in a plane. For example, the initial chain may rotate such that the rotated initial chain forms a first angle θ with the restricted potential energy axis 125. In various embodiments, the first angle θ is greater than 0° and less than 90°. In an exemplary embodiment, the first angle θ is in the range of approximately 5° - 15°. In an exemplary embodiment, using one of the external atomic objects (e.g., object A or object D in the first configuration) as a rotation point, the initial chain rotates about the rotation point.

[0095] Between illustration 304 and illustration 306, the time-dependent potential field causes an initial rotating chain (e.g., including aligned atomic objects in a set of atomic objects) to be compressed to form a compressed arrangement of the set of atomic objects. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a compressive potential energy that causes the set of atomic objects to be compressed along the confinement potential axis. For example, the compressive potential energy can cause the atomic objects to feel a push outward from a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects B and C) in the direction of the confinement potential axis 125. For example, the initial rotating chain can be compressed along the confinement potential axis 125. For example, the confinement ratio (the intensity ratio of the confinement potential to the TT potential) can be reduced to Y:1, where Y can be close to 1 and / or less than 1. For example, as shown in illustration 306, the confinement ratio can be in the range of about 1.2:1 to 0.8:1. In an exemplary embodiment, the confinement ratio is reduced by increasing the intensity of the TT potential. For example, in an exemplary embodiment, the confinement potential generated by applying a voltage to the RF guide 112 can be substantially constant over time (e.g., the time average of the confinement potential during a first time period can be substantially equal to the time average of the confinement potential during a second time period). In an exemplary embodiment, compressing the initial rotating chain causes object B and object C to move to opposite sides of the confinement potential axis 125.

[0096] Between illustration 306 and 308, the time-dependent potential field causes the compressed arrangement of the set of atomic objects to rotate through a second angle in a second direction to form a rotated compressed arrangement of the set of atomic objects. In an exemplary embodiment, the second angle is twice the first angle θ. For example, in illustration 306, the angle between the confinement potential axis 125 and the rotation potential axis 135 is the first angle θ, and in illustration 308, the angle between the confinement potential axis 125 and the rotation potential axis 135 is the negative of the first angle (e.g., -θ). For example, between illustration 306 and illustration 308, the axis of the rotation potential rotates through an angle of 2θ in the second direction. The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise in the plane, then the rotation in the second direction is clockwise in the plane. Similarly, if the rotation in the first direction is clockwise in the plane, then the rotation in the second direction is counterclockwise in the plane. In an exemplary embodiment, the rotation of the compressed arrangement of the set of atomic objects rotates about a point located at the center of the set of atomic objects (e.g., center point 140) to form a rotated compressed arrangement. In an exemplary embodiment, the center of the set of atomic objects is the point where the virtual line connecting object A and object D intersects the virtual line connecting object C and object B.

[0097] Between illustrations 308 and 310, the time-dependent potential field causes the rotationally compressed arrangement of a set of atomic objects to be decompressed to form an off-axis final chain. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a decompression potential energy that causes the set of atomic objects to be decompressed along the confinement potential axis. For example, the decompression potential energy can cause the atomic objects to feel a push inward in the direction of the confinement potential axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects B and C). For example, the confinement ratio can be increased to X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be in the range of approximately 1.5 to 4.0. In an exemplary embodiment, the confinement ratio is increased by reducing the strength of the TT potential energy. For example, the rotationally compressed arrangement of the set of atomic objects can be decompressed or extended along the confinement potential axis 125. For example, the rotationally compressed arrangement of the set of atomic objects can be decompressed, extended, and / or stretched so that the rhombus shape of the rotationally compressed arrangement is transformed into an aligned and / or linear shape of the off-axis final chain.

[0098] Between illustrations 310 and 312, the time-dependent potential field causes the off-axis final chain to rotate through a first angle θ in a first direction to form a final chain. The first direction is in the plane. For example, the off-axis chain can rotate such that the atomic objects in the final chain are aligned along the confinement potential axis 125. In an exemplary embodiment, the off-axis final chain rotates about a center point 140 to form a final chain. In an exemplary embodiment, the confinement ratio experienced by the final chain is approximately the same as the confinement ratio experienced by the initial chain.

[0099] As can be seen in illustration 312, according to an exemplary embodiment, the final chain has a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D. However, object B and object C have changed positions between the initial chain and the final chain. For example, the initial chain can be ordered object A, object B, object C, object D, and the final chain can be ordered object A, object C, object B, object D.

[0100] In various embodiments, when the atomic objects are not positioned along the ion trap axis 101, due to the confinement potential, the atomic objects experience heating (e.g., acquisition of thermal energy). This heating mechanism is referred to herein as RF heating. The farther the atomic objects are from the ion trap axis 101, the more RF heating the atomic objects experience. Figure 3 The exemplary deterministic reshaping and / or reordering functions shown keep all atomic objects closer to the ion trap axis 101 (e.g., which is substantially aligned with the confinement potential axis 125) than a simple 180° rotation of the initial chain used to form the final chain. Thus, when performing Figure 3The RF heating experienced by the atomic object during the deterministic reshaping and / or reordering function shown is significantly less than the RF heating experienced by the atomic object when performing a simple 180° rotation. Additionally, the voltage applied to perform the Figure 3 deterministic reshaping and / or reordering function shown requires a lower voltage than the voltage typically required to perform a simple 180° rotation of the initial chain to form the final chain.

[0101] In various embodiments, a time-dependent potential energy can be used to compress and rotate or decompress and rotate an atomic object in a time-overlapped manner. For example, the compression of the initial chain of rotations and the continued rotation of the atomic object about the center point 140 can occur simultaneously, semi-simultaneously, etc. For example, the compression can occur while the rotation continues. Similarly, the decompression of the atomic object and the rotation of the atomic object can occur in a time-overlapped manner. For example, once the rotation of the atomic object is initiated (e.g., during an early portion of the rotation), the confinement ratio can be adjusted from X:1 to Y:1. Then, for an intermediate portion of the rotation of the atomic object, the confinement ratio can be maintained at Y:1 and then adjusted from Y:1 to X:1 during the ending portion of the rotation.

[0102] Another exemplary deterministic reshaping and / or reordering function

[0103] Figure 4 Shows an initial state of a set of atomic objects and multiple snapshots of a set of atomic objects as each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed, resulting in a final state of the set of atomic objects. In various embodiments, the atomic objects in a set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element.

[0104] Illustration 402 shows an initial state of a set of atomic objects at an initial time T = t0. In the initial state, the set of atomic objects is in an initial chain in a first configuration. When the set of atomic objects is in the first configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device such as the ion trap plane 103) and in a chain aligned along a confinement potential axis 125 within the plane (in an exemplary embodiment, defined by the confinement device), where objects B and C are adjacent to each other and are disposed between objects A and D. In an exemplary embodiment, the confinement potential axis 125 is substantially aligned with the ion trap axis 101. As described above, objects B and C are of a first atomic object type, and objects A and D are not of the first atomic object type. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is an atomic object type different from the first atomic object type. In an exemplary embodiment, in the initial state of the set of atomic objects, the confinement potential dominates the potential experienced by the atomic objects within the confinement device. For example, when the set of atomic objects is in the initial state, the confinement ratio (i.e., the intensity ratio of the confinement potential to the TT potential) is X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be within a range such that the confinement potential is within the stable region of the ion trap 100.

[0105] In an exemplary embodiment, the potential energy generating element generates a potential field that causes the atomic objects in the set of atomic objects to traverse a trajectory such that the atomic objects move through the positions shown in Illustrations 404, 406, 408, 410, 412, and reach the final state shown in Illustration 414 at a final time T = t f . Between Illustration 402 and Illustration 404, the time-dependent potential field causes the initial chain (e.g., including the aligned atomic objects in the set of atomic objects) to rotate through a rotation angle α1 in a first direction to form a rotated chain at time T = t1. The first direction is within the plane. For example, the initial chain can rotate when the rotation potential axis 135 rotates through a rotation angle α1 with respect to the confinement potential axis 125. In an exemplary embodiment, the initial chain rotates about a center point 140 of the set of atomic objects (e.g., the point where the confinement potential axis 125 intersects the rotation potential axis 135).

[0106] Between illustration 404 and illustration 406, the time-dependent potential field causes the initial rotating chain (e.g., including aligned atomic objects in a set of atomic objects) to be compressed to form a compressed arrangement of the set of atomic objects. For example, the initial rotating chain can be compressed along the confinement potential axis 125. For example, the confinement ratio (the ratio of the confinement potential to the strength of the TT potential) can be reduced to Y:1, where Y can be close to 1 and / or less than 1. For example, as shown in illustration 406, the confinement ratio can be in the range of about 1.2:1 to 0.8:1. In an exemplary embodiment, the confinement ratio is reduced by adjusting the strength of the TT potential. For example, a drive action sequence can be determined such that the TT potential rotates about the center point 140. Additionally, a drive action sequence can be determined such that the TT potential is sufficient to rotate objects B and C about the center point 140, but due to the mass difference between objects B and C and objects A and D, objects A and D do not feel a force from the TT potential sufficient to cause objects A and D to rotate about the center point 140. For example, objects A, B, C, and D experience the confinement potential generated by the RF guide 112 and the TT potential generated by applying a voltage to the TT electrode 116. The combined potential (e.g., the superposition of the confinement potential and the TT electrode) is sufficient to cause atomic objects having a mass similar to the mass of objects B and C to rotate about the center point 140, but not sufficient to cause atomic objects having a mass similar to the mass of objects A and D (e.g., smaller than the mass of objects B and C) to rotate about the center point 140. In an exemplary embodiment, the change in the confinement ratio and the change in the TT potential cause the compression of the initial rotating chain and cause objects B and object C to move to opposite sides of the confinement potential axis 125. For example, the potential generating element can be controlled (e.g., by the controller 30) to generate a compression potential that causes the set of atomic objects to be compressed along the confinement potential axis. For example, the compression potential can cause the atomic objects to feel a push outward from a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects B and C) in the direction of the confinement potential axis 125. Due to the rotational potential, objects B and C can continue to rotate about the center point 140. For example, at time T = t2, the rotational potential axis 135 has rotated through the rotation angle α2 such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the rotation angle α2.

[0107] Between diagrams 406 and 410, the time-dependent potential field causes the compressed arrangement of a set of atomic objects to rotate to form a rotated compressed arrangement of the set of atomic objects. In various embodiments, due to the continued rotation of the rotational potential energy, objects B and C continue to rotate in the first direction. For example, the rotation angle α between the confinement potential axis 125 and the rotational potential axis 135 increases from α2 at time T = t2 to α3 at time T = t3 (as shown in diagram 408) and α4 at time T = t4 (as shown in diagram 410). Objects A and D may rotate in the second direction about the center of rotation 140 in response to experiencing the rotational potential energy. In an exemplary embodiment, the center point 140 serving as the center of rotation is located at the intersection between the rotational potential axis and the confinement potential axis 125. The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise rotation in the plane, then the rotation in the second direction is clockwise rotation in the plane. Similarly, if the rotation in the first direction is clockwise rotation in the plane, then the rotation in the second direction is counterclockwise rotation in the plane. Diagram 408 shows an intermediate point of the rotation between the compressed arrangement and the rotated compressed arrangement.

[0108] Between diagrams 410 and 412, the time-dependent potential field causes the rotated compressed arrangement of a set of atomic objects to be decompressed to form an off-axis final chain. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a decompression potential energy that causes the set of atomic objects to be decompressed along the confinement potential axis. For example, the decompression potential energy can cause the atomic objects to feel an inward push in the direction of the confinement potential axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects B and C). For example, a change in the confinement ratio (e.g., the relative strength of the confinement potential and the rotational TT potential) can cause the rotated compressed arrangement of the set of atomic objects to decompress or extend along the confinement potential axis 125. For example, the rotated compressed arrangement of the set of atomic objects can decompress, extend, and / or stretch to transform the diamond shape of the rotated compressed arrangement into the aligned and / or linear shape of the off-axis final chain. For example, the confinement ratio can increase to X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be within the range defined by the stable region of the ion trap 100. In an exemplary embodiment, the confinement ratio is increased by adjusting the strength of the TT potential energy. Objects B and C may continue to rotate about the center point 140 in the first direction in response to experiencing the rotational potential energy. For example, at time T = t4, the rotational potential axis has rotated through the rotation angle α4 such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the rotation angle α4. When objects A and D continue to rotate about the center point 140 in the second direction, an off-axis final chain is formed at time T = t4.

[0109] Between illustrations 412 and 414, the time-dependent potential field causes the off-axis final chain to rotate in a first direction such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the final rotation angle α f , and a final chain is formed. For example, the final chain can be aligned along the confinement potential axis 125 and / or be substantially aligned along the ion trap axis 101. In an exemplary embodiment, the final rotation angle α f is approximately 180°. The first direction is in a plane. For example, the off-axis chain can rotate such that the atomic objects in the final chain are aligned along the confinement potential axis 125. In various embodiments, the center point 140 serves as the center of rotation. For example, the off-axis final chain rotates about the center point 140 in the first direction to form the final chain.

[0110] As can be seen in illustration 414, according to an exemplary embodiment, the final chain has a first configuration in which object B and object C are adjacent to each other and are disposed between object A and object D. However, object B and object C have changed positions between the initial chain and the final chain. In various embodiments, the positions of object A and object D in the final chain are the same as their positions in the initial chain, but object B and object C have changed positions. For example, the initial chain can be the ordered objects A, B, C, D, and the final chain can be the ordered objects A, C, B, D.

[0111] From Figure 4 and the above, it should be understood that objects B and C rotate about the center point of a group of atomic objects by a final rotation angle of, for example, 180°. However, during the rotation of objects B and C, the group of atomic objects is not held in a collinear chain. Thus, all atomic objects remain closer to the confinement potential axis 125 (e.g., which is substantially aligned with the ion trap axis 101). As described above, the farther an atomic object is from the ion trap axis 101, the greater the RF heating the atomic object experiences. Thus, various embodiments provide for objects B and C to switch positions with a lower level of atomic object RF heating than a simple 180° rotation of the initial chain to form the final chain. Additionally, the voltage applied to perform Figure 4 the deterministic reshaping and / or reordering function shown requires a lower voltage than the voltage typically required to perform a simple 180° rotation of the initial chain to form the final chain.

[0112] In various embodiments, a time-dependent potential energy (e.g., a superposition of a confinement potential and a TT potential) can be used to compress and rotate or decompress and rotate atomic objects in a time-overlapped manner. For example, the compression of an initial chain of rotations and the continued rotation of the atomic object about a center point 140 can occur simultaneously, semi-simultaneously, etc. For example, the compression can occur while the rotation continues. Similarly, the decompression of the atomic object and the rotation of the atomic object can occur in a time-overlapped manner. For example, once the rotation of the atomic object is initiated (e.g., during an early part of the rotation), the confinement ratio can be adjusted from X:1 to Y:1. Then for an intermediate part of the rotation of the atomic object, the confinement ratio can be maintained at Y:1, and then adjusted from Y:1 to X:1 during an ending part of the rotation. In an exemplary embodiment, illustration 404 and / or 406 show at least a portion of an early part of the rotation, illustration 408 shows an intermediate part of the rotation, and illustrations 410 and / or 412 show an ending part of the rotation.

[0113] Yet another exemplary deterministic reshaping and / or reordering function

[0114] Figure 5 Shows an initial state of a set of atomic objects and multiple snapshots of the set of atomic objects as each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed, resulting in a final state of the set of atomic objects. In various embodiments, the atomic objects in the set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element.

[0115] Illustration 502 shows an initial state of a set of atomic objects at an initial time T = t0. In the initial state, the set of atomic objects is in an initial chain in a second configuration. When the set of atomic objects is in the second configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device such as ion trap plane 103) and in a chain aligned along a confinement potential axis 125 within the plane (in an exemplary embodiment, defined by the confinement device), where object A and object D are adjacent to each other and are disposed between object B and object C. In an exemplary embodiment, the confinement potential axis 125 is substantially aligned with the ion trap axis 101. As described above, objects B and C are of a first atomic object type, and objects A and D are not of the first atomic object type. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is an atomic object type different from the first atomic object type. In an exemplary embodiment, in the initial state of the set of atomic objects, the confinement potential dominates the potential experienced by the atomic objects within the confinement device. For example, when the set of atomic objects is in the initial state, the confinement ratio (i.e., the intensity ratio of the confinement potential to the TT potential) is X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be greater than zero and within the range defined by the stable region of the ion trap 100.

[0116] In an exemplary embodiment, a potential energy generating element generates a potential field that causes the atomic objects in the set of atomic objects to traverse a trajectory such that the atomic objects move through the positions shown in illustrations 504, 506, 508, 510, 512, and reach the final state shown in illustration 514 at a final time T = t f . Between illustration 502 and illustration 504, the time-dependent potential field causes the initial chain (e.g., including the aligned atomic objects in the set of atomic objects) to rotate in a first direction in response to the rotation of the rotational potential axis 135 by a rotation angle α1 between times T = t0 and T = t1 to form a rotated chain. The first direction is within the plane. For example, the initial chain can rotate in response to experiencing a rotational potential that has rotated such that the rotational potential axis 135 forms a rotation angle α1 with the confinement potential axis 125. In an exemplary embodiment, the initial chain rotates about a center point 140 (e.g., the point where the confinement potential axis 125 intersects the rotational potential axis 135).

[0117] Between illustration 504 and illustration 506, the time-dependent potential field causes an initially rotating chain (e.g., including aligned atomic objects in a set of atomic objects) to be compressed to form a compressed arrangement of the set of atomic objects. For example, a change in the confinement ratio can cause the initially rotating chain to be compressed along the confinement potential axis 125. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a compressive potential energy that causes the set of atomic objects to be compressed along the confinement potential axis. For example, the compressive potential energy can cause the atomic objects to feel a push outward from a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects A and D) in the direction of the confinement potential axis 125. For example, the confinement ratio (the ratio of the strength of the confinement potential to the TT potential) can be reduced to Y:1, where Y can be close to 1 and / or less than 1. For example, as shown in illustration 506, the confinement ratio can be in the range of about 1.2:1 to 0.8:1. In an exemplary embodiment, Y is within the range defined by the stable region of the ion trap 100. In an exemplary embodiment, the confinement ratio is reduced by adjusting the strength of the TT potential. For example, a drive action sequence can be determined such that the TT potential rotates about the center point 140. Additionally, a drive action sequence can be determined such that the rotational potential energy is sufficient to rotate objects B and C about the center point 140, but due to the mass difference between objects B and C and objects A and D, objects A and D do not feel a force from the rotational potential energy (e.g., generated by applying a voltage to the TT electrode 116) sufficient to cause objects A and D to rotate about the center point 140. For example, objects A, B, C, and D experience a confinement potential generated by the RF rails 112 and a TT potential generated by applying a voltage to the TT electrode 116, and the combination of these potentials provides a non-rotational potential energy (e.g., which defines the confinement potential axis 125) and a rotational potential energy (e.g., which defines the rotational potential axis 135). The combined potential energy (e.g., the superposition of the confinement potential and the potential energy generated by applying a voltage to the TT electrode 116) is sufficient to cause atomic objects having a mass similar to the mass of objects B and C to rotate about the center point 140, but not sufficient to cause atomic objects having a mass similar to the mass of objects A and D (e.g., smaller than the mass of objects B and C) to rotate about the center point 140. In an exemplary embodiment, the change in the confinement ratio and the change in the TT potential cause the compression of the initially rotating chain and cause objects B and object C to move to opposite sides of the confinement potential axis 125. Objects B and C can continue to rotate about the center point 140 such that at time T = t2, in response to the rotational potential axis 135 rotating through a rotation angle α2, the angle between the confinement potential axis 125 and the rotational potential axis 135 is the rotation angle α2.

[0118] Between illustrations 506 and 510, a time-dependent potential field (e.g., a superposition of a confinement potential and a TT potential) causes a compressed arrangement of a set of atomic objects to rotate to form a rotated compressed arrangement of the set of atomic objects. For example, between illustrations 506 and 510, the rotational potential continues to rotate as shown by the rotation of the rotational potential axis 135. In various embodiments, as the rotational potential axis 135 continues to rotate, objects B and C continue to rotate in a first direction through a rotation angle α such that the rotation angle α increases from α2 at time T = t2 to α3 at time T = t3 (as shown in illustration 508) and α4 at time T = t4 (as shown in illustration 510). Objects A and D may rotate in a second direction about the rotation center 140. In various embodiments, since objects A and D have a smaller mass than objects B and C, objects A and D feel a steeper potential barrier caused by the confinement potential and / or non-rotational potential compared to objects B and C. In an exemplary embodiment, the center point 140 used as the rotation center is located at the intersection between the confinement potential axis 125 and the rotational potential axis 135. In an exemplary embodiment, the confinement potential axis 125 and the rotational potential axis 135 intersect at the center point 140 of the set of atomic objects. The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is a counterclockwise rotation in the plane, the rotation in the second direction is a clockwise rotation in the plane. Similarly, if the rotation in the first direction is a clockwise rotation in the plane, the rotation in the second direction is a counterclockwise rotation in the plane. Illustration 508 shows an intermediate point of the rotation between the compressed arrangement and the rotated compressed arrangement.

[0119] Between illustrations 510 and 512, the time-dependent potential field causes the rotationally compressed arrangement of a set of atomic objects to be decompressed to form an off-axis final chain. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a decompression potential energy that causes the set of atomic objects to be decompressed along the confinement potential energy axis. For example, the decompression potential energy can cause the atomic objects to feel an inward push in the direction of the confinement potential energy axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential energy axis and between objects A and D). For example, a change in the confinement ratio (e.g., the relative strength of the confinement potential energy to the rotational TT potential energy) can cause the rotationally compressed arrangement of the set of atomic objects to decompress or extend along the confinement potential energy axis 125. For example, the rotationally compressed arrangement of the set of atomic objects can decompress, extend, and / or stretch such that the diamond shape of the rotationally compressed arrangement is transformed into an aligned and / or linear shape of the off-axis final chain. For example, the confinement ratio can be increased to X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be within the range defined by the stable region of the ion trap 100. In an exemplary embodiment, the confinement ratio is increased by adjusting the strength of the TT potential energy (e.g., by decreasing the absolute value of the voltage applied to the TT electrode 116). Objects B and C can continue to rotate about the center point 140 in the first direction in response to the continued rotation of the rotational potential energy such that at time T = t4, the rotational potential energy has rotated through a rotational angle α4 such that the angle between the confinement potential energy axis 125 and the rotational potential energy axis 135 is the rotational angle α4. When objects A and D continue to rotate about the center point 140 in the second direction, an off-axis final chain is formed at time T = t4.

[0120] Between illustrations 512 and 514, the time-dependent potential field causes the off-axis final chain to rotate in the first direction such that the angle between the confinement potential energy axis 125 and the rotational potential energy axis 135 is the final rotational angle α f , and a final chain is formed. For example, the final chain can be aligned along an axis and / or be substantially aligned along the ion trap axis 101. In an exemplary embodiment, the final rotational angle α f is approximately 180°. The first direction is in a plane. For example, the off-axis chain can rotate such that the atomic objects in the final chain are aligned along the confinement potential energy axis 125. In various embodiments, the center point 140 serves as the center of rotation. For example, the off-axis final chain rotates about the center point 140 in the first direction to form the final chain.

[0121] As can be seen in illustration 514, according to an exemplary embodiment, the final chain has a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C. However, object B and object C have changed positions between the initial chain and the final chain. In various embodiments, the positions of object A and object D in the final chain are the same as their positions in the initial chain, but object B and object C have changed positions. For example, the initial chain can be the ordered objects B, A, D, C, and the final chain can be the ordered objects C, A, D, B. From Figure 5 and as understood above, objects B and C rotate about a center point of a set of atomic objects through a final rotation angle of, for example, 180°. However, during the rotation of objects B and C, the set of atomic objects is not held in a collinear chain. Thus, all atomic objects remain closer to the confinement potential axis 125 (e.g., which is substantially aligned with the ion trap axis 101). As described above, the farther an atomic object is from the ion trap axis 101, the greater the RF heating experienced by the atomic object. Thus, various embodiments provide for objects B and C to switch positions with a lower level of RF heating of the atomic objects than a simple 180° rotation of the initial chain to form the final chain. Additionally, the voltage applied to perform Figure 5 the deterministic reshaping and / or reordering function shown requires a lower voltage than the voltage typically required to perform a simple 180° rotation of the initial chain to form the final chain.

[0122] In various embodiments, a time-dependent potential (e.g., a superposition of a confinement potential and a TT potential and / or a superposition of a non-rotating potential and a rotating potential) can be used to compress and rotate or decompress and rotate atomic objects in a time-overlapped manner. For example, the compression of a rotating initial chain and the continued rotation of the atomic objects about the center point 140 can occur simultaneously, semi-simultaneously, etc. For example, the compression can occur while the continued rotation occurs. Similarly, the decompression of the atomic objects and the rotation of the atomic objects can occur in a time-overlapped manner. For example, a time-dependent potential is generated by superposing a non-rotating potential and a rotating potential. When the rotation angle α is 90°, the axial compression (e.g., compression along the confinement potential axis 125 and / or the ion trap axis 101) is maximum, causing compression and subsequent decompression of a set of atomic objects. For example, once the rotation of the atomic objects is initiated (e.g., during an early part of the rotation), the confinement ratio can be adjusted from X:1 to Y:1. Then for an intermediate part of the rotation of the atomic objects, the confinement ratio can be held at Y:1, and then adjusted from Y:1 to X:1 during an end part of the rotation. In an exemplary embodiment, illustration 504 and / or 506 shows at least a part of an early part of the rotation, illustration 508 shows an intermediate part of the rotation, and illustrations 510 and / or 512 show an end part of the rotation.

[0123] Yet another exemplary deterministic reshaping and / or reordering function

[0124] Figure 6 shows an initial state of a set of atomic objects and multiple snapshots of a set of atomic objects when each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed, resulting in a final state of the set of atomic objects. Specifically, Figure 6 shows an exemplary deterministic reshaping and / or reordering function, in which a set of atomic objects is reshaped from a first configuration to a second configuration, or vice versa. In various embodiments, the atomic objects in a set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element.

[0125] In various embodiments, FIGS. 602 to 608 are the same as the process of FIGS. 402 to 408 with respect to Figure 4 , FIGS. 610R to 616R are the same as the process of FIGS. 508 to 514 with respect to Figure 5 , and FIGS. 610L to 616L are opposite to the process of FIGS. 508 to 502. For example, in an exemplary embodiment, step / operation 204 (e.g., solving a sequence of actuator actions) may be performed for the deterministic reshaping and / or reordering function in Figure 4 and Figure 5 , and portions of the sequence of actuator actions determined for the deterministic reshaping and / or reordering function in Figure 4 and Figure 5 may be spliced together to provide a sequence of actuator actions for performing the deterministic reshaping and / or reordering function in Figure 6 .

[0126] FIG. 602 shows an initial state of a set of atomic objects at an initial time T = t0. In the initial state, the set of atomic objects is in an initial chain in a first configuration. When the set of atomic objects is in the first configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device such as ion trap plane 103) and in a chain aligned along a confinement potential axis 125 within the plane (in an exemplary embodiment, defined by a confinement device), where objects B and C are adjacent to each other and are disposed between objects A and D. FIGS. 616R and 616L show the state at a final time T = t fTwo possible final states of a set of atomic objects, where the atomic objects are in the final chain in the second configuration. For example, option R (corresponding to diagrams 610R, 612R, 614R, and 616R) causes object B to be in the rightmost position of the final chain, and option L (corresponding to diagrams 610L, 612L, 614L, and 616L) causes object B to be in the leftmost position of the final chain. When the set of atomic objects is in the second configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device such as the ion trap plane 103) and in a chain aligned along the confinement potential axis 125 within the plane (in an exemplary embodiment, defined by the confinement device), where objects A and D are adjacent to each other and are disposed between objects B and C. It should be understood that Figure 6 can be read in reverse (e.g., from diagram 616R or 616L to diagram 602) to provide a deterministic reshaping and / or reordering function, where the initial state is the second configuration and the final state is the first configuration.

[0127] In an exemplary embodiment, the confinement potential axis 125 is substantially aligned with the ion trap axis 101. As described above, objects B and C are of the first atomic object type, and objects A and D are not of the first atomic object type. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is a different atomic object type from the first atomic object type. In an exemplary embodiment, in the initial state of a set of atomic objects, the confinement potential dominates the potential experienced by the atomic objects within the confinement device. For example, when the set of atomic objects is in the initial state, the confinement ratio (i.e., the intensity ratio of the confinement potential to the TT potential) is X:1, where X is greater than 1. For example, in an exemplary embodiment, X is greater than 1 and within the range defined by the stable region of the ion trap 100.

[0128] In an exemplary embodiment, the potential generating element generates a potential field that causes the atomic objects in a set of atomic objects to traverse a trajectory such that the atomic objects move through the positions shown in any of diagrams 604, 606, 608, and 610R, 612R, 614R, and 616R or 610L, 612L, 614L, and 616L, depending on the situation at the final time T = t fThe desired order of the final chain provided in the final state as shown in diagrams 616R and 616L. Between diagram 602 and diagram 604, the time-dependent potential field causes the initial chain (e.g., including aligned atomic objects in a set of atomic objects) to rotate in a first direction to form a rotated chain as the rotational potential rotates through a first sequence of angles β, such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the first sequence of angles β1. The first direction is in a plane. For example, the rotational potential can be rotated such that the rotational potential axis 135 forms the first sequence of angles β1 with the confinement potential axis 125 at time T = t1. In an exemplary embodiment, the center point 140 of a set of atomic objects is used as the rotation point, and the initial chain rotates about this rotation point. In various embodiments, the center point 140 is the point where the confinement potential axis 125 intersects the rotational potential axis 135.

[0129] Between diagram 604 and diagram 606, the time-dependent potential field causes the rotated initial chain (e.g., including aligned atomic objects in a set of atomic objects) to be compressed to form a compressed arrangement of a set of atomic objects. For example, the potential generating element can be controlled (e.g., by controller 30) to generate a compression potential that causes a set of atomic objects to be compressed along the confinement potential axis. For example, the compression potential can cause the atomic objects to feel a push outward from a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects B and C) in the direction of the confinement potential axis 125. For example, a change in the confinement ratio can cause the rotated initial chain to be compressed along the confinement potential axis 125. For example, the confinement ratio (the intensity ratio of the confinement potential to the TT potential) can be reduced to Y:1, where Y can be close to 1 and / or less than 1. For example, as shown in diagram 506, the confinement ratio can be in the range of about 1.2:1 to 0.8:1. In an exemplary embodiment, the confinement ratio is reduced by adjusting the intensity of the TT potential. In an exemplary embodiment, the change in the confinement ratio causes compression and / or rotation of the rotated initial chain such that objects B and C move to opposite sides of the confinement potential axis 125. Objects B and C can continue to rotate about the center point 140 in response to the continued rotation of the rotational potential such that at time T = t2, the rotational potential axis 135 has rotated through a first sequence of angles β2 such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the first sequence of angles β2.

[0130] Between diagram 606 and 608, the time-dependent potential field causes the compressed arrangement of a set of atomic objects to continue to rotate to form a rotated compressed arrangement of a set of atomic objects. In various embodiments, objects B and C continue to rotate in the first direction in response to the rotational potential continuing to rotate through a first sequence of angles β such that the first sequence of angles β increases from β2 at time T = t2 to a transition angle β at time T = t3.m , as shown in FIG. 508. In various embodiments, the transition angle β m is in the range of approximately 70° to 110°. For example, in an exemplary embodiment, the transition angle β m is approximately 90°. Objects A and D can rotate about the center point 140 in a second direction. In various embodiments, since objects A and D have a smaller mass than objects B and C, objects A and D feel a steeper potential barrier due to the non-rotational potential energy compared to objects B and C. In an exemplary embodiment, the center point 140 serving as the rotation center is located at the intersection of the rotational potential energy axis 135 and the confinement potential energy axis 125. The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise rotation in the plane, then the rotation in the second direction is clockwise rotation in the plane. Similarly, if the rotation in the first direction is clockwise rotation in the plane, then the rotation in the second direction is counterclockwise rotation in the plane.

[0131] Between FIG. 608 and FIGS. 610R or 610L, the time-dependent potential field causes the rotating compressed arrangement (e.g., including aligned atomic objects in a set of atomic objects) to be further compressed to form an intermediate arrangement of the set of atomic objects shown in FIGS. 610R and 610L. For example, the first compressed arrangement structure of the rotation can be further compressed along the confinement potential energy axis 125. For example, the confinement ratio (the ratio of the strength of the confinement potential energy to the strength of the TT potential energy) can be reduced to Z:1, where Z is less than Y. In an exemplary embodiment, the confinement ratio is reduced by increasing the strength of the TT potential energy. In an exemplary embodiment, when in the second compressed arrangement, objects A and D are substantially aligned along the confinement potential energy axis 125, and the rotational potential energy axis 135 is substantially orthogonal or perpendicular to the confinement potential energy axis 125. As shown in FIGS. 610R and 610L, at time T = t4, the angle between the confinement potential energy axis 125 and the rotational potential energy axis 135 connecting the exchanged atomic objects (e.g., objects B and C) is the initial second sequence angle γ1. In various embodiments, the initial second sequence angle is approximately equal to the transition angle β m .

[0132] Continuing option R, between FIG. 610R and 612R, the time-dependent potential field causes the intermediate arrangement of the set of atomic objects to rotate in the first direction to form a rotating intermediate arrangement of the set of atomic objects at time T = t5, as shown in FIG. 612R. In various embodiments, objects B and C rotate in response to the rotation axis through the initial second sequence angle γ1 at time T = t4 to the second sequence angle γ at time T = t5 2Rrotate in the first direction at a second sequence angle. In various embodiments, objects B and C rotate about a center point 140 in the first direction. In an exemplary embodiment, the center point 140 is located at the intersection between the rotational potential energy axis 135 and the confinement potential energy axis 125 (which, in the exemplary embodiment, is substantially aligned with the ion trap axis 101). The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise rotation in the plane, then the rotation in the second direction is clockwise rotation in the plane. Similarly, if the rotation in the first direction is clockwise rotation in the plane, then the rotation in the second direction is counterclockwise rotation in the plane.

[0133] Between illustrations 612R and 614R, the time-dependent potential field causes the rotational intermediate arrangement of a set of atomic objects to be decompressed and continue to rotate to form an off-axis final chain at time T = t6, as shown in illustration 614R. For example, the rotational intermediate arrangement of a set of atomic objects can be decompressed or extended along the confinement potential energy axis 125. For example, the rotationally compressed arrangement of a set of atomic objects can be decompressed, extended, and / or stretched such that the diamond shape of the rotationally compressed arrangement is transformed into the aligned and / or linear shape of the off-axis final chain. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a decompression potential energy that causes a set of atomic objects to be decompressed along the confinement potential energy axis. For example, the decompression potential energy can cause the atomic objects to feel an inward push in the direction of the confinement potential energy axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential energy axis and between objects A and D). For example, the confinement ratio can be increased to X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be greater than 1 and within the range defined by the stable region of the ion trap 100. In an exemplary embodiment, the confinement ratio is increased by adjusting the strength of the TT potential energy (e.g., reducing the absolute value of the voltage applied to the TT electrode 116). Objects B and object C can continue to rotate about the center point 140 in the first direction in response to the continued rotation of the rotational potential energy, such that at time T = t6, the rotational potential energy axis 135 has rotated through the second sequence angle γ 3R such that the angle between the confinement potential energy axis 125 and the rotational potential energy axis 135 is the second sequence angle γ 3R . When objects A and D continue to rotate about the center point 140 in the second direction, an off-axis final chain is formed at time T = t6.

[0134] Between illustrations 614R and 616R, the time-dependent potential field causes the off-axis final chain to rotate in the first direction such that the angle between the confinement potential energy axis 125 and the rotational potential energy axis 135 is the final second sequence angle γ fR and at time T = t fA final chain is formed there. For example, the final chain can be aligned along the confinement potential axis 125 and / or be substantially aligned along the ion trap axis 101. In an exemplary embodiment, the final second sequence angle γ fR is approximately 180°. The first direction is in a plane. For example, the off-axis chain can be rotated such that the atomic objects in the final chain are aligned along the confinement potential axis 125. In various embodiments, the center point 140 serves as the center of rotation. For example, the off-axis final chain rotates about the center point 140 in the first direction to form the final chain.

[0135] Relative to option L, between diagrams 610L and 612L, the time-dependent potential field causes an intermediate arrangement of a set of atomic objects to rotate in a second direction to form a rotated intermediate arrangement of the set of atomic objects at time T = t5, as shown in diagram 612L. In various embodiments, objects B and C respond to the rotation of the confinement potential axis from the initial second sequence angle γ1 at time T = t4 to the second sequence angle γ 2L by rotating through a second sequence angle in the second direction. For example, the confinement potential axis 135 rotates in the second direction, and the rotation of objects B and C responds to the rotation of the confinement potential axis 135. In various embodiments, objects B and C rotate about the center point 140 in the second direction. In an exemplary embodiment, the center point 140 is located at the intersection between the confinement potential axis 135 and the confinement potential axis 125 (which is substantially aligned with the ion trap axis 101 in the exemplary embodiment). The second direction is in a plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise rotation in the plane, then the rotation in the second direction is clockwise rotation in the plane. Similarly, if the rotation in the first direction is clockwise rotation in the plane, then the rotation in the second direction is counterclockwise rotation in the plane.

[0136] Between illustrations 612L and 614L, the time-dependent potential field causes the rotation intermediate arrangement of a set of atomic objects to be decompressed and continue to rotate to form an off-axis final chain at time T = t6, as shown in illustration 614L. For example, the rotation intermediate arrangement of a set of atomic objects can be decompressed or extended along the confinement potential axis 125. For example, the rotationally compressed arrangement of a set of atomic objects can be decompressed, extended, and / or stretched such that the diamond shape of the rotationally compressed arrangement is transformed into the aligned and / or linear shape of the off-axis final chain. For example, the potential energy generating element can be controlled (e.g., by controller 30) to generate a decompression potential energy that causes a set of atomic objects to be decompressed along the confinement potential axis. For example, the decompression potential energy can cause the atomic objects to feel an inward push in the direction of the confinement potential axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects A and D). For example, the confinement ratio can be increased to X:1, where X is greater than 1. For example, in an exemplary embodiment, X can be greater than 1 and within the range defined by the stable region of the ion trap 100. In an exemplary embodiment, the confinement ratio is increased by adjusting the strength of the TT potential energy (e.g., decreasing the absolute value of the voltage applied to the TT electrode 116). Objects B and C can continue to rotate about the center point 140 in the second direction in response to the continued rotation of the rotational potential energy such that at time T = t6, the rotational potential axis 135 has rotated through a second sequence angle γ 3L , such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the second sequence angle γ 3L . Objects A and D can rotate about the center point 140 in the first direction, and the off-axis final chain is formed at time T = t6.

[0137] Between illustrations 614L and 616L, the time-dependent potential field causes the off-axis final chain to rotate in the second direction such that the angle between the confinement potential axis 125 and the rotational potential axis 135 is the final second sequence angle γ fL , and a final chain is formed at time T = t f . For example, the final chain can be aligned along the confinement potential axis 125 and / or be substantially aligned along the ion trap axis 101. In an exemplary embodiment, the final second sequence angle γ fL is approximately 0°. The first direction is in the plane. For example, the off-axis chain can rotate such that the atomic objects in the final chain are aligned along the confinement potential axis 125. In various embodiments, the center point 140 serves as the center of rotation. For example, the off-axis final chain rotates about the center point 140 in the second direction to form the final chain.

[0138] As can be seen in FIGS. 616R and 616L, according to an exemplary embodiment, the final chain has a second configuration in which object A and object D are adjacent to each other and are disposed between object B and object C. Thus, the deterministic reshaping and / or reordering function has transformed a set of atomic objects from a first configuration to a second configuration and is capable of controlling which of object B and object C is in the rightmost or leftmost position of the final chain.

[0139] In various embodiments, a time-dependent potential energy can be used to compress and rotate or decompress and rotate atomic objects in a time-overlapped manner. For example, compression of the initial chain that is rotating and continued rotation of the atomic objects about a center point 140 can occur simultaneously, semi-simultaneously, etc. For example, compression can occur while continued rotation occurs. For example, the axial compression experienced by objects B and C can change when objects B and C rotate about center point 140 and / or when the confinement ratio changes, thereby causing compression and / or decompression of a set of atomic objects along the confinement potential axis 125 and / or the ion trap axis 101. Similarly, decompression of the atomic objects and rotation of the atomic objects can occur in a time-overlapped manner. For example, once rotation of the atomic objects is initiated (e.g., during an early portion of the rotation), the confinement ratio can be adjusted from X:1 to Y:1. Then for a first intermediate portion of the rotation of the atomic objects, the confinement ratio can be held at Y:1, and then adjusted from Y:1 to Z:1 during a second intermediate portion of the rotation of the atomic objects. Then the confinement ratio can be adjusted from Z:1 to Z:1 during an end portion of the rotation, where X, Y, and Z are all within a range defined by the stable region of the ion trap 100. In an exemplary embodiment, FIGS. 604 and / or 606 show at least a portion of an early portion of the rotation, FIG. 608 shows at least a portion of a first intermediate portion of the rotation, FIGS. 610R and 610L show at least a portion of a second intermediate portion of the rotation, and FIGS. 612R, 612L, and / or 614R, 614L show an end portion of the rotation.

[0140] As described above, the deterministic reordering and / or reshaping function can be performed in reverse (e.g., from FIGS. 616R or 616L to FIG. 602) to reshape and / or reorder a set of atomic objects from a second configuration to a first configuration. For example, when the deterministic reordering and / or reshaping function is performed to transform a set of atomic objects in a second configuration to a set of atomic objects in a first configuration, the potential energy generating element of the confinement device can be controlled to generate a time-dependent potential field that causes the initial chain in the first configuration to rotate through a first sequence of angles β in a first direction, and the confinement ratio can be decreased to Z:1 (in series or overlapped in time) such that the initial chain is transformed into a rhombic arrangement (e.g., as shown in FIGS. 610R and 610L). At the attainment of the transition angle β mThereafter, the confinement ratio may be increased to Y:1 and then to X:1, and the rotation of objects B and C may continue from the transition angle to the final second sequence angle in a first or second direction determined based on the desired final order of a set of atomic objects to form a final chain in the second configuration.

[0141] Yet another exemplary deterministic reshaping and / or reordering function

[0142] Figure 7 Multiple snapshots of a set of atomic objects are shown of an initial state of the set of atomic objects and when each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed to result in a final state of the set of atomic objects. In various embodiments, the atomic objects in the set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element. In Figure 7 the deterministic reshaping and / or reordering function shown, the initial state of the set of atomic objects is the third configuration and the final state of the set of atomic objects is the fourth configuration. It should be understood that the deterministic reshaping and / or reordering function may be performed in the Figure 7 opposite direction of the time arrow shown to deterministically reshape and / or reorder a set of atomic objects from an initial state of the set of atomic objects in the fourth configuration to a final state of the set of atomic objects in the third configuration.

[0143] Illustration 702 shows an initial state of a set of atomic objects. In the initial state, the set of atomic objects is in an initial chain in a third configuration. When the set of atomic objects is in the third configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device) and in a chain aligned along a confinement potential axis 125 within the plane (in an exemplary embodiment, defined by a confinement device), where object B and object C are adjacent to each other, and object A and object D are adjacent to each other. In an exemplary embodiment, the confinement potential axis 125 is substantially aligned with the ion trap axis 101. In an exemplary embodiment, the confinement potential axis 125 is an axis and / or line that is substantially parallel to the ion trap axis 101 and passes through a point equidistant between object B and object C (and / or any pair of atomic objects in the set of atomic objects when the set of atomic objects is in the initial or final state). For example, the confinement potential axis 125 can be an axis and / or line that is substantially parallel to the ion trap axis 101. In various embodiments, the rotational potential axis 135 intersects the center point 140 of the confinement potential axis 125 of the set of atomic objects. As described above, objects B and C are of a first atomic object type, and objects A and D are not of the first atomic object type. Objects B and C have a greater mass than objects A and D. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is an atomic object type different from the first atomic object type.

[0144] In an exemplary embodiment, in the initial state of a set of atomic objects, the confinement potential dominates the potential experienced by the atomic objects within the confinement device. For example, when the set of atomic objects is in the initial state, the confinement ratio, i.e., the ratio of the confinement potential (e.g., generated by the voltage applied to the RF rails 112) to the intensity of the TT potential, is X:1, where X is greater than 1. For example, in an exemplary embodiment, X is such that the voltage applied to the RF rails 112 and the voltage applied to the TT electrodes 116 are within the stable region of the ion trap 100. Generally speaking, the stable region of the ion trap 100 is defined based on the geometry of the ion trap 100. For example, the stable region can be a first stable region and can be a voltage region of the ion trap 100 where ions can be trapped in a stable manner within the ion trap 100. For example, X can be a value greater than one such that there is a preferred confinement direction (e.g., along and / or substantially parallel to the axis 101) within the ion trap 100 and such that trapping within the ion trap 100 is feasible.

[0145] In an exemplary embodiment, a potential energy generating element generates a potential field that causes an atomic object in a set of atomic objects to traverse a trajectory such that the atomic object moves through the positions shown in diagrams 704, 706, 708, 710 and reaches the final state shown in diagram 712. Although diagrams 704, 706, 708 and 710 are split to show different steps in the movement of the atomic object, in various embodiments, some of these steps may occur simultaneously. For example, in an exemplary embodiment, the steps shown in diagrams 704 and 706 occur simultaneously and / or the steps shown in diagrams 708 and 710 occur simultaneously.

[0146] Between diagram 702 and diagram 704, a time-dependent potential field causes an initial chain (e.g., including aligned atomic objects in a set of atomic objects) to rotate through a first angle θ in a first direction to form a rotated chain. In various embodiments, the initial chain rotates through a first angle θ in a first direction about a center point 140 to form a rotated chain. The first direction is within plane 103. For example, the initial chain may rotate in response to the rotation of a rotational potential energy such that the rotational potential energy axis 135 forms a first angle θ with the confinement potential energy axis 125. In various embodiments, the first angle θ is greater than 0° and less than 90°. In an exemplary embodiment, the first angle θ is in the range of approximately 5° - 15°.

[0147] Between diagram 704 and diagram 706, a time-dependent potential field causes the rotated initial chain (e.g., including aligned atomic objects in a set of atomic objects) to be compressed to form a compressed arrangement of the set of atomic objects. For example, the rotated initial chain may be compressed along the confinement potential energy axis 125. For example, the potential energy generating element may be controlled (e.g., by controller 30) to generate a compression potential energy that causes the set of atomic objects to be compressed along the confinement potential energy axis. For example, the compression potential energy may cause the atomic objects to feel a push outward from a point inside the set of atomic objects (e.g., a point located along the confinement potential energy axis and between object A and C) in the direction of the confinement potential energy axis 125. For example, the confinement ratio (the intensity ratio of the confinement potential energy to the TT potential energy) may be reduced to Y:1, where Y may be close to 1 and / or less than 1. For example, as shown in diagram 706, the confinement ratio may be in the range of about 1.2:1 to 0.8:1. In an exemplary embodiment, the confinement ratio is reduced by increasing the intensity of the TT potential energy. For example, in an exemplary embodiment, the confinement potential energy generated by applying a voltage to the RF rail 112 may be substantially constant over time (e.g., the time average of the confinement potential energy in a first time period may be substantially equal to the time average of the confinement potential energy in a second time period). In an exemplary embodiment, compressing the rotated initial chain causes object C and object A to move to opposite sides of the confinement potential energy axis 125.

[0148] Between diagrams 706 and 708, the time-dependent potential field causes a compressed arrangement of a set of atomic objects to rotate through a second angle in a second direction to form a rotated compressed arrangement of the set of atomic objects. In an exemplary embodiment, the second angle is greater than twice the first angle θ. For example, in diagram 706, the angle between the confinement potential axis 125 and the rotational potential axis 135 is the first angle θ, and in diagram 708, the angle between the confinement potential axis 125 and the rotational potential axis 135 has a sign opposite to that of the first angle θ and a greater absolute value. For example, between diagram 706 and diagram 708, the axis of the rotational potential rotates through an angle >2θ in the second direction. The second direction is in the plane and in the direction opposite to the first direction. For example, if the rotation in the first direction is counterclockwise in the plane, then the rotation in the second direction is clockwise in the plane. Similarly, if the rotation in the first direction is clockwise in the plane, then the rotation in the second direction is counterclockwise in the plane. In an exemplary embodiment, the rotation of the compressed arrangement of the set of atomic objects rotates about a point (e.g., center point 140) located at the center of the set of atomic objects to form a rotated compressed arrangement. In an exemplary embodiment, the center of the set of atomic objects is the point at which a virtual line connecting the exchanged atomic objects (e.g., object A and object C) intersects a virtual line connecting the non-exchanged atomic objects (e.g., object B and object D).

[0149] Between illustrations 708 and 710, the time-dependent potential field undergoes a series of decompression and rotation steps. For example, the time-dependent potential field may cause an initially rotationally compressed arrangement of a set of atomic objects to alternatively be decompressed and rotated multiple times to form an off-axis final chain. For example, the potential energy generating element may be controlled (e.g., by controller 30) to generate a decompression potential energy that causes a set of atomic objects to be decompressed along the confinement potential axis. For example, the decompression potential energy may cause the atomic objects to feel a push inward in the direction of the confinement potential axis 125 towards a point inside the set of atomic objects (e.g., a point located along the confinement potential axis and between objects A and C). For example, the confinement ratio may be increased to X:1 through a series of decompression steps alternated with rotation steps, where X is greater than 1. For example, in an exemplary embodiment, X may be in the range of about 1.5 to 4.0. In an exemplary embodiment, the confinement ratio is increased by reducing the strength of the TT potential energy. For example, an initially rotationally compressed arrangement of a set of atomic objects may be decompressed or extended along the confinement potential axis 125. For example, an initially rotationally compressed arrangement of a set of atomic objects may be decompressed, extended, and / or stretched such that the diamond shape of the rotationally compressed arrangement is transformed into an aligned and / or linear shape of the off-axis final chain. By alternating small decompression and rotation steps, sudden snapping motions of the atomic objects that occur when the atomic objects reform into a chain can be avoided and / or reduced. The reduction and / or avoidance of sudden snapping motions reduces heating of the atomic objects during deterministic reshaping and / or reordering operations, and / or reduces and / or avoids random reordering events of the atomic objects during the performance of the reshaping and / or reordering operations.

[0150] Between illustrations 710 and 712, the time-dependent potential field causes the off-axis final chain to rotate in a first direction by an angle greater than a first angle θ, for example, to form a final chain. For example, the rotational potential axis 135 may be rotated in the first direction by an angle greater than the first angle θ such that the rotational potential axis 135 is substantially parallel to the confinement potential axis 125 in illustration 712. The first direction is in a plane. For example, the off-axis chain may be rotated such that the atomic objects in the final chain are aligned along the confinement potential axis 125. In an exemplary embodiment, the off-axis final chain rotates about a center point 140 to form a final chain. In an exemplary embodiment, the confinement ratio experienced by the final chain is approximately the same as the confinement ratio experienced by the initial chain.

[0151] As can be seen in illustration 712, according to an exemplary embodiment, the final chain has a fourth configuration where object B and object C are not adjacent to each other, and object A and object D are not adjacent to each other. For example, objects C and A have changed positions between the initial chain and the final chain. For example, the initial chain may be ordered object B, object C, object A, object D, and the final chain may be ordered object B, object A, object C, object D.

[0152] In various embodiments, the time-dependent potential energy can cause object C and object A to rotate 180°, such that object C and object A switch positions between the initial state and the final state. However, during the second half of the rotation (e.g., between the 90° rotation position and the 180° rotation position), multiple decompression and rotation steps can be performed in an alternating manner. For example, during the first half of the rotation (e.g., between the 0° rotation position and the 90° rotation position), the compression ratio is adjusted from X:1 to Y:1. During the second half of the rotation, the compression ratio is adjusted from Y:1 to X:1 via a series of discrete steps.

[0153] In various embodiments, when an atomic object is not positioned along the ion trap axis 101, due to the confinement potential energy, the atomic object experiences heating (e.g., acquisition of thermal energy). This heating mechanism is referred to herein as RF heating. The farther the atomic object is from the ion trap axis 101, the more RF heating the atomic object experiences. Figure 7 The exemplary deterministic reshaping and / or reordering functions shown keep all atomic objects relatively close to the ion trap axis 101 (e.g., which is substantially aligned with the confinement potential energy axis 125) compared to a simple 180° rotation of the initial chain of atomic objects to form the final chain. Thus, when performing Figure 7 the deterministic reshaping and / or reordering functions shown, the RF heating experienced by the atomic objects is significantly less than the RF heating experienced by the atomic objects during reshaping and / or reordering functions in which the atomic objects are not kept relatively close to the ion trap axis 101.

[0154] In various embodiments, the time-dependent potential energy can be used to compress and rotate atomic objects in a time-overlapped manner. For example, the compression of the initial chain of rotations and the continued rotation of the atomic objects about the center point 140 can occur simultaneously, semi-simultaneously, etc. For example, the compression can occur while the rotation continues. Similarly, the decompression of the atomic object and the rotation of the atomic object can occur in a time-overlapped manner. For example, once the rotation of the atomic object is initiated (e.g., during the early part of the rotation), the confinement ratio can be adjusted from X:1 to Y:1. Then for the middle part of the rotation of the atomic object, the confinement ratio can be held at Y:1, and then adjusted from Y:1 to X:1 via multiple discrete steps during the ending part of the rotation.

[0155] Yet another exemplary deterministic reshaping and / or reordering function

[0156] Figure 8shows an initial state of a set of atomic objects and multiple snapshots of the set of atomic objects as each object in the set of atomic objects traverses a trajectory such that a deterministic reshaping and / or reordering function is performed to result in a final state of the set of atomic objects. In various embodiments, the atomic objects in the set of atomic objects traverse corresponding trajectories in response to experiencing a time-dependent potential field generated by a potential energy generating element. In Figure 8 the illustrated deterministic reshaping and / or reordering function, the initial state of the set of atomic objects is a third configuration, and the final state of the set of atomic objects is a third configuration. However, between the initial state and the final state, objects B and C have changed positions with objects A and D, as can be seen in illustrations 802 and 810. It should be understood that the deterministic reshaping and / or reordering function can be performed in Figure 8 the opposite direction of the time arrow shown in the illustration to deterministically reshape and / or reorder a set of atomic objects from an initial state of the set of atomic objects in a third configuration shown in illustration 810 to a final state of the set of atomic objects in a third configuration shown in illustration 802.

[0157] Illustration 802 shows an initial state of a set of atomic objects. In the initial state, the set of atomic objects is in an initial chain in a third configuration. When the set of atomic objects is in the third configuration, objects A, B, C, and D are in a plane (in an exemplary embodiment, defined by a confinement device) and in a chain aligned along a confinement potential energy axis 125 within the plane (in an exemplary embodiment, defined by a confinement device), where objects B and C are adjacent to each other, and objects A and D are adjacent to each other. In an exemplary embodiment, the confinement potential energy axis 125 is substantially aligned with the ion trap axis 101. In an exemplary embodiment, the confinement potential energy axis 125 is an axis and / or line that is substantially parallel to the ion trap axis 101 and passes through the center point 140 of the set of atomic objects. For example, the confinement potential energy axis 125 can be an axis and / or line that is substantially parallel to the ion trap axis 101. As described above, objects B and C are of a first atomic object type, and objects A and D are not of the first atomic object type. Objects B and C have a greater mass than objects A and D. In an exemplary embodiment, objects A and D are of the same atomic object type as each other, which is an atomic object type different from the first atomic object type.

[0158] In an exemplary embodiment, in an initial state of a set of atomic objects, a confinement potential dominates the potential energy experienced by the atomic objects within a confinement device. For example, when a set of atomic objects is in an initial state, a confinement ratio, i.e., the ratio of the confinement potential (e.g., generated by a voltage applied to the RF rails 112) to the strength of the TT potential, is X:1, where X is greater than 1. For example, in an exemplary embodiment, X is such that the voltage applied to the RF rails 112 and the voltage applied to the TT electrodes 116 are within a stable region of the ion trap 100. Generally, the stable region of the ion trap 100 is defined based on the geometry of the ion trap 100. For example, the stable region may be a first stable region and may be a voltage region of the ion trap 100 where ions can be trapped in a stable manner within the ion trap 100. For example, X may be a value greater than one such that there is a preferred confinement direction (e.g., along and / or substantially parallel to the axis 101) within the ion trap 100 and such that trapping within the ion trap 100 is feasible.

[0159] In an exemplary embodiment, a potential energy generating element generates a potential field that causes an atomic object within a set of atomic objects to traverse a trajectory such that the atomic object moves through the positions shown in diagrams 804, 806, and 808 and reaches a final state shown in diagram 810. In various embodiments, the potential field comprises and / or is a superposition of a non-rotating potential energy (e.g., which defines a confinement potential axis 125) and a rotating potential energy (e.g., which defines a rotating potential axis 135).

[0160] Between diagram 802 and diagram 804, a time-dependent potential field causes an initial chain (e.g., comprising aligned atomic objects within a set of atomic objects) to be pushed away from the confinement potential axis 125. In various embodiments, the TT potential may generate a radial pushing potential energy that causes the atomic objects to be pushed away from the confinement potential axis 125. It should be understood that the potential energy and / or force experienced by the atomic objects is mass-dependent due to the potential energy in the radial direction of the confinement device (e.g., in a direction transverse to and / or perpendicular to the confinement potential axis 125 or the ion trap axis 101). Heavier atomic objects (objects B and C) experience a flatter potential barrier compared to the steeper potential barriers experienced by lighter atomic objects (objects A and D). Thus, objects B and C move more in response to the radial pushing potential energy. Thus, as shown in diagram 804, objects B and C are pushed further away from the confinement potential axis 125 by the radial pushing potential energy than objects A and D.

[0161] As shown in illustration 806, objects B and C have been pushed far enough away from objects A and D such that the movement of objects B and C is generally decoupled from the movement of objects A and D. Between illustration 806 and 810, the radial push potential energy can be decreased such that the atomic objects return to the confinement potential energy axis 125. For example, the time evolution of the amplitude / magnitude of the radial push potential energy can include a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. For example, the amplitude magnitude of the radial push potential energy can have the form of a triangular wave pulse over time such that the radial push potential energy increases to a maximum value and then decreases again.

[0162] Between at least a portion of the time between illustration 802 and 810, a rotational potential energy (as shown by rotational potential energy axis 135) can be applied. For example, in addition to and / or at least partially overlapping with the radial push potential energy, a rotational potential energy can be applied (e.g., by applying a voltage to the TT electrodes). In various embodiments, the rotational potential energy rotates through a rotational angle. In various embodiments, the rotational angle (e.g., the angle through which the rotational potential energy axis 135 rotates) is approximately 180°.

[0163] As can be seen in illustration 810, according to an exemplary embodiment, the final chain has a third configuration in which objects B and object C are adjacent to each other and objects A and D are adjacent to each other. For example, objects B and C and objects A and D have changed positions between the initial chain and the final chain. For example, the initial chain can be the ordered objects A, D, B, C, and the final chain can be the ordered objects B, C, A, D.

[0164] In various embodiments, a deterministic reshaping and / or reordering function is performed to transform a set of atomic objects from the initial state shown in illustration 802 to the final state shown in illustration 810 using a rotational potential energy similar to that described above with respect to Figure 3 For example, the potential energy generating element can be controlled to generate a time-dependent potential energy that causes the rotational potential energy axis to rotate through a first angle relative to the confinement potential energy axis in a first direction, compress a set of atomic objects, rotate the rotational potential energy axis through a second angle relative to the confinement potential energy axis in a second direction, decompress a set of atomic objects, and rotate the rotational potential energy axis through a third angle relative to the confinement potential energy axis in the first direction. In addition to the rotational potential energy and the confinement potential energy, the time-dependent potential energy can include a radial push potential energy. For example, the time evolution of the amplitude / magnitude of the radial push potential energy can include a monotonic increase to a maximum value and then a monotonic decrease to a minimum value. For example, the amplitude magnitude of the radial push potential energy can have the form of a triangular wave pulse over time such that the radial push potential energy increases to a maximum value and then decreases again. The result of a set of atomic objects experiencing a time-dependent potential energy that includes a confinement potential energy, a rotational potential energy, and a radial push potential energy can be similar to Figure 8Trajectories that are those shown but have a different behavior from the axis of rotational potential energy 135.

[0165] In various embodiments, time-dependent potentials including confinement potential, rotational potential, and radial push potential can be used to provide groups of atoms in various final configurations (e.g., a first configuration, a second configuration, a third configuration, and / or a fourth configuration) by tuning the timing and / or the maximum amplitude / magnitude of the time evolution of the radial push potential.

[0166] Technical advantages

[0167] Various embodiments provide a technical solution to the technical problem of deterministically reshaping and / or reordering a group of atomic objects confined within an atomic object confinement device. Conventional techniques for reordering a group of atomic objects confined within an atomic object rotate the entire group of atomic objects. For example, according to the conventional technique of reordering a group of atomic objects from Figure 5 Illustration 502 in to Illustration 514, the entire atomic object chain would rotate 180° about the center of rotation located between Object A and Object D on the axis of confinement potential energy 125. However, such conventional techniques require applying a high-power driver action sequence (e.g., a high voltage) to the potential energy generating element (e.g., electrode 116) and / or such conventional techniques result in a random reordering of the atomic objects. Thus, various embodiments provide an improvement over conventional techniques for reordering atomic objects within a confinement device such that a lower-power driver action sequence (e.g., a lower voltage) can be used and provide a deterministic reordering of a group of atomic objects. For example, experimental results show that an exemplary embodiment of the deterministic reshaping and / or reordering function described herein reduces the required voltage applied to the TT electrode 116 by more than half compared to simply rotating the initial chain to form the final chain. As used herein, the term "deterministic" means that the order of the atomic objects and / or the position of the atomic objects in the final state is pre-determined and / or known before the start of the deterministic reshaping and / or reordering function and / or is determined by the reshaping and / or reordering function (as opposed to a spontaneous or random reordering of the atomic objects). Additionally, various embodiments of the deterministic reshaping and / or reordering function can be performed faster than conventional reordering techniques (e.g., due to a smaller angle of rotation and / or keeping the atomic objects closer to the axis of confinement potential energy 125 during the execution of the function). Furthermore, conventional techniques do not provide a deterministic reshaping of a group of atomic objects. For example, conventional techniques do not provide a function to transform a group of atomic objects from a first configuration in which Object B and Object C are adjacent to each other and are disposed between Object A and Object D to a second configuration in which Object A and Object D are adjacent to each other and are disposed between Object B and Object C or vice versa.

[0168] In various embodiments, where the deterministic reshaping and / or reordering function is performed by a quantum computer to reorder qubit sets and / or qubit-cooled ion pairs, the improvements provided by the various embodiments enable the quantum computer to compile command sequences faster and operate at a faster clock speed compared to a quantum computer using traditional reordering techniques.

[0169] Accordingly, the various embodiments provide technical improvements to the field of quantum computer operation (e.g., for trapped-ion quantum computers, etc.) and to the field of controlling atomic objects within an atomic object confinement device.

[0170] Exemplary quantum computer including an ion trap device

[0171] As described above, the deterministic reshaping and / or reordering function is performed by the controller 30 of the quantum computer 910. Figure 9 A schematic diagram of an exemplary quantum computer system 900 including a confinement device (e.g., ion trap 100) according to an exemplary embodiment is provided. In various embodiments, the quantum computer system 900 includes a computing entity 10 and a quantum computer 910. In various embodiments, the quantum computer 910 includes a controller 30, a cryostat and / or vacuum chamber 40 that encloses the confinement device (e.g., ion trap 100), and one or more manipulation sources 60. In an exemplary embodiment, the one or more manipulation sources 60 may include one or more lasers (e.g., optical lasers, microwave sources, etc.). In various embodiments, the one or more manipulation sources 60 are configured to manipulate and / or cause a controlled quantum state evolution of one or more atomic objects within the confinement device. For example, in an exemplary embodiment, where the one or more manipulation sources 60 include one or more lasers, the lasers may provide one or more laser beams to the confinement device within the cryogenic chamber and / or vacuum chamber 40. In various embodiments, the quantum computer 910 includes one or more voltage sources 50. For example, the voltage source 50 may include a plurality of TT voltage drivers and / or voltage sources and / or at least one RF driver and / or voltage source. In an exemplary embodiment, the voltage source 50 may be electrically coupled to corresponding potential energy generating elements (e.g., TT electrodes 116) of the confinement device (e.g., ion trap 100).

[0172] In various embodiments, computing entity 10 is configured to allow a user to provide input to quantum computer 910 (e.g., via a user interface of computing entity 10) and receive output from quantum computer 910, view the output, etc. Computing entity 10 can communicate with controller 30 of quantum computer 910 via one or more wired or wireless networks 20 and / or via direct wired and / or wireless communication. In an exemplary embodiment, computing entity 10 can convert, configure, format, etc., information / data, quantum computing algorithms, etc. into a computing language, executable instructions, command sets, etc. that can be understood and / or implemented by controller 30.

[0173] In various embodiments, controller 30 is configured to control voltage source 50, a cryogenic system and / or a vacuum system that control temperature and pressure within cryogenic chamber and / or vacuum chamber 40, manipulation source 60, and / or control various environmental conditions (e.g., temperature, pressure, etc.) within cryogenic chamber and / or vacuum chamber 40 and / or is configured to manipulate and / or cause the controlled evolution of the quantum state of one or more atomic objects within a confinement device by other systems. For example, controller 30 can cause the controlled evolution of the quantum state of one or more atomic objects within a confinement device to execute a quantum circuit and / or algorithm. In various embodiments, the atomic objects confined within the confinement device serve as qubits of quantum computer 910.

[0174] Exemplary controller

[0175] In various embodiments, the confinement device is incorporated into quantum computer 910. In various embodiments, quantum computer 910 further includes controller 30 configured to control various elements of quantum computer 910. For example, controller 30 can be configured to control voltage source 50, a cryogenic system and / or a vacuum system that control temperature and pressure within cryogenic chamber and / or vacuum chamber 40, manipulation source 60, and / or control environmental conditions (e.g., temperature, humidity, pressure, etc.) within cryogenic chamber and / or vacuum chamber 40 and / or is configured to manipulate and / or cause the controlled evolution of the quantum state of one or more atomic objects within a confinement device by other systems.

[0176] As Figure 10As shown, in various embodiments, the controller 30 may include various controller elements, including a processing element 1005, a memory 1010, a drive controller element 1015, a communication interface 1020, an analog-to-digital converter element 1025, etc. For example, the processing element 1005 may include a programmable logic device (CPLD), a microprocessor, a coprocessing entity, an application-specific instruction set processor (ASIP), an integrated circuit, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices and / or circuits, etc. and / or a controller. The term circuit may refer to a fully hardware implementation or a combination of hardware and a computer program product. In an exemplary embodiment, the processing element 1005 of the controller 30 includes a clock and / or communicates with a clock.

[0177] For example, the memory 1010 may include non-transitory memory such as volatile and / or non-volatile memory, such as one or more of the following: a hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. In various embodiments, the memory 1010 may store qubit records corresponding to a quantum computer (e.g., in qubit-recorded data storage, qubit-recorded databases, qubit-recorded tables, etc.), calibration tables, executable queues, computer program code (e.g., one or more computer languages, a dedicated controller language, etc.), etc. for qubits. In an exemplary embodiment, the execution of at least a portion of the computer program code stored in the memory 1010 (e.g., by the processing element 1005) causes the controller 30 to perform one or more steps, operations, processes, programs, etc. described herein for tracking the phase of atomic objects within an atomic system and causing phase adjustment of one or more manipulation sources and / or the resulting signals.

[0178] In various embodiments, the drive controller element 1010 may include one or more drives and / or controller elements each configured to control one or more drives. In various embodiments, the drive controller element 1010 may include a drive and / or a drive controller. For example, the drive controller may be configured to cause one or more corresponding drives to be operated in accordance with executable instructions, commands, etc. scheduled and executed by the controller 30 (e.g., by the processing element 1005). In various embodiments, the drive controller element 615 may enable the controller 30 to operate the manipulation source 60. In various embodiments, the drive may be a laser drive; a vacuum component drive; a drive for controlling the flow of current and / or voltage applied to TT, RF, and / or other electrodes for maintaining and / or controlling the ion trapping potential energy of the ion trap 100 (and / or other drives for providing a drive action sequence to the potential energy generating element of the confinement device); a cryogenic and / or vacuum system component drive; and so on. For example, the drive may control and / or include a TT and / or RF voltage drive and / or a voltage source that provides voltage and / or electrical signals to the TT electrode 116 and / or the RF rail 112. In various embodiments, the controller 30 includes means for transmitting and / or receiving signals from one or more optical receiver components (such as cameras, MEM cameras, CCD cameras, photodiodes, photomultiplier tubes, etc.). For example, the controller 30 may include one or more analog-to-digital converter elements 1025 configured to receive signals from one or more optical receiver components, calibration sensors, etc.

[0179] In various embodiments, the controller 30 may include a communication interface 1020 for interacting and / or communicating with the computing entity 10. For example, the controller 30 may include the communication interface 1020 to receive executable instructions, command sets, etc. from the computing entity 10 and provide outputs received from the quantum computer 910 (e.g., from the light collection system) and / or results of processing the outputs to the computing entity 10. In various embodiments, the computing entity 10 and the controller 30 may communicate via a direct wired and / or wireless connection and / or one or more wired and / or wireless networks 20.

[0180] Exemplary computing entity

[0181] Figure 11 An illustrative schematic diagram of an exemplary computing entity 10 that may be used in conjunction with embodiments of the present invention is provided. In various embodiments, the computing entity 10 is configured to allow a user to provide input to the quantum computer 910 (e.g., via the user interface of the computing entity 10) and receive, display, analyze, etc. outputs from the quantum computer 910.

[0182] As Figure 11As shown, computing entity 10 may include antenna 1112, transmitter 1104 (e.g., radio component), receiver 1106 (e.g., radio component), and processing element 1108, which respectively provides signals to transmitter 1104 and receives signals from receiver 1106. The signals respectively provided to transmitter 1104 and received from receiver 1106 may include information / data signaling according to the air interface standard of the applicable wireless system for communicating with various entities such as controller 30, other computing entities 10, etc. In this regard, computing entity 10 may be operable with one or more air interface standards, communication protocols, modulation types, and access types. For example, computing entity 10 may be configured to receive and / or provide communications using a wired data transmission protocol such as Fiber Distributed Data Interface (FDDI), Digital Subscriber Line (DSL), Ethernet, Asynchronous Transfer Mode (ATM), Frame Relay, Data Over Cable Service Interface Specification (DOCSIS), or any other wired transmission protocol. Similarly, computing entity 10 may be configured to communicate via a wireless external communication network using any of a variety of protocols such as General Packet Radio Service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA), Global System for Mobile Communications (GSM), Enhanced Data Rates for GSM Evolution (EDGE), Time Division-Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized (EVDO), High Speed Packet Access (HSPA), High Speed Downlink Packet Access (HSDPA), IEEE802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), Ultra Wideband (UWB), Infrared (IR) protocol, Near Field Communication (NFC) protocol, Wibree, Bluetooth protocol, Wireless Universal Serial Bus (USB) protocol, and / or any other wireless protocol. Computing entity 10 may use such protocols and standards to communicate using the following: Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), TLS / SSL / Secure HTTP, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), Hypertext Markup Language (HTML), etc.

[0183] Via these communication standards and protocols, computing entity 10 can communicate with various other entities using concepts such as Unstructured Supplementary Service Information / Data (USSD), Short Message Service (SMS), Multimedia Messaging Service (MMS), Dual-Tone Multi-Frequency signaling (DTMF), and / or Subscriber Identity Module dial pad (SIM dial pad). Computing entity 10 can also download changes, add-ons, and updates, for example, to its firmware, software (e.g., including executable instructions, applications, program modules), and operating system.

[0184] Computing entity 10 may also include a user interface device that includes one or more user input / output interfaces (e.g., a display 1116 and / or a speaker / speaker driver coupled to processing element 1108 and a touch screen, keyboard, mouse, and / or microphone coupled to processing element 1108). For example, the user output interface may be configured to provide interchangeably applications, browsers, user interfaces, interfaces, dashboards, screens, web pages, pages, and / or similar terms used herein that are executed on computing entity 10 and / or accessible via the computing entity, to cause the display or auditory presentation of information / data, and to interact therewith via one or more user input interfaces. The user input interface may include any of a plurality of devices that allow computing entity 10 to receive data, such as a keypad 1118 (hard or soft), a touch display, a sound / voice or motion interface, a scanner, a reader, or other input devices. In an embodiment that includes keypad 1118, keypad 1118 may include (or cause the display of) conventional numeric keys (0-9) and associated keys (#, *) for operating computing entity 10, as well as other keys, and may include a full set of alphabetic keys or a set of keys that can be enabled to provide a full set of alphanumeric keys. In addition to providing input, the user input interface may also be used, for example, to activate or deactivate certain functions, such as a screen saver and / or sleep mode. Through such input, computing entity 10 can collect information / data, user interactions / inputs, etc.

[0185] The computing entity 10 may also include a volatile storage device or memory 1122 and / or a non-volatile storage device or memory 1124 that can be embedded and / or removed. For example, the non-volatile memory can be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. The volatile memory can be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. The volatile and non-volatile storage devices or memories can store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functions of the computing entity 10.

[0186] Conclusion

[0187] Those skilled in the art to which the present invention pertains will, after benefiting from the foregoing description and the teachings presented in the related drawings, conceive of many modifications and other embodiments of the invention set forth herein. Accordingly, it is to be understood that the invention is not limited to the specific embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a general and descriptive sense only and not for purposes of limitation.

Claims

1. A method for deterministically reordering a set of atomic objects within an atomic object confinement device, the method comprising: Providing a plurality of atomic objects in the atomic object confinement device, wherein: The atomic object confinement device includes a plurality of potential energy generating elements, The plurality of atomic objects include object A, object B, object C, and object D, Object B and object C are of a first atomic type, and Object A and object D are not of the first atomic type; and Controlling a potential energy generating element among the plurality of potential energy generating elements to form a time-dependent potential field within the atomic object confinement device, the time-dependent potential field causing object A, object B, object C, and object D to move along corresponding reordering trajectories, the time-dependent potential field including a confinement potential energy and a rotational potential energy, the reordering trajectories including: An initial chain including object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis of the confinement potential energy, Rotation of object B and object C in a first direction caused by a rotational potential energy axis defined by the rotational potential energy rotating in the first direction such that the rotational potential energy axis rotates relative to the confinement potential energy axis by a rotation angle; and Re-aligning the set of atomic objects into a final chain including object A, object B, object C, and object D that are substantially aligned along the confinement potential energy axis and in a different order relative to the initial chain, Wherein during a start portion of the rotation, a confinement ratio of the time-dependent potential energy is adjusted to cause compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis, Wherein during an end portion of the rotation, the confinement ratio of the time-dependent potential energy is adjusted to cause decompression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis.

2. The method according to claim 1, wherein one of the following holds: (a) Object B and object C among object A, object B, object C, and object D in the initial chain have switched positions in the final chain, (b) Object A and object D among object A, object B, object C, and object D in the initial chain have switched positions in the final chain, or (c) Object A and object D among object A, object B, object C, and object D in the initial chain are object B and object C of the final chain.

3. The method according to claim 1, wherein the rotation angle is approximately 180°, and during a middle portion of the rotation, the set of atomic objects is not collinear, the middle portion being between an early portion and an end portion of the rotation.

4. The method according to claim 1, wherein after the angle between the rotational potential energy axis and the confinement potential energy axis reaches a transition angle, the confinement ratio of the time-dependent potential energy is adjusted to cause one of the following: (a) further compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis, or (b) partial decompression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis, and wherein (a) the rotational angle is the transition angle, and (b) after the rotational potential energy axis rotates through the rotational angle in the first direction, the rotational potential energy axis rotates in a second direction such that the rotational potential energy axis rotates through a second sequence of angles relative to the confinement potential energy axis, the second direction being opposite to the first direction, and wherein the transition angle is in the range of approximately 70° to 110°.

5. A system for performing a deterministic reordering function, the system comprising: An atomic object confinement device, the atomic object confinement device including a plurality of potential energy generating elements; And One or more drivers configured to provide a sequence of driver actions to the plurality of potential energy generating elements to control a time-dependent potential field generated by the plurality of potential energy generating elements, the system being configured to: Operate the one or more drivers to cause the plurality of potential energy generating elements to form the time-dependent potential field within the atomic object confinement device, the time-dependent potential field causing objects A, B, C, and D to move along corresponding reordering trajectories, wherein: Objects B and C are of a first atomic type, and objects A and D are not of the first atomic type, The time-dependent potential field includes a confinement potential energy and a rotational potential energy, The reordering trajectories include: An initial chain, the initial chain including objects A, B, C, and D substantially aligned along the confinement potential energy axis of the confinement potential energy, the initial chain being in (1) a first configuration in which objects B and C are adjacent to each other and are disposed between objects A and D, or (2) a second configuration in which objects A and D are adjacent to each other and are disposed between objects B and C, Rotation of objects B and C in a first direction by a rotational potential energy axis defined by the rotational potential energy rotating in the first direction such that the angle between (a) the rotational potential energy axis and (b) the confinement potential energy axis is a transition angle, Compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis during a start portion of the rotation of the rotational potential energy axis through the first sequence of angles, After the angle between the (a) described rotational potential energy axis and the (b) described confinement potential energy axis reaches the transition angle, when the initial chain is in the first configuration, further compression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis, or, when the initial chain is in the second configuration, partial decompression of the set of atomic objects in a direction substantially aligned with the confinement potential energy axis, Rotation of object B and object C in the first direction or the second direction caused by rotation of the rotational potential energy axis in the first direction or the second direction, such that the rotational potential energy axis rotates relative to the confinement potential energy axis through a second sequence of angles, and During the ending portion of the rotation, decompression of the set of atomic objects in a direction substantially aligned with the axis, When the rotational potential energy axis has rotated through the second sequence of angles, the set of atomic objects is arranged in a final chain, The final chain includes objects A, B, C, and D substantially aligned along the confinement potential energy axis, and When the initial chain is in the first configuration, the final chain is in the second configuration, and when the initial chain is in the second configuration, the final chain is in the first configuration.

6. The system according to claim 5, wherein the first angle is greater than 0° and less than 90°, or the first angle is greater than 5° and less than 60°.

7. The system according to claim 5, wherein the compression and decompression are caused by adjusting the confinement ratio of the time-dependent potential energy.

8. A computer program product comprising a non-transitory machine-readable storage medium storing executable instructions that, when executed by a processor of a controller, cause the controller to operate one or more drivers to provide a sequence of driver actions to a potential energy generating element of an atomic object confinement device such that the potential energy generating element forms a time-dependent potential field that causes objects A, B, C, and D to move along corresponding reordering trajectories, wherein: Objects B and C are of a first atomic type, and objects A and D are not of the first atomic type, The time-dependent potential field includes a confinement potential energy and a rotational potential energy, The reordering trajectories include: An initial chain that includes objects A, B, C, and D substantially aligned along the confinement potential energy axis of the confinement potential energy, the initial chain being in a first configuration in which objects B and C are adjacent to each other and are disposed between objects A and D, Rotation of the initial chain caused by rotation of the rotational potential energy in a first direction to form a rotated initial chain such that the rotational potential energy axis defined by the rotational potential energy rotates a first angle relative to the confinement potential energy axis, Compression of the rotated initial chain in a direction substantially parallel to the confinement potential energy axis such that object B is further from the confinement potential energy axis than object A, and object C is further from the confinement potential energy axis than object D, thereby forming a compressed configuration, Rotation of the compression configuration in the second direction caused by rotation of the rotational potential energy in the second direction, such that the axis of the rotational potential energy rotates relative to the axis of the confinement potential energy through a second angle that is substantially equal to twice the first angle, and the second direction is opposite to the first direction, thereby providing a rotational configuration, decompression of the rotational configuration along the axis of the confinement potential energy, thereby forming an off-axis final chain, and rotation of the off-axis final chain in the first direction caused by rotation of the axis of the rotational potential energy relative to the axis of the confinement potential energy through a third angle in the first direction, thereby providing a final chain, the third angle being substantially equal to the first angle, and the final chain includes objects A, B, C, and D that are substantially aligned along the axis of the confinement potential energy, where objects B and C are in relative positions with respect to the initial chain.

9. The computer program product according to claim 8, wherein the temporal evolution of the rotational potential energy includes: a first rotation of the axis of the rotational potential energy relative to the axis of the confinement potential energy of the confinement potential energy through a first angle in a first direction; a second rotation of the axis of the rotational potential energy relative to the axis of the confinement potential energy through a second angle in a second direction, where the second direction is opposite to the first direction and the second angle is substantially equal to twice the first angle; and a third rotation of the axis of the rotational potential energy relative to the axis of the confinement potential energy through a third angle in the first direction, where the third angle is substantially equal to the first angle.

10. The computer program product according to claim 8, wherein the temporal evolution of the rotational potential energy includes a rotation of the axis of the rotational potential energy relative to the axis of the confinement potential energy of the confinement potential energy through an angle of approximately 180°.

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