A set of quantum gates including arbitrary angle gates and / or global gates

Abstract

A QCCD-based quantum computer includes two-qubit gate primitives, such as global single-qubit gates and any-angle rotation- and / or phase-independent antisymmetric two-qubit gates, and is configured to perform any-angle two-qubit gates using individual single-qubit gates that are not individually addressed.

Description

[Technical field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Patent Application No. 63 / 270,901, filed October 22, 2021, the entire contents of which are incorporated herein by reference.

[0002] Various embodiments relate to performing quantum gates on qubits of a quantum computer. For example, various embodiments relate to performing arbitrary angle gates and / or global gates on qubits of a quantum computer. For example, various embodiments relate to a quantum computer configured to perform arbitrary angle gates and / or global gates on qubits. [Background technology]

[0003] Quantum Charge Coupled Device (QCCD) architecture is a type of architecture that can be used for large-scale quantum computing. According to QCCD architecture, multiple atomic objects are confined by an atomic object confinement device, and the controlled evolution of the quantum states of the atomic objects is used to perform quantum computing. The controlled evolution of the quantum states of the atomic objects is realized by implementing various single-qubit and multi-qubit gates (e.g., two-qubit gates) according to quantum circuits. A gate set is considered to be generic when the gate primitives of the gate set can be used to construct any gate.

[0004] To perform a single qubit gate, the atomic object on which the gate is performed must be physically isolated from its neighboring atomic objects. In this case, the atomic object must be transported, which is a relatively slow process (compared to the performance of the gate) and causes the atomic object to heat up. To account for this heating, a cooling operation is performed on the atomic object, which is an even slower process. Through the application of efforts, ingenuity, and new technologies, many of the shortcomings of such conventional atomic object confinement devices and systems incorporating such atomic object confinement devices, as well as the gate sets used by those devices and systems, have been overcome by developing solutions configured in accordance with embodiments of the present invention, many examples of which are detailed herein. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] U.S. Pat. No. 11,037,776 [Patent Document 2] U.S. Patent Application Serial No. 63 / 199,279 [Patent Document 3] U.S. Patent Application Serial No. 63 / 235,007 [Patent Document 4] U.S. Patent Application Serial No. 16 / 716,973 Summary of the Invention [Means for solving the problem]

[0006] Exemplary embodiments relate to performing quantum gates on qubits of a quantum computer. Various embodiments relate to performing quantum gates on qubits of a QCCD-based quantum processor. Various embodiments provide any two-qubit gate, referred to herein as a general two-qubit gate. Various embodiments provide a general two-qubit gate quantum computer controller configured to cause the execution of a general two-qubit gate (or a general multiple-qubit gate or a general single-qubit gate), and / or a quantum processor and / or computer configured to execute a general two-qubit gate (or a general multiple-qubit gate or a general single-qubit gate). Various embodiments provide a single two-qubit gate that is executed at least in part via execution of a two-qubit gate primitive.

[0007] According to a first aspect, a method is provided for performing a general two-qubit gate using a QCCD-based quantum processor. In an exemplary embodiment, the method includes the steps of providing a first atomic object and a second atomic object, the second atomic object being located in physical proximity to the first atomic object, causing a controller configured to control various operations of the QCCD-based quantum processor to perform a first frame rotation of the first atomic object and a first frame rotation of the second atomic object, causing the controller to perform a first phase-independent two-qubit gate corresponding to the first arbitrary angle rotation for the first atomic object and the second atomic object, and causing the controller to perform a first phase-independent two-qubit gate corresponding to the first arbitrary angle rotation for the first atomic object and the second atomic object. causing, by the controller, to perform a second frame rotation of the first atomic object and a second frame rotation of the second atomic object; causing, by the controller, to perform a second arbitrary-angle phase-independent two-qubit gate for the first atomic object and the second atomic object corresponding to the second arbitrary-angle rotation; causing, by the controller, to perform a third frame rotation of the first atomic object and a third frame rotation of the second atomic object; and causing, by the controller, to perform a third phase-independent two-qubit gate for the first atomic object and the second atomic object corresponding to the third arbitrary angle.

[0008] In an exemplary embodiment, the second frame rotation and the third frame rotation each comprise a respective one or more global single qubit gates, each global single qubit gate having the same effect on the first atomic object and the second atomic object.

[0009] In an exemplary embodiment, the second frame rotation and the third frame rotation are each performed by a respective pair of single qubit gate operation signals incident on both the first atomic object and the second atomic object.

[0010] In an exemplary embodiment, the pair of single qubit gate operation signals comprises a first operation signal and a second operation signal, the first operation signal and the second operation signal (a) co-propagating and (b) having a frequency difference corresponding to an energy difference between a first state in the qubit space and a second state in the qubit space.

[0011] In an exemplary embodiment, the first, second and third phase-independent two-qubit gates are each implemented by a respective pair of two-qubit gate operating signals incident on both the first atomic object and the second atomic object.

[0012] In an exemplary embodiment, the two-qubit gate operation signal pair comprises a third operation signal and a fourth operation signal, where the third operation signal and the fourth operation signal (a) propagate at a relative angle of 90 degrees, (b) are linearly polarized, and (c) are vertically linearly polarized.

[0013] In an exemplary embodiment, at least one characteristic of at least one of the third operating signal or the fourth operating signal is controlled based on a functional representation of the operating signal characteristic as a function of an input signal to a modulator configured to adjust the respective operating signal of the third operating signal or the fourth operating signal, where the at least one characteristic is at least one of a power level, a frequency, or a duration.

[0014] In an exemplary embodiment, the phase of at least one of (a) the first atomic object or (2) the second atomic object is physically updated before the first frame rotation is performed.

[0015] In an exemplary embodiment, a cooling step is performed prior to performing the first phase-independent two-qubit gate.

[0016] In an illustrative embodiment, after performing a cooling step prior to performing the first phase-independent two-qubit gate, no further cooling is performed on the first atomic object and the second atomic object until after the third phase-independent two-qubit gate is performed.

[0017] According to another aspect, a quantum computer is provided. In an exemplary embodiment, the quantum computer includes an atomic object confinement device configured to confine two or more atomic objects, one or more manipulation sources, and a controller. The controller is configured to control the one or more manipulation sources and the atomic object confinement device to cause the one or more manipulation sources to generate and provide two or more pairs of manipulation signals, such that each of the two or more pairs of manipulation signals is incident on two atomic objects, and at least one of the two or more pairs of manipulation signals is configured to cause an antisymmetric two-qubit gate to be performed on the two atomic objects, and a combined effect of the two or more pairs of manipulation signals incident on the two atomic objects is to perform a respective single-qubit gate.

[0018] In an exemplary embodiment, the two atomic objects comprise a first atomic object and a second atomic object, the first atomic object and the second atomic object being spaced apart by a separation distance corresponding to a selected phase difference of at least one of the manipulation signals.

[0019] In an exemplary embodiment, each single qubit gate is an arbitrary angle single qubit gate.

[0020] In an exemplary embodiment, the controller is further configured to track respective AC Stark shifts imposed on each of the two atomic objects as a result of the two or more pairs of manipulation signals being incident on the two atomic objects.

[0021] In an exemplary embodiment, the individual single-qubit gates that are generated are part of a controllable gate set that does not require qubit addressing.

[0022] According to another aspect, there is provided a quantum computer configured to perform a general gate, the quantum computer comprising: an atomic object confinement device configured to confine two or more atomic objects, one or more manipulation sources, and a controller configured to control the one or more manipulation sources and the atomic object confinement device. In an exemplary embodiment, the controller controls one or more manipulation sources and atomic object confinement devices to cause a first atomic object to be confined at a first location and a second atomic object to be confined at a second location, where the first location is proximate to the second location; incident a first frame rotation pair of manipulation signals on the first atomic object and the second atomic object to perform a first frame rotation of the first atomic object and a first frame rotation of the second atomic object; incident a first two-qubit gate pair of manipulation signals on the first atomic object and the second atomic object to perform a first phase-independent two-qubit gate corresponding to the first arbitrary angle rotation on the first atomic object and the second atomic object; incident a second frame rotation pair of manipulation signals on the first atomic object and the second atomic object; performing a second frame rotation of the first atomic object and a second frame rotation of the second atomic object; incident a second two-qubit gate pair of manipulation signals to the first atomic object and the second atomic object to perform a second phase-independent two-qubit gate corresponding to the second arbitrary angle rotation for the first atomic object and the second atomic object; incident a third frame rotation pair of manipulation signals to the first atomic object and the second atomic object to perform a third frame rotation of the first atomic object and a third frame rotation of the second atomic object; and incident a third two-qubit gate pair of manipulation signals to the first atomic object and the second atomic object to perform a third phase-independent two-qubit gate corresponding to the third arbitrary angle rotation for the first atomic object and the second atomic object.

[0023] In an exemplary embodiment, the first atomic object and the second atomic object are respective qubits of a quantum computer.

[0024] In an exemplary embodiment, the controller is further configured to determine at least one characteristic of the at least one manipulation signal of at least one of the first two-qubit gate pair, the second two-qubit gate pair, or the third two-qubit gate pair based on a functional representation of the manipulation signal characteristic as a function of an input signal to a modulator configured to adjust the at least one manipulation signal, where the at least one characteristic is at least one of a power level, a frequency, or a duration.

[0025] In an exemplary embodiment, the controller is further configured to control the atomic object confinement device to maintain the first atomic object at the first position and the second atomic object at the second position for at least a period of time that begins when a first two-qubit gate pair of the manipulation signal is incident on the first atomic object and the second atomic object and ends when a third two-qubit gate pair of the manipulation signal is incident on the first atomic object and the second atomic object.

[0026] In an exemplary embodiment, the general gate is a general two-qubit gate.

[0027] In an exemplary embodiment, the general gate is a general single qubit gate.

[0028] Having thus described the invention in general terms, reference is now made to the accompanying drawings, in which: [Brief description of the drawings]

[0029] [Figure 1] FIG. 1 is a schematic diagram illustrating an exemplary quantum computing system in accordance with various embodiments. [Diagram 2]FIG. 1 is a partial energy level diagram of a qubit space defined based on hyperfine splitting of an atomic object, in accordance with an illustrative embodiment. [Diagram 3] FIG. 2 illustrates a Bloch sphere representation of an exemplary qubit in accordance with an exemplary embodiment. [Figure 4] FIG. 1 is a schematic diagram illustrating a global single qubit gate in accordance with an example embodiment. [Diagram 5] FIG. 1 is a schematic diagram illustrating a two-qubit gate configuration according to an example embodiment. [Figure 6] 1 is a flowchart illustrating a process, procedure, and / or operation for performing general gating in accordance with an example embodiment. [Figure 7] 11 is a flowchart illustrating processes, procedures, and / or operations for generating operating signals used to implement general gating in accordance with an exemplary embodiment. [Figure 8] 1 is a flowchart illustrating processes, procedures, and / or operations for performing individual single qubit gates using global single qubit primitives and / or two qubit gate primitives, in accordance with an example embodiment. [Figure 9] 1 is a flowchart illustrating processes, procedures, and / or operations for performing an individual single qubit gate using a global single qubit gate and a two-qubit gate in accordance with an example embodiment. [Figure 10] FIG. 1 is a schematic diagram of an example controller for a quantum computer, in accordance with various embodiments. [Figure 11] FIG. 1 is a schematic diagram of an example computing entity of a quantum computer system that may be used in accordance with example embodiments. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0030] The present invention will now be described in more detail below with reference to the accompanying drawings. The drawings show some, but not all, embodiments of the present invention. In fact, the present invention may be embodied in many different forms and should not be construed as being limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term "or" (also indicated by " / ") is used in both the alternative and connective sense unless otherwise indicated. The terms "exemplary" and "exemplary" are used as examples that do not indicate a level of quality. The terms "generally" and "approximately" refer to within engineering and / or manufacturing limits / tolerances and / or user measurement capabilities unless otherwise indicated. Like numbers refer to like elements throughout.

[0031] I. Definition Various embodiments relate to a QCCD-based quantum processor and / or a quantum computer comprising a QCCD-based quantum processor. In general, a QCCD-based quantum processor includes an atomic object confinement device configured to confine atomic objects. At least some of the atomic objects are used as quantum bits of the quantum processor. The controlled evolution of the quantum states of the atomic objects used as quantum bits of the quantum processor enables the quantum processor to perform quantum computations by executing quantum circuits and / or algorithms.

[0032] An atomic object confinement apparatus is a device or apparatus used to confine or capture atomic objects. In various embodiments, the atomic object confinement apparatus is fabricated and / or fabricated on a chip (e.g., having a silicon substrate and various electrical components and / or elements fabricated on the silicon substrate). In various embodiments, the atomic object confinement apparatus is an ion trap (e.g., a surface ion trap, a Paul trap, etc.).

[0033] In various embodiments, the atomic object is an ion, an atom, a neutral, polarized or ionized molecule, a charged particle, or the like, or a group or crystal of ions, atoms, molecules, charged particles, or the like.

[0034] As described in more detail elsewhere herein, an isolated qubit may be represented and / or modeled as a Bloch sphere, with the current state of the qubit being a point on the Bloch sphere. Performing a single-qubit gate on a qubit generally involves one or more manipulation signals being incident on an atomic object, thereby affecting the quantum state of the qubit embodied by the atomic object (e.g., causing a controlled evolution of the quantum state). Executing a gate moves the point on the Bloch sphere representing the current state of the qubit to a new and / or updated position. In general, performing a gate on a qubit corresponds to a unitary operator acting on the current state of the qubit.

[0035] Because the Bloch sphere is a sphere with unit radius (also called the unit sphere) and a point representing the current state of a qubit remains on the surface of the unit sphere, the execution of a single qubit gate may be represented and / or modeled as a rotation of a vector (herein called the qubit vector) that points from the center of the unit sphere to a point on the surface of the unit sphere. Traditional single qubit gates accommodate set rotations of the qubit vector (e.g., rotations of Π / 2). Exemplary embodiments provide general single qubit gates that accommodate rotations of the qubit vector through any angle. The arbitrary angle may be selected for each gate rather than a set angle.

[0036] Various embodiments include performing a single-qubit gate on two qubits that affects each of the qubits in the same way. Such a gate is referred to herein as a global single-qubit gate. For example, a global single-qubit gate may be performed on two or more qubits to apply the same rotation to each of the two or more qubits.

[0037] In various embodiments, a frame rotation is performed on two qubits (e.g., a first qubit and a second qubit). The frame rotation is a rotation of a local reference frame of the Bloch sphere representation of the qubits. In various embodiments, the frame rotation includes one or more individual single qubit gates. In various embodiments, the frame rotation may be an individually addressed single qubit gate (referred to herein as an individually addressed frame rotation) or a global single qubit gate (referred to herein as a global frame rotation).

[0038] Various embodiments include the implementation of a two-qubit gate. A two-qubit gate is a gate that is implemented on two qubits, where the effect of the gate on at least one of the qubits (i.e., the rotation of the qubit vector caused by the gate) is based on the state of the other qubit of the two. In other words, the two-qubit gate creates an interaction and / or entanglement between the states of the two qubits.

[0039] In various embodiments, a gate set is defined that includes one or more global single qubit gate primitives and one or more two qubit gate primitives. As used herein, a gate primitive is an element of the defined gate set that may be used as a standalone gate (e.g., may be used as a gate itself) or may be used as a component or step in a gate. For example, executing a particular gate may include executing multiple gate primitives such that the collective or cumulative effect of the multiple gate primitives corresponds to the execution of the particular gate. For example, the gate primitives of the gate set are the building blocks from which all of the available gates of a quantum processor may be generated.

[0040] Various embodiments relate to the execution of individual single qubit gates compiled from at least one two-qubit gate primitive. As used herein, an individual single qubit gate is a gate that affects (more than a possible phase shift) the state of only one qubit. For example, an individual single qubit gate may be generated by a combination of a global single qubit gate primitive and a two-qubit gate primitive executed on two qubits. Executing the combination of the global single qubit gate primitive and the two-qubit gate primitive on two qubits updates the state of one of the two qubits by more than a possible change in phase, and does not update the state of the other of the two qubits (e.g., due to an AC Stark shift, etc.). For example, an individual single qubit gate may have roughly the same effect (up to a possible change in phase) as an individually addressed single qubit gate, but without the need to individually address the target qubit.

[0041] Various embodiments provide global single qubit gates and / or individual single qubit gates that do not require qubit addressing, in particular qubit addressing which requires that a qubit be physically isolated and / or separated from other qubits, such that the manipulation signals used to implement an addressed gate are generally incident only on the addressed qubit (in a multidimensional atomic object confinement device, addressed single qubit gates may be implemented in parallel in different sections of the atomic object confinement device using the same manipulation signals).

[0042] In various embodiments, to perform a gate on two qubits, the two qubits must be located close to each other. As used herein, the two qubits are close to each other when a manipulation signal is incident on both of the two qubits. For example, the two qubits are located close enough to each other that they are both contained within the spot size of the manipulation signal used to perform the gate.

[0043] Various embodiments relate to the implementation of phase-independent two-qubit gates. In general, a phase-independent gate is one whose corresponding unitary operator commutes with any rotation about the z-axis (defined as shown in FIG. 2).

[0044] Various embodiments relate to performing antisymmetric two-qubit gates. In general, antisymmetric two-qubit gates affect two qubits where the gate is performed in an asymmetrical different manner. For example, performing an asymmetric two-qubit gate on two qubits causes a first qubit vector representing the state of a first qubit of the two qubits to undergo a first rotation and a second qubit vector representing the state of a second qubit of the two qubits to undergo a second rotation, where the first rotation and the second rotation are not equal to each other.

[0045] II. An Example Quantum Computer Various embodiments provide an atomic object confinement device, a quantum processor comprising an atomic object confinement device, a quantum computer comprising an atomic object confinement device, and / or methods used therewith. For example, an atomic object confinement device may confine two or more atomic objects therein. A controlled evolution of a quantum state of one or more of the two or more atomic objects may be performed (e.g., according to a quantum circuit) using one or more general and / or global gates. For example, an atomic object captured and / or confined by an atomic object confinement device and acted upon by an operational signal may be used by a qubit of a quantum processor. For example, a quantum computer is configured to perform one or more general gates for two qubits in various embodiments. For example, a quantum computer is configured to perform one or more individual single qubit gates generated using at least one two-qubit gate primitive.

[0046] 1 illustrates a schematic diagram of an exemplary quantum computer system 100 including an atomic object confinement device 70 (e.g., an ion trap, a surface trap, a Paul trap, etc.) according to an exemplary embodiment. In various embodiments, quantum computer system 100 includes a computing entity 10 and a quantum computer 110. In various embodiments, quantum computer 110 includes a controller 30 and a quantum processor 115. In various embodiments, quantum processor 115 includes the atomic object confinement device 70 sealed in a cryogenic and / or vacuum chamber 40, one or more voltage sources 50, one or more manipulation sources 60, one or more magnetic field generators 80 (e.g., 80A, 80B), etc.

[0047] In the illustrated embodiment, the atomic object confinement device 70 comprises radio frequency (RF) rail electrodes 72 (e.g., 72A, 72B) and a sequence of capture and / or transport (TT) electrodes 74 (e.g., 74A, 74B, 74C). In various embodiments, the RF rail electrodes 72 and the TT electrodes 74 define a one-dimensional atomic object confinement device or a two-dimensional atomic object confinement device. Some non-limiting exemplary atomic object confinement devices are described by U.S. Patent No. 11,037,776, issued June 15, 2021, U.S. Patent Application No. 63 / 199,279, filed December 17, 2020, and U.S. Patent Application No. 63 / 235,007, filed August 19, 2021, the contents of which are hereby incorporated by reference in their entirety.

[0048] In an exemplary embodiment, the one or more manipulation sources 60 comprise 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 atomic object confinement device 70. For example, the one or more manipulation sources 60 comprise respective manipulation sources 60 configured to generate and provide a first manipulation signal, a second manipulation signal, a third manipulation signal, a fourth manipulation signal, etc. In an exemplary embodiment, at least some of the manipulation signals are laser beams, laser pulse trains, etc. For example, in an exemplary embodiment, the one or more manipulation sources 60 comprise one or more lasers, which may provide one or more laser beams to the confinement device within the cryogenic and / or vacuum chamber 40. The laser beams may be used to perform various operations (e.g., parallel operations), such as performing one or more quantum gates on one or more qubits and / or atomic objects, co-cooling one or more atomic objects, reading qubits and / or determining the quantum state of the atomic objects, initializing atomic objects into qubit space, etc. In various embodiments, the actuation sources 60 are controlled by respective driver controller elements 1015 of the controller 30 (see FIG. 10).

[0049] In various embodiments, the quantum computer 110 comprises one or more voltage sources 50. For example, the voltage sources 50 may comprise a plurality of TT voltage drivers and / or voltage sources and / or at least one RF driver and / or voltage source. The voltage sources 50 may be electrically coupled to corresponding potential generating elements (e.g., TT electrodes 156, RF rail electrodes, RF bus electrodes) of the atomic object confinement device 70 in an exemplary embodiment. For example, the voltage sources 50 are configured to provide (RF) oscillating voltage signals to the RF rail electrodes and RF bus electrodes of the atomic object confinement device 70. For example, the voltage sources 50 are configured to provide control voltage signals to the TT electrodes of the sequence of TT electrodes 74. In various embodiments, the voltage sources 50 are controlled by respective driver controller elements 1015 of the controller 30.

[0050] In various embodiments, the quantum computer 110 comprises one or more magnetic field generators 80 (e.g., 80A, 80B). For example, the magnetic field generators may be an internal magnetic field generator 80A disposed within the cryogenic and / or vacuum chamber 40 and / or an external magnetic field generator 80B disposed outside the cryogenic and / or vacuum chamber 40. In various embodiments, the magnetic field generator 80 is a permanent magnet, a Helmholtz coil, an electromagnet, or the like. In various embodiments, the magnetic field generator 80 is configured to generate a magnetic field having a particular magnitude in one or more regions of the atomic object confinement device 70 and a particular magnetic field direction in one or more regions of the atomic object confinement device 70. In an exemplary embodiment, the particular magnetic field direction defines the z-direction of a Bloch sphere representation of the qubit. In an exemplary embodiment, the particular magnitude is substantially equal to 5.9 Gauss. In an exemplary embodiment, the operation of the one or more magnetic field generators 80 is controlled by the controller 30. In an exemplary embodiment, at least one of the magnetic field generators 80 is a permanent magnet and is therefore not controlled by the controller 30.

[0051] In various embodiments, computing entity 10 is configured to enable a user to provide input to quantum computer 110 (e.g., via a user interface of computing entity 10) and receive, view, etc., output from quantum computer 110. Computing entity 10 may communicate with a controller 30 of quantum computer 110 via one or more wired or wireless networks 20 and / or direct wired and / or wireless communication. In an exemplary embodiment, computing entity 10 may translate, organize, format, etc., information / data, quantum circuits, quantum computing algorithms, etc., into a computing language, executable instructions, command sets, etc. that controller 30 can understand and / or implement.

[0052] In various embodiments, controller 30 is configured to control voltage source 50, a cryogenic system and / or vacuum system controlling the temperature and pressure within cryogenic and / or vacuum chamber 40, manipulation source 60, magnetic field generator 80, and / or other systems configured to control various environmental conditions (e.g., temperature, pressure, etc.) within cryogenic and / or vacuum chamber 40 and / or to manipulate and / or cause a controlled evolution of a quantum state of one or more atomic objects within atomic object confinement device 70. For example, controller 30 may cause a controlled evolution of a quantum state of one or more atomic objects within atomic object confinement device 70 to execute a quantum circuit and / or algorithm. For example, controller 30 is configured in various embodiments to execute a quantum circuit comprising one or more general gates and / or one or more global gates.

[0053] In various embodiments, the atomic objects confined within atomic object confinement device 70 are used as qubits in quantum computer 110 and / or quantum processor 115. For example, quantum processor 115 may include multiple multi-atomic object crystals, each multi-atomic object crystal comprising a first atomic object used as a quantum processor qubit atomic object (embodied a qubit of quantum processor 115) and a second atomic object used as a co-cooling atomic object used in cooling the qubit atomic objects of the same multi-atomic object crystal.

[0054] III. Example Qubit Representations In various embodiments, the atomic object confined by the atomic object confinement device is used as a qubit in a quantum processor and / or quantum computer. For example, a two-state subspace of the quantum state of the atomic object is defined as a qubit space. In various embodiments, the qubit space is defined as two hyperfine states. For example, FIG. 2 illustrates a partial energy diagram 200 of an exemplary atomic object. The qubit space 210 is defined as including two different hyperfine states. For example, in an exemplary embodiment in which the atomic object is a monovalent ion of ytterbium, the hyperfine states of the qubit space 210 may be the F=0, m=0 state of the S-manifold and the F=1, m=1 state of the S-manifold. In various embodiments, the two states of the qubit space 210 are separated by a particular frequency separation v s (For example, the energy difference between two states in the quantum bit space 210 is hν s In an exemplary embodiment in which the atomic objects are singly charged ions of ytterbium, the particular frequency separation v s is approximately 12.64GHz.

[0055] As noted above, the Bloch sphere representation can be used to generally describe or model qubits. Figure 3 shows the relationship between the qubit vector r Q 3 shows an exemplary Bloch sphere representation 300 of a qubit in qubit state |Q〉 represented by a point on the unit sphere corresponding to qubit vector r. A first state of the qubit space 210 is defined at the intersection of the surface of the unit sphere with the positive z-axis, and a second state of the qubit space 210 is defined at the intersection of the surface of the unit sphere with the negative z-axis. Q is the quantum bit vector r Q and the azimuth angle that describes its relationship to the positive z-axis

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[0056] In various embodiments, frame rotation is implemented (e.g., in an exemplary embodiment, as a global single-qubit gate). As used herein, frame rotation is a unitary operation that rotates the local frame of reference of the Bloch sphere representation of a qubit with respect to an externally defined frame of reference. For example, in various embodiments, the externally defined frame of reference is defined by aligning the z-axis with the magnetic field direction. For example, frame rotation is implemented by rotating the qubit vector r Q is aligned with the externally defined z-axis, and the qubit vector r Q is aligned with the externally defined z-axis, the local frame of reference on the Bloch sphere is realigned to the externally defined frame of reference, and so on for the qubit vector r Q may be configured to rotate the

[0057] In various embodiments, performing a gate (e.g., a global single qubit gate, a two qubit gate, etc.) on a qubit causes the qubit to accumulate a phase shift (e.g., an AC Stark shift, etc.). For example, interaction of a manipulation signal with an atomic object may result in a phase shift of the qubit. In various embodiments, a quantum computer (e.g., controller 30) is configured to track (in real-time or quasi-real-time) the phase shift of the qubits and update the respective qubit records corresponding to the qubits to track the phase shift accumulated by each qubit. In various embodiments, the gates may be modified to account for the accumulated phase shift of the qubits and / or the gates may be implemented to modify the phase of the qubits based on the accumulated phase shift of the qubits. For example, U.S. Patent Application Serial No. 16 / 716,973, filed December 17, 2019, describes several examples of tracking the phase shift accumulated by a qubit and physically accounting for the accumulated phase shift.

[0058] IV. Example Gate Set Primitives As explained above, a gate set is defined by a set of gate set primitives. The gate set primitives may be used as standalone gates and / or as building blocks for constructing additional gates. In various embodiments, the gate set primitives include global single-qubit gates and two-qubit gates.

[0059] In an exemplary embodiment in which the atomic object is an ion, the set of gates is based on the Pauli group on one qubit. The elements of the Pauli group on one qubit are:

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[0060] In various embodiments, the gate set comprises a gate primitive that is a global single qubit gate. A global single qubit gate can be implemented on two or more qubits by positioning the two or more qubits in close proximity to one another such that a first manipulation signal and a second manipulation signal are incident on both (all) of the two or more qubits. Each of the two or more qubits is rotated in the same way (e.g., as described by a unitary evolution U). For example, a global single qubit gate can be implemented on two or more qubits by positioning the two or more qubits in close proximity to one another such that a first manipulation signal and a second manipulation signal are incident on both (all) of the two or more qubits. Each of the two or more qubits is rotated in the same way (e.g., as described by a unitary evolution U).

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[0061] FIG. 4 illustrates a configuration for performing an exemplary global single qubit gate on a first qubit embodied as a first atomic object 402A and a second qubit embodied as a second atomic object 402B. The first atomic object 402A and the second atomic object 402B are aligned along an axis 405. In various embodiments, a magnetic field B present at the location of the first atomic object 402A and the second atomic object 402B has a magnetic field direction that forms an angle β with the axis 405. In an exemplary embodiment, the angle β is substantially equal to 45 degrees. The first atomic object 402A and the second atomic object 402B are separated by a separation distance Δx. In various embodiments, the separation distance Δx is configured such that the first atomic object 402A and the second atomic object 402B are proximate to each other such that the first manipulation signal 410 and the second manipulation signal 420 are incident on both the first atomic object and the second atomic object. For example, the separation distance Δx is equal to or less than a spot size of the first operating signal 410 and / or the second operating signal 420 at the positions of the first atomic object 402A and the second atomic object 402B. In an exemplary embodiment, the first operating signal 410 and the second operating signal 420 are focused to a spot size of about 35 μm at the positions of the first atomic object 402A and the second atomic object 402B.

[0062] In various embodiments, the first and second operating signals 410, 420 are configured to induce stimulated Raman transitions in the first and second atomic objects 402A, 402B. In an exemplary embodiment, the first and second operating signals 410, 420 are phase-locked to each other. In an exemplary embodiment, the first and second operating signals 410, 420 are laser beams having a wavelength of about 372.5 nm, and the frequency offset between the first and second operating signals 410, 420 is about v s For example, in an exemplary embodiment, the third steering signal has a frequency of about c / (372.5 nm) (where c is the speed of light) and the fourth steering signal has a frequency of about c / (372.5 nm)±vs In various embodiments, the first steering signal 410 and the second steering signal 420 are co-propagating laser beams (e.g., laser beams propagating with respective propagation directions substantially parallel to each other). In various embodiments, the first steering signal 410 and the second steering signal 420 are both σ+-polarized Raman laser beams. In an exemplary embodiment, the first steering signal 410 and the second steering signal 420 propagate in a direction substantially parallel to the magnetic field direction. For example, the first steering signal 410 and the second steering signal 420 form an angle β with the axis 405 in an exemplary embodiment.

[0063] In various embodiments, a global single qubit gate is used as a frame rotation, for example, a global single qubit gate may be used to rotate the local frame of reference of each qubit for which a global single qubit gate is also implemented.

[0064] In various embodiments, a Molmer-Sorensen (MS) gate may be used as the two-qubit gate primitive. The MS gate performs the transformation

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[0065] Because it may be technically difficult to maintain phase coherence between the first and second operating signals 410, 420 used to perform a global single qubit gate and the third and fourth operating signals 510, 520 used to perform a two-qubit gate (see FIG. 5 ), a phase-independent rotating MS gate is used in various embodiments. For example, the MS gate performs an initial frame rotation on the first and second qubits using the third and fourth operating signals 510, 520, then performs an MS gate, and then performs an end frame rotation on the first and second qubits (using another instance of the third and fourth operating signals 510, 520) to realign the local reference frame with an externally defined reference frame. In an exemplary embodiment, the first frame rotation causes the phase-independent MS gate to interact in the z-base, whereby the unitary operator for the two-qubit gate primitive is

number

[0066] In an exemplary embodiment, another phase-independent two-qubit gate is included that includes two MS gate primitives executed in succession with a π / 2 phase update between a first instance of the MS gate primitive and a second MS gate primitive. The result of the sequence of MS gate primitives is the unitary operator

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[0067] In various embodiments, the unitary gate U i The Δθ in (Δθ, Δφ) is set to a particular angle that provides a perfect entanglement generator. For example, in an exemplary embodiment, Δθ is set to π / 2. In another exemplary embodiment, Δθ is set to π / 4 (e.g., U i (π / 4,△φ)). The sqrt(iSWAP) gate is a perfect entanglement generator (e.g., it can be used to form two-qubit Bell states), but requires half the full rotation angle as the standard iSWP gate (e.g., typically U i (π / 2, △φ)). As explained in more detail elsewhere in this specification, reducing the total rotation angle can reduce the error. Thus, sqrt(iSWAP) generally contains smaller errors than other full entanglement generators that require larger total rotation angles.

[0068] FIG. 5 illustrates an exemplary phase-independent two-qubit gate (e.g., a phase-independent MS gate U ) for a first qubit embodied as a first atomic object 402A and a second qubit embodied as a second atomic object 402B. ZZ , phase-independent iSWAP, and / or sqrt(iSWP) qubit gates U i 4 illustrates a configuration for performing a third manipulation signal 510 and a fourth manipulation signal 520 on both the first and second atomic objects 402A and 402B. The first atomic object 402A and the second atomic object 402B are aligned along an axis 405. In various embodiments, a magnetic field B present at the location of the first atomic object 402A and the second atomic object 402B has a magnetic field direction that forms an angle β with the axis 405. In an exemplary embodiment, the angle β is substantially equal to 45 degrees. The first atomic object 402A and the second atomic object 402B are spaced apart along the axis 405 by a separation distance Δx. In various embodiments, the separation distance Δx is configured such that the first atomic object 402A and the second atomic object 402B are in close proximity to each other such that the third manipulation signal 510 and the fourth manipulation signal 520 are incident on both the first atomic object and the second atomic object. For example, the separation distance Δx is equal to or less than a spot size of the third operating signal 510 and / or the fourth operating signal 520 at the positions of the first atomic object 402A and the second atomic object 402B. In an exemplary embodiment, the third operating signal 510 and the fourth operating signal 520 are focused to a spot size of about 35 μm at the positions of the first atomic object 402A and the second atomic object 402B.

[0069] In an exemplary embodiment, when performing phase-independent iSWAP and / or sqrt(iSWAP) 2 qubit gates, the separation distance Δx is utilized for the symmetric iSWAP and / or sqrt(iSWAP) portion of the interaction (e.g., (XX+YY) interaction) such that Δφ=nπ=ΔkΔx, where n is a positive number and Δk is the magnitude of the wave vector difference between the third manipulation signal 510 and the fourth manipulation signal 520. In an exemplary embodiment, ΔkΔx≈27π. In an exemplary embodiment, when performing phase-independent iSWAP and / or sqrt(iSWAP) 2 qubit gates, the separation distance Δx is utilized for the antisymmetric iSWAP and / or sqrt(iSWAP) portion of the interaction (e.g., (XX-YX) interaction) such that Δφ=(n+1 / 2)π=ΔkΔx. In an exemplary embodiment, ΔkΔx≈27.5π.

[0070] In various embodiments, the third manipulation signal 510 and the fourth manipulation signal 520 are configured to cause the first atomic object 402A and the second atomic object 402B to produce a two-qubit gate. In an exemplary embodiment, the third manipulation signal 510 and the fourth manipulation signal 520 are phase-locked to each other. In an exemplary embodiment, the third manipulation signal 510 and the fourth manipulation signal 520 are laser beams having a wavelength of about 372.5 nm, and the frequency offset between the first manipulation signal 510 and the second manipulation signal 520 is about v s For example, in an exemplary embodiment, the third steering signal has a frequency of about c / (372.5 nm) and the fourth steering signal has a frequency of about c / (372.5 nm)±v s In various embodiments, the third steering signal 510 and the fourth steering signal 520 are propagating laser beams having a relative angle α between them. In an exemplary embodiment, the angle α is about 90 degrees. For example, in an exemplary embodiment, the wave vector difference is parallel to the z direction (e.g.,

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[0071] In various embodiments, the gate set may further include "software" single qubit gates, which are executed by using the tracked phase of a qubit (e.g., stored in the respective qubit record) to update the phase of future single qubit gates executed for a given qubit. Such "software" gates may be

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[0072] In various embodiments, various quantum circuits are constructed using gate set primitives including global single qubit gates, phase-independent two qubit gates, and "software" gates, gates constructed from gate set primitives, etc. For example, various gate primitives may be used to construct and / or implement general gates and / or individual single qubit gates, including two qubit gate primitives.

[0073] V. Example Implementation of General Gates Various embodiments include the execution of a general gate (e.g., a general two-qubit gate), a quantum computer controller configured to cause a quantum computer and / or quantum processor to execute the general gate, and / or a quantum computer configured to execute the general gate. In various embodiments, the general gate is a two-qubit any-angle gate.

[0074] In various embodiments, the two-qubit gates of the gate set are in the group SU(2 m ), where m is the number of qubits acted upon by the gate. For example, for a two-state qubit space 210, a two-qubit gate configured to act on two qubits is an element of the group SU(4). In general, SU(2 m ) is a 2 with determinant 1. m ×2 m is the Lie group of unitary matrices. Using the gate set primitives, any two-qubit gate V can be constructed, where V∈SU(2 m In the example where m = 2, any two-qubit gate V can be written as

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[0075] In an exemplary embodiment, the two-qubit gate is U M (θ x ,θ y ,θ z )=U G (π / 2, π / 2)U ZZ (θ x )U G (π / 2,-π / 2)U G (π / 2,0)U ZZ (θ y )U G (π / 2,-π)U ZZ (θ z In various embodiments, U M The gate is decomposed into three 2-qubit gates and 3-5 frame rotations.

[0076] A new problem that arises when implementing a general gate is that Rz(θ) is the gate U M Since it does not commute with , in order to synchronize the phase between qubits to which a general gate is applied, U M The point is that any software gates should be physically applied before executing the gate. In various embodiments, the software gates are physically applied by including any AC Stark shifts from the history of the qubits (e.g., as indicated by their respective qubit records). For example,

number

[0077] 6 presents a flow chart illustrating various processes, procedures, actions, etc. for performing a general two-qubit gate. Beginning at step / action 602, two or more atomic objects are confined by atomic object confinement device 70. For example, quantum computer controller 30 may operate and / or cause operation of one or more voltage sources 50 to generate confining potentials via a sequence of RF rail electrodes 72 and / or TT electrodes 74 to confine two or more atomic objects by atomic object confinement device 70.

[0078] Controller 30 may cause the quantum processor to begin implementing and / or executing a quantum circuit. For example, controller 30 may control operation of voltage source 50 to transport various atomic objects confined by atomic object confinement device 70 to specific locations within the atomic object confinement device, and control operation of manipulation source 60 to cause one or more manipulation signals to be incident on specific locations on the various atomic objects to perform one or more operations and / or functions of the quantum processor (e.g., single qubit gate, two qubit gate, qubit initialization (e.g., initializing the atomic objects to a quantum state within qubit space), reading a qubit, etc.). At some point during the implementation and / or execution of the quantum circuit, a first qubit embodied by a first atomic object and a second qubit embodied by a second atomic object are caused to interact and / or a two qubit gate (e.g., a general two qubit gate) is performed on the qubits.

[0079] In step / operation 604, a first frame rotation is performed. For example, a first individually addressed single qubit gate U(π / 2,π / 2) for the first atomic object is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a first instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the first instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the first instance of each of the first manipulation signal 410 and the second manipulation signal 420, and the length of time that the first instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object are configured such that the first atomic object undergoes a Δθ rotation of π / 2. For example, the qubit vector r of each of the first qubits (embodied by the first atomic object) is QThe polar angle θ of is modified (e.g., changed in value) by π / 2. The phase difference between the first instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the respective qubit vector r Q Azimuth angle of

number

[0080] In step / action 606, the physical phase of at least one of the first qubit or the second qubit is updated. A new challenge in implementing general gates is that R z (θ) is gate U M Since , ...

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[0081] In step / action 608, the first atomic object and the second atomic object are transported to respective positions within the atomic object confinement device 70 in close proximity to one another. In an exemplary embodiment, the first atomic object and / or the second atomic object are transported such that the first atomic object and the second atomic object are adjacent and / or proximate to one another (e.g., no other atomic objects are disposed between the first atomic object and the second atomic object). For example, the controller 30 operates and / or causes operation of the voltage source 50 such that control voltage signals are provided to the sequence of TT electrodes 74 that move the first atomic object from a respective previous position to the first position and / or move the second atomic object from a respective previous position to the second position. The first position and the second position are in close proximity to one another.

[0082] During transport of the first atomic object to the first location and / or the second atomic object to the second location, heating of the atomic objects may occur. In step / operation 610, a cooling operation may be performed to cool the first atomic object and / or the second atomic object. In an exemplary embodiment, the cooling operation is a co-cooling operation. For example, the controller 30 may cause one or more manipulation sources 60 to provide a manipulation signal incident on a co-cooled atomic object located sufficiently close to each of the first and / or second atomic objects, such that the co-cooled atomic object is available to remove heat from the first and / or second atomic objects.

[0083] In various embodiments, U M From the beginning to the end of the execution of the gate, the first atomic object is located at the first position and the second atomic object is located at the second position. M Since all of the gate primitives used to construct the gates are either two-qubit gates or global single-qubit gates, U MThere is no transport of the first atomic object and / or the second atomic object during execution of the gate, and therefore the cooling operation only needs to be performed once (prior to executing the first phase-independent two-qubit gate).

[0084] In conventional two-qubit gates, it is common to build two-qubit gates from gate primitives that include individual single-qubit gates (e.g., individually addressed single-qubit gates) that operate on only one qubit. Thus, in a conventional scenario, the first and second atomic objects are transported into close proximity to each other to initiate two-qubit execution multiple times (e.g., three times) throughout the gate's execution, then separated and transported back. Thus, conventional two-qubit gates require multiple (e.g., three) cooling operations. Such additional execution of cooling operations significantly increases the execution time of the two-qubit gate and introduces memory errors, drift errors, and other gate errors. Thus, embodiments of the present invention improve upon conventional two-qubit gates in that only one cooling operation (e.g., one-third of the number required in conventional two-qubit gates) is required to execute the gate (without significant heating errors), and the cooling operations associated with memory and / or drift errors are also significantly reduced.

[0085] In step / operation 612, a first phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the first phase-independent two-qubit gate primitive is a phase-independent rotating MS gate U ZZ (θ x ) Various embodiments are directed to a phase-independent rotating MS gate U ZZ (θ x ) is used as the phase-independent two-qubit gate primitive, while in other embodiments the first phase-independent two-qubit gate primitive is a symmetric iSWAP and / or sqrt(iSWAP) gate U i (θ x,π). For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object. The power present in the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, the frequency of the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, and / or the duration that the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on (e.g., interacts with) the first atomic object and the second atomic object may be determined by the rotation angle θ x The method is configured to cause an interaction between a first atomic object and a second atomic object characterized by:

[0086] In step / action 614, a second frame rotation is performed. For example, a global single qubit gate and / or a pair of global single qubit gates, U G (π / 2,-π / 2)U G(π / 2,0) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a second instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 and the length of time that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. For example, the qubit vectors r of each of the first qubit (embodied by the first atomic object) and the second qubit (embodied by the second atomic object) may be configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. Q The polar angle θ of is modified (e.g., changed in value) by π / 2. The phase difference between the second instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the qubit vectors r Q Azimuth angle of

number

[0087] In an exemplary embodiment, to complete the second frame rotation, the controller 30 may cause one or more manipulation sources 60 to generate and provide a second instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in a third instance of each of the first manipulation signal 410 and the second manipulation signal 420, and the length of time that the third instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object, are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. For example, the qubit vectors r of each of the first qubit (embodied by the first atomic object) and the second qubit (embodied by the second atomic object) may be configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. Q The polar angle θ of is modified (e.g., changed in value) by π / 2. The phase between the third instances of each of the first and second operating signals 410 and 420 is, in the exemplary embodiment, a phase vector r Q Azimuth angle of

number

[0088] In step / operation 616, a second phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the second phase-independent two-qubit gate primitive is a phase-independent rotating MS gate U ZZ (θ yIn an exemplary embodiment, the second phase-independent two-qubit gate primitive is an asymmetric iSWAP and / or sqrt(iSWAP) gate U i (θ y , π). For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object. The power present in the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, the frequency of the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, and / or the duration that the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on (e.g., interacts with) the first atomic object and the second atomic object may be determined by the rotation angle θ y The method is configured to cause an interaction between a first atomic object and a second atomic object characterized by:

[0089] In step / action 618, a third frame rotation is performed. For example, the second global single qubit gate U G(π / 2, -π) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 and the length of time that the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. For example, the qubit vectors r of each of the first qubit (embodied by the first atomic object) and the second qubit (embodied by the second atomic object) may be configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. Q The polar angle θ of is modified (e.g., changed in value) by π / 2. The phase difference between the fourth instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the qubit vectors r Q Azimuth angle of

number

[0090] In step / action 620, a third phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the third phase-independent two-qubit gate primitive is a phase-independent rotating MS gate U ZZ (θ z In an exemplary embodiment, the second phase-independent two-qubit gate primitive is an asymmetric iSWAP and / or sqrt(iSWAP) gate Ui (θ z ,π). For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a third instance of each of the third manipulation signals 510 and the fourth manipulation signals 520 such that the third instance of each of the third manipulation signals 510 and the fourth manipulation signals 520 is incident on both the first atomic object and the second atomic object. The power present in the third instance of each of the third manipulation signals 510 and the fourth manipulation signals 520, the frequency of the first instance of each of the third manipulation signals 510 and the fourth manipulation signals 520, and / or the duration that the third instance of each of the third manipulation signals 510 and the fourth manipulation signals 520 is incident on (e.g., interacting with) the first atomic object and the second atomic object is configured to produce an interaction between the first atomic object and the second atomic object characterized by a rotation angle θz.

[0091] In various embodiments, when a general two-qubit gate is the last gate of a quantum circuit performed on a first atomic object or a second atomic object, a single-qubit gate (e.g., an individually addressed single-qubit gate) is performed on the first atomic object or the second atomic object (e.g., prior to reading them).

[0092] Some exemplary algorithms that require two-qubit arbitrary-angle gates (e.g., two-qubit gates corresponding to arbitrary rotations) include quantum approximate optimization algorithms (QAOA) and quantum Fourier transforms (QFTs). Traditionally, these arbitrary-angle gates are decomposed into two fixed-angle gates with a total rotation of π. In another example, U MA standard decomposition of the gate includes three π / 2 MS gates with a total rotation of 3π / 2. However, many of the errors in MS gates (e.g., amplitude gate errors, detuning errors, phase noise errors, etc.) are monotonically increasing functions of the total rotation angle. Thus, reducing the total rotation angle while still achieving the desired gate reduces the gate error. In general, the average total rotation of a general two-qubit gate is about 0.75π, resulting in a significant reduction in error. Thus, the general two-qubit gate described herein provides a general gate with fewer / smaller errors compared to conventional general gates generated using fixed angles (e.g., corresponding to rotations of any angle).

[0093] VI. Exemplary Calibration of an Arbitrary Angle and Generation of an Operating Signal Therefrom In various embodiments, a two-qubit arbitrary angle gate is provided. One potential challenge for implementing a two-qubit arbitrary angle gate is that the calibration of the operation signal that affects the desired arbitrary angle is difficult, since the calibration involves verifying the implementation over a continuous range (e.g., a continuous range of possible arbitrary angles / rotations) rather than a set of discrete values ​​(e.g., a set of fixed angles / rotations).

[0094] In various embodiments, the manipulation signals (e.g., the first manipulation signal 410, the second manipulation signal 420, the third manipulation signal 510, or the fourth manipulation signal 520) are generated by a respective manipulation source 60, such as a laser. For example, the manipulation source 60 may comprise a laser configured to generate a laser beam. The laser beam is then passed to a modulator, such as an acousto-optical modulator (AOM). The AOM is configured to modulate and / or control the amplitude, frequency, and / or phase of the manipulation signal based on an (electrical) input signal. Any angle rotation performed by the gate is proportional to the energy incident on and / or delivered to the first atomic object and / or the second atomic object by the pair of manipulation signals (e.g., the first and second manipulation signals 410, 420 or the third and fourth manipulation signals 510, 520). For example, any angle rotation performed by the gate is a function of the power level of each of the manipulation signals incident on the first atomic object and / or the second atomic object, the frequency of each of the manipulation signals incident on the first atomic object and / or the second atomic object, and the duration and / or time of each of the manipulation signals incident on and / or interacting with the first atomic object and / or the second atomic object.

[0095] 7 presents a flow chart illustrating processes, procedures, operations, etc. for generating operating signals for use in calibrating an arbitrary angle and performing an arbitrary angle gate. In various embodiments, the processing device 1005 of the controller 30 (see FIG. 10) and / or the processing device 1108 of the computing entity 10 (see FIG. 11) executes computer-executable code and / or instructions (e.g., stored in memory 1010, 1122, 1124) to perform the processes, procedures, operations, etc. of FIG.

[0096] Beginning with step / action 702, a characteristic of the manipulation signal (e.g., power, frequency, duration, and / or combinations thereof of the manipulation signal) is measured for a plurality of modulator input signal parameter values. For example, the power (e.g., energy per period) provided by the manipulation signal is measured at a plurality of modulator input signal parameter values. In another example, the frequency and / or frequency spectrum of the manipulation signal may be measured at a plurality of modulator input signal parameter values. In another example, the duration of the provided manipulation signal is measured at a plurality of modulator input signal parameter values. In various embodiments, various combinations of power, frequency, and / or duration of the provided manipulation signal are measured at a plurality of modulator input signal parameter values. In various embodiments, the measurements are performed and / or controlled by the controller 30 and / or the computing entity 10. For example, the controller 30 may control the manipulation source 60 such that a sequence of manipulation signals is generated, with each manipulation signal of the sequence being generated based at least in part on a respective modulator input signal parameter value. In an exemplary embodiment, the respective modulator input signal parameters include a voltage level of the electrical input signal, a frequency of the electrical input signal, etc.

[0097] For example, the controller 30 and / or computing entity 10 may apply a first input signal to the AOM and cause the manipulation source 60 to generate a manipulation signal that is adjusted and / or modulated (e.g., in amplitude / power, frequency, phase, duration, and / or combinations thereof) by the AOM. The characteristics (e.g., power, frequency, duration, and / or combinations thereof) of the resulting manipulation signal are measured and / or determined (e.g., using a photodetector and / or an array of photodetectors configured to generate an electrical signal indicative of the received optical power, frequency, and / or duration). The input signal parameter values ​​of the first input signal and the resulting measured manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) are recorded. The process is repeated multiple times for different input signal parameter values, thereby adequately sampling the parameter space of input signal parameter values. For example, the controller 30 and / or computing entity 10 may generate and / or store multiple data points including the input signal parameter values ​​and the respective measured manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof).

[0098] At step / operation 704, a function approximation of the measured relationship between the steering signal characteristic (e.g., power, frequency, duration, and / or combinations thereof) and the input signal parameter value is determined. For example, the controller 30 and / or computing entity 10 may process and / or analyze the data points generated at step / operation 702 to determine a function approximation of the data points. In an exemplary embodiment, the function approximation corresponds to the steering signal power and has the functional form

number

[0099] In various embodiments, the first function fit is determined for any positive angle of rotation and the second function fit is determined for any negative angle of rotation. For example, the beat signal frequency ω characterizing the interference of the third steering signal 510 and the fourth steering signal 520 may be determined as b ω b =ω0±ω z,2 ±δ, where ω z,2 is the axial antiphase mode of the third and / or fourth operating signals 510, 520, and 2π / δ≈t gate = 35 μs, where t gate is the duration for which the gate is executed (e.g., the time that the third and fourth operating signals 510, 520 are incident on the first and second atomic objects that execute the gate). In various embodiments, ω b =2πν s and ν s is the frequency separation between the third operating signal 510 and the fourth operating signal 520. In various embodiments, the two-qubit rotation U ZZ (θ) but using -δ to rotate the two qubits U ZZ (-θ).

[0100] After a time, the controller 30 determines that an arbitrary angle two qubit gate is to be performed on the first qubit embodied by the first atomic object and the second qubit embodied as the second atomic object. In step / operation 706, in response to determining that the arbitrary angle two qubit gate is to be performed, manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) corresponding to the arbitrary angle are determined. For example, the controller 30 may determine the manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) required to perform the arbitrary angle two qubit gate.

[0101] In step / operation 708, appropriate modulator input signal parameter values ​​are determined. For example, the appropriate modulator input signal parameter values ​​are determined based at least in part on the determined manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) corresponding to the arbitrary angle and a function approximation of a relationship between the manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) and the modulator input signal parameter values ​​(and / or the inverse of the function approximation). For example, the controller 30 determines the appropriate modulator input signal parameter values ​​based on the function approximation (and / or the inverse thereof) and the determined manipulation signal characteristics (e.g., power, frequency, duration, and / or combinations thereof) corresponding to the arbitrary angle. In an exemplary embodiment, a resulting AC Stark shift for the first atomic object and / or the second atomic object (e.g., induced by performing an arbitrary angle two-qubit gate) is also determined.

[0102] In step / operation 710, third and fourth operation signals 510, 520 are generated having respective characteristics (e.g., power, frequency, duration, and / or combinations thereof) corresponding to the arbitrary angle. For example, the controller 30 causes the operation source 60 to generate and provide the third operation signal and the fourth operation signal for performing the arbitrary angle two qubit gate. The third operation signal 510 and the fourth operation signal 520 have respective power, frequency, duration, and / or combinations thereof corresponding to the arbitrary angle and are generated at least in part based on applying an electrical input signal to one or more AOMs according to the determined appropriate modulator input signal parameter values. The third and fourth operation signals 510, 520 are provided to be incident on the first atomic object and the second atomic object to perform the arbitrary angle two qubit gate.

[0103] VII. Example Implementations of Individual Single-Qubit Gates Using Global Single-Qubit Gate and / or Two-Qubit Gate Primitives Various embodiments relate to the implementation of individual single qubit gates. Various embodiments relate to the implementation of individual single qubit gates including at least one two-qubit gate primitive and / or at least one global single qubit gate. As used herein, an individual single qubit gate is a gate that affects (more than a possible phase shift) the state of only one qubit. For example, an individual single qubit gate may be generated by performing a combination of a global single qubit gate primitive and a two-qubit gate primitive on two qubits. Performing a combination of a global single qubit gate primitive and a two-qubit gate primitive on two qubits results in an update and / or modification of the state of a first bit of the two qubits and no update and / or modification of the state of a second bit of the two qubits beyond a possible change in phase (e.g., due to an AC Stark shift, etc.).

[0104] In various embodiments, each single qubit gate is a general gate. In various embodiments, each single qubit gate is a fixed angle gate. For example, the rotation angle is selected from a set of possible rotation angles (e.g., −π, −π / 2, π / 2, and π, as one non-limiting example).

[0105] 8 presents a flow chart illustrating various processes, procedures, actions, etc. for performing individual single qubit gates using global single qubit gate primitives and / or two qubit gate primitives. Beginning at step / action 802, two or more atomic objects are confined by atomic object confinement device 70. For example, quantum computer controller 30 may operate and / or cause operation of one or more voltage sources 50 to generate confinement potentials by sequences of RF rail electrodes 72 and / or TT electrodes 74 to confine two or more atomic objects by atomic object confinement device 70.

[0106] Controller 30 may cause the quantum processor to begin implementing and / or executing a quantum circuit. For example, controller 30 may control operation of voltage source 50 to transport various atomic objects confined by atomic object confinement device 70 to specific locations within the atomic object confinement device, and control operation of manipulation source 60 to cause one or more manipulation signals to be incident on the various atomic objects at the specific locations to perform one or more operations and / or functions of the quantum processor (e.g., single qubit gate, two qubit gate, qubit initialization (e.g., initializing the atomic objects to a quantum state in qubit space, reading a qubit, etc.)). At some point during the implementation and / or execution of the quantum circuit, an individual single qubit gate is performed on a first qubit embodied by a first atomic object.

[0107] In step / operation 804, the first atomic object and the second atomic object are transported to respective positions within the atomic object confinement device 70 in proximity to one another. In an exemplary embodiment, the first atomic object and / or the second atomic object are transported such that the first atomic object and the second atomic object are adjacent and / or proximate to one another (e.g., no other atomic objects are disposed between the first atomic object and the second atomic object). For example, the controller 30 operates and / or causes the operation of the voltage source 50 such that a control voltage signal is provided to a sequence of the TT electrodes 74 that moves the first atomic object from a respective previous position to the first position and / or moves the second atomic object from a respective previous position to the second position. The first position and the second position are in proximity to one another. For example, the quantum circuit may indicate that the first qubit and the second qubit interact with one another before and / or after performing individual single qubit gates.

[0108] During transporting the first atomic object to the first location and / or transporting the second atomic object to the second location, heating of the atomic objects may occur. In step / operation 806, a cooling operation may be performed to cool the first atomic object and / or the second atomic object. In an exemplary embodiment, the cooling operation is a joint cooling operation. For example, the controller 30 may cause one or more manipulation sources 60 to provide a manipulation signal incident on a jointly-cooled atomic object located sufficiently close to each of the first and / or second atomic objects, such that the jointly-cooled atomic object is available to remove heat from the first and / or second atomic objects.

[0109] In step 808, an individual single qubit gate is performed for the first qubit by executing a sequence of gate primitives for the first qubit and the second qubit. In an exemplary embodiment, the sequence of gate primitives consists of only global single qubit gates and two qubit gates. For example, a sequence of gate primitives that have the combined effect of individual single qubit gates does not include gate primitives that are individually addressed gates (e.g., gates that are performed for only one qubit).

[0110] In an exemplary embodiment, the executed sequence of gate primitives that has the effect of implementing individual single qubit gates is represented by one or more antisymmetric iSWAPs.

number

number

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[0111] 9 presents a flowchart illustrating various processes, procedures, operations, etc. that may be performed to execute a sequence of gate primitives (consisting of global single qubit gates and two qubit gates) to execute individual single qubit gates. For example, the steps / operations illustrated in FIG. 9 may be performed (e.g., by controller 30) as part of step / operation 808.

[0112] A non-limiting example individual qubit gate implemented by executing a sequence of gate primitives consisting of a global single qubit gate and (only) two qubit gates (including one or more antisymmetric two qubit gates):

number

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[0113] In various embodiments, when using individual single qubit gates implemented by executing a sequence of global single qubit gates and two-qubit gates, rather than individual single qubit gates addressed to that particular qubit (either to the exclusion of all other qubits or by the vicinity of that particular qubit), the phase of each qubit is tracked (e.g., in the respective qubit record (e.g., stored in memory 1010) and / or by using software gates) and compiled into various SU(4) gates as they are applied to the qubit. In various embodiments, such tracking of qubit phase and compiling of SU(4) gates to take qubit phase into account does not require additional hardware since the addressed individual single qubit gates also require qubit phase tracking.

[0114] FIG. 9 illustrates a process, procedure, operation, etc., for performing an example individual single qubit gate of an arbitrary angle Y rotation gate. Starting at step / operation 902, a first frame rotation is performed. For example, a first global single qubit gate UG(π-θ y , π / 2) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a first instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the first instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the first instance of each of the first manipulation signal 410 and the second manipulation signal 420, and the length of time that the first instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object may be π-θ yFor example, a qubit vector r of a first qubit (embodied by a first atomic object) and a second qubit (embodied by a second atomic object) may be configured to undergo a Δθ rotation. Q The polar angle θ is π-θ y The phase difference between the first instances of each of the first operating signal 410 and the second operating signal 420 is modulated (e.g., changed in value) by a qubit vector r Q Azimuth angle of

number

[0115] In step / action 904, a first phase-independent two-qubit gate primitive is executed. In the illustrated embodiment, a first phase-independent asymmetric two-qubit gate primitive U i (π / 2,π / 2) is executed. For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the first instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object to execute the first antisymmetric gate.

[0116] In step / action 906, a second frame rotation is performed. For example, a second global single qubit gate U G(π / 2,π) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a second instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 and the length of time that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. For example, the qubit vectors r of the first qubit (embodied by the first atomic object) and the first qubit (embodied by the second atomic object) may be configured to rotate by Δθ of π / 2. Q The polar angle θ of is modified (e.g., changed in value) by π / 2. The phase difference between the second instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the qubit vectors r Q Azimuth angle of

number

[0117] In step / operation 908, a second phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the second phase-independent two-qubit gate primitive is a phase-independent rotating MS gate U ZZ(π / 2). For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object. The power present in the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, the respective frequencies of the second instances of each of the third manipulation signal 510 and the fourth manipulation signal 520, and the duration that the second instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to produce an interaction between the first atomic object and the second atomic object characterized by a rotation angle of π / 2.

[0118] In step / action 910, a third frame rotation is performed. For example, a third global single qubit gate U G (θ y ,π) is performed. For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a third instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the third instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the third instance of each of the first manipulation signal 410 and the second manipulation signal 420, as well as the length of time that the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object, may be determined to be θ yFor example, the first quantum bit (embodied by the first atomic object) and the second quantum bit (embodied by the second atomic object) are configured to undergo a Δθ rotation by a qubit vector r Q The polar angle θ is θ y The phase difference between the fourth instances of each of the first operating signal 410 and the second operating signal 420 is modulated (e.g., changed in value) by a qubit vector r Q Azimuth angle of

number

[0119] In step / operation 912, a third phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the third phase-independent asymmetric two-qubit gate primitive is i (π / 2,π / 2) is executed. For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a third instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the third instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object to execute the second antisymmetric gate.

[0120] In step / action 914, a fourth frame rotation is performed. For example, a fourth global single qubit gate U G(π / 2, π / 2) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the fourth instance of each of the first manipulation signal 410 and the second manipulation signal 420 and the length of time that the second instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π / 2. For example, the qubit vectors r of each of the first qubit (embodied by the first atomic object) and the second qubit (embodied by the second atomic object) may be configured to rotate by Δθ of π / 2. Q The polar angle θ of is modified (e.g., changed in value) by π / 2. The phase difference between the fourth instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the qubit vectors r Q Azimuth angle of

number

[0121] In step / operation 916, a fourth phase-independent two-qubit gate primitive is executed. In an exemplary embodiment, the second phase-independent two-qubit gate primitive is a phase-independent rotating MS gate U ZZ(π / 2). For example, the controller 30 may cause the one or more manipulation sources 60 to generate and provide a fourth instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 such that the fourth instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on both the first atomic object and the second atomic object. The power present in the fourth instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, the respective frequency of the fourth instance of each of the third manipulation signal 510 and the fourth manipulation signal 520, and / or the duration that the fourth instance of each of the third manipulation signal 510 and the fourth manipulation signal 520 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to produce an interaction between the first atomic object and the second atomic object characterized by a rotation angle of π / 2.

[0122] In step / action 918, a fifth frame rotation is performed. For example, the third global single qubit gate U G(π,π) is performed. For example, the controller 30 may cause one or more manipulation sources 60 to generate and provide a fifth instance of each of the first manipulation signal 410 and the second manipulation signal 420 such that the fifth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on both the first atomic object and the second atomic object. The power present in the fifth instance of each of the first manipulation signal 410 and the second manipulation signal 420 and the length of time that the fifth instance of each of the first manipulation signal 410 and the second manipulation signal 420 is incident on (e.g., interacts with) the first atomic object and the second atomic object are configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π. For example, the qubit vectors r of each of the first qubit (embodied by the first atomic object) and the second qubit (embodied by the second atomic object) may be configured to cause both the first atomic object and the second atomic object to undergo a Δθ rotation of π. Q The polar angle θ of is modified (e.g., changed in value) by π. The phase difference between the fourth instances of each of the first operating signal 410 and the second operating signal 420 is a phase difference between the qubit vectors r Q Azimuth angle of

number

[0123] The result of performing an exemplary individual single-qubit gate is that a Y rotation of any angle has been performed on the first qubit, and a unit gate has been performed on the second qubit.

[0124] VIII. Technical Advantages A general technical problem in the field of quantum computing is to reduce errors accumulated during the execution of a quantum circuit. Various embodiments provide a technical solution to this technical problem by using a two-qubit arbitrary angle gate that uses a global single-qubit gate.

[0125] Various quantum circuits require the use of general (single qubit, two qubit, and / or multi-qubit) gates. Variational algorithms (e.g., variational quantum eigensolvers (VQE), etc.), QAQA, QFT, Hamiltonian simulation techniques, and volumetric tests are examples of computations that are beneficial to run on and / or require the use of a quantum computer and have implementations that include any-angle gates. A conventional decomposition of a general two qubit gate includes three fixed-angle two qubit gates and three to five addressed single qubit gates. Due to the need for atomic object transport to execute the addressed single qubit gates, a cooling operation is performed before each of the three fixed-angle two qubit gates. The cooling operation is relatively slow compared to other functions and / or operations performed by the quantum computer, and is subject to memory errors and drift errors (e.g., operation source power, frequency, and / or phase drift, atomic object phase drift, etc.). Various embodiments reduce the number of cooling operations that need to be performed during the execution of a general two qubit gate by three. Thus, various embodiments significantly reduce errors that occur in performing a general two-qubit gate due to the need to perform multiple cooling operations.

[0126] A conventional decomposition of a general two-qubit gate includes three fixed-angle two-qubit gates. The fixed angle is conventionally set to π / 2, so that the total rotation angle when performing a two-qubit arbitrary-angle gate is 3π / 2. In an exemplary embodiment, the inventors found that in a sample of 10,000 arbitrary-angle SU(4) gates, the average total rotation angle is about 3π / 4, i.e., half the total rotation angle of the conventional general two-qubit gate decomposition. Conventionally, MS gates are used as two-qubit gates in the decomposition of a general two-qubit gate. However, many errors in ME gates (e.g., amplitude error, detuning error, phase noise error, spontaneous emission, etc.) increase monotonically with the total rotation angle. Thus, various embodiments reduce the gate error caused by performing a general two-qubit gate by reducing the total rotation angle.

[0127] As noted above, when using individually addressed single qubit gate primitives, the atomic objects may need to be moved away from one another to perform the individually addressed single qubit gate, and then transported back close to one another to perform the two qubit gate. Each time the atomic objects are transported back close to one another, a cooling operation must be performed to reduce heating errors. Thus, various embodiments advance the field of quantum computing by providing global single qubit gates and individual single qubit gates (e.g., single qubit gates that do not require addressing and / or include at least one two qubit gate, such as an antisymmetric gate).

[0128] Additionally, various embodiments provide solutions to technical problems identified by the inventors during the process of the present invention relating to operational signal power, frequency, duration, and / or combinations thereof, calibration and physical phase updates.

[0129] Thus, the various embodiments advance the fields of quantum computing and QCCD-based quantum computing by providing arbitrary angle gates, including arbitrary angle rotation, and / or individual single qubit gates that do not require addressing.

[0130] IX. Exemplary Controllers In various embodiments, the atomic object confinement device is incorporated into quantum computer 110. In various embodiments, quantum computer 110 comprises a controller 30 configured to control various elements of quantum computer 110. For example, controller 30 may be configured to control voltage source 50, a cryogenic and / or vacuum system that controls the temperature and pressure within cryogenic and / or vacuum chamber 40, manipulation source 60, magnetic field generator 80, and / or other systems that control the environmental conditions (e.g., temperature, humidity, pressure, etc.) within cryogenic and / or vacuum chamber 40 and manipulate and / or cause the controlled evolution of quantum states of one or more atomic objects within atomic object confinement device 70.

[0131] As shown in FIG. 10, in various embodiments, the controller 30 may comprise various controller elements including processing elements and / or devices 1005, memory 1010, driver controller elements 1015, communication interfaces 1020, analog-to-digital converter elements 1025, etc. For example, the processing elements and / or devices 1005 may comprise programmable logic devices (CPLDs), microprocessors, co-processing entities, application specific instruction set processors (ASIPs), integrated circuits, application specific integrated circuits (ASICs), field programmable gate arrays (FPGAs), programmable logic arrays (PLAs), hardware accelerators, other processing devices and / or circuits, etc., and / or controllers. The term circuitry may refer to an entire hardware embodiment or a combination of a hardware product and a computer program product. In an exemplary embodiment, the processing elements and / or devices 1005 of the controller 30 comprise and / or communicate with a clock. For example, the processing elements and / or devices 1005 are configured to determine how to cause the quantum processor 115 to execute a quantum circuit (e.g., using parallel and / or simultaneous operations) and then control various aspects of the quantum computer (e.g., by providing instructions to respective driver controller elements 1015) to cause the quantum processor 115 to execute the quantum circuit. In various embodiments, executing the quantum circuit includes executing one or more arbitrary angle gates and / or one or more global gates.

[0132] For example, the memory 1010 may comprise non-transitory memory, such as volatile and / or non-volatile memory storage, such as one or more of hard disks, ROM, PROM, EPROM, EEPROM, flash memory, MMCs, SD memory cards, memory sticks, 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, registered memory, and the like. In various embodiments, the memory 1010 may store qubit records corresponding to qubits of the quantum computer (e.g., in a qubit record data store, a qubit record database, a qubit record table, etc.), one or more functional representations of manipulation signal power, frequency, duration, and / or combinations thereof as functions of input signals (e.g., input signal parameter values) provided to modulators configured to adjust the respective manipulation signals, calibration tables, executable cues, computer program code (e.g., in one or more computer languages, specialized controller languages, etc.), one or more libraries, one or more waveform sequences for forming control voltage signals for controlling transport of atomic objects along the one-dimensional trapping regions and through junctions connecting the one-dimensional trapping regions, and associated metadata, etc. In an exemplary embodiment, the qubit records corresponding to each qubit track the phase of the respective qubit, any AC Stark shifts applied to the phase of the qubit, the results of any software gates on the phase of the qubit, etc.In an exemplary embodiment, execution of at least a portion of the computer program code stored in memory 1010 (e.g., by the processing element and / or device 1005) causes the controller 30 to perform one or more steps, operations, processes, procedures, etc. described herein for tracking the phase, position, etc. of atomic objects and / or poly-atomic object crystals within an atomic system and for adjusting the phase of one or more manipulation sources and / or signals generated thereby.

[0133] In various embodiments, the driver controller element 1015 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 1015 may comprise a driver and / or a driver controller. For example, the driver controller may be configured to operate one or more corresponding drivers according to executable instructions, commands, etc., scheduled and executed by the controller 30 (e.g., by the processing element and / or device 1005). In various embodiments, the driver controller element 1015 may enable the controller 30 to operate the manipulation source 60, the voltage source 50, the magnetic field generator 80, etc. In various embodiments, the drivers may be laser drivers; vacuum component drivers; drivers for controlling the flow of currents and / or voltages applied to TT electrodes, RF rail electrodes, RF bus electrodes, and / or other electrodes used to maintain and / or control magnetic fields in various regions of the atomic object confinement apparatus 70, maintain and / or control the trapping potential of the atomic object confinement apparatus 70, and / or transport one or more atomic objects; cryogenic and / or vacuum system component drivers, etc. For example, the driver may control and / or comprise a TT and / or RF voltage driver and / or a voltage source 50 that provides a voltage and / or an electrical signal (e.g., an oscillating voltage signal and / or a control voltage signal) to the TT electrode and / or the RF rail electrode.

[0134] In various embodiments, the controller 30 comprises means for communicating and / or receiving signals from one or more receiver components, such as photodetectors, cameras, MEMs cameras, CCD cameras, photodiodes, photomultiplier tubes, etc., of a light collection system configured to capture, detect, measure, etc., optical signals generated by atomic objects captured and / or confined by the atomic object confinement device 70. For example, the controller 30 may comprise one or more analog-to-digital converter elements 1025 configured to receive signals from the one or more receiver components, calibration sensors, etc.

[0135] In various embodiments, the controller 30 may comprise a communications interface 1020 for interfacing and / or communicating with the computing entity 10. For example, the controller 30 may comprise a communications interface 1020 for receiving executable instructions, command sets, etc. from the computing entity 10 and for providing to the computing entity 10 output received from the quantum computer 110 (e.g., from an optical collection system) and / or results of processing the output. 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.

[0136] X. Exemplary Computing Entities 11 presents an exemplary schematic diagram of an exemplary computing entity 10 that may be used in connection with embodiments of the present invention. In various embodiments, computing entity 10 is configured to enable a user to provide input to quantum computer 110 (e.g., via a user interface of computing entity 10) and receive, display, analyze, etc. output from quantum computer 110.

[0137] As shown in FIG. 11, the computing entity 10 may include an antenna 1112, a transmitter 1104 (e.g., wireless), a receiver 1106 (e.g., wireless), and a processing element 1108 that respectively provides signals to the receiver 1106 and receives signals from the transmitter 1104. The signals respectively provided to the receiver 1106 and received from the transmitter 1104 may include signaling information / data according to an air interface standard of the applicable wireless system to communicate with various entities, such as the controller 30, other computing entities 10, etc. In this regard, the computing entity 10 may be capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. For example, the computing entity 10 may be configured to receive and / or provide communications using 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, the computing entity 10 may be configured to communicate with any of the following mobile radio access networks: 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 ... The wireless device may be configured to communicate over a wireless external communications network using any of a wide variety of protocols, such as IEEE 802.11 (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.The computing entity 130 may use such protocols and standards to communicate with a wide variety of networks, including Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, 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 (HMM), HyperText Markup Language (HKLM ... Communication is done using a variety of language (HTML, etc.).

[0138] Through these communication standards and protocols, computing entity 10 communicates 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 Dialer (SIM dialer). Computing entity 10 also downloads, for example, changes, add-ons, and updates to the firmware, software (including, for example, executable instructions, applications, program modules), and operating system of computing entity 10.

[0139] The computing entity 10 may also comprise a user interface device comprising one or more user input / output interfaces (e.g., a display 1116 and / or a speaker / speaker driver coupled to the processing element 1108, as well as a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 1108). For example, the user output interface may be configured to provide applications, user interfaces, interfaces, dashboards, screens, web pages, pages, and / or similar terms used interchangeably herein that are executed on and / or accessible via the computing entity 10 to cause information / data to be displayed or audibly presented and to interact with the computing entity 10 via one or more user interfaces. The user input interface may comprise a number of devices that enable the computing entity 10 to receive data, such as a keypad 1118 (hard or soft), a touch display, a voice / speech or motion interface, a scanner, reader, or other input device. In embodiments including a keypad 1118, the keypad 1118 may include (or display) conventional numeric (0-9) and related keys (#, *), as well as other keys used to operate the computing entity 10, and may include a full set of alphabetic keys, or a set of keys that may be activated to provide a full set of alphanumeric keys. The user input interface may be used to provide input as well as to activate or deactivate certain features, such as a screen saver and / or sleep mode. Such input may enable the computing entity 10 to gather information / data, user interaction / input, etc.

[0140] The computing entity 10 may also include volatile storage or memory 1122 and / or non-volatile storage or memory 1124, which may be embedded and / or removable. For example, the non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. The volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, registered memory, etc. The volatile and non-volatile storage or memory may 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 perform the functionality of the computing entity 10.

[0141] XI. Conclusion Many modifications and other embodiments of the inventions described herein will come to mind to one skilled in the art to which this invention pertains and having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. It is to be understood, therefore, 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 generic and descriptive sense and not for purposes of limitation. [Explanation of symbols]

[0142] 10. Quantum Computers 30 Controller 40 Cryogenic and / or Vacuum Chambers 50 Voltage Source 60 Operation source 70 Atomic Object Containment Device 72, 72A, 72B, 72C Radio Frequency (RF) Rail Electrodes 74, 74A, 74B, 74C Capture and / or Transport (TT) Electrodes 80, 80A, 80B Magnetic Field Generator 100 Quantum Computer System 110 Quantum Computer 115 Quantum Processor 156 TT electrode 200 Partial Energy Diagram 210 qubit space 300 Bloch sphere representation 402A First Atomic Object 402B Second Atomic Object 405 Axis 410 First operating signal 420 Second operating signal 510 Third Operation Signal 520 Fourth Operation Signal 1005 Processing device 1010 Memory 1015 Driver Controller Element 1020 Communication Interface 1025 A / D Converter

Claims

1. 1. A method for performing a general two-qubit gate using a QCCD-based quantum processor, comprising: providing a first atomic object and a second atomic object confined by an element of the QCCD quantum processor; causing, by a controller configured to control various operations of the QCCD-based quantum processor, a first frame rotation of the first atomic object and the first frame rotation of the second atomic object; causing, by the controller, to transport the first atom object and the second atom object such that the second atom object is located in close physical proximity to the first atom object; performing a first phase-independent two-qubit gate on the first atomic object and the second atomic object corresponding to a rotation of a first arbitrary angle; performing a second frame rotation of the first atomic object and a second frame rotation of the second atomic object; performing a second arbitrary-angle phase-independent two-qubit gate on the first atomic object and the second atomic object corresponding to a rotation through a second arbitrary angle; performing a third frame rotation of the first atomic object and a third frame rotation of the second atomic object; performing a third phase-independent two-qubit gate corresponding to a third arbitrary angle on the first atomic object and the second atomic object; A method comprising:

2. The method of claim 1, wherein each of the second frame rotation and the third frame rotation comprises one or more respective global single quantum bit gates, each global single quantum bit gate acting on the first atomic object and the second atomic object.

3. 2. The method of claim 1 , wherein the first, second, and third phase-independent two-qubit gates are each implemented by a respective pair of two-qubit gate operating signals being incident on both the first atomic object and the second atomic object, and wherein at least one characteristic of at least one operating signal of the respective pair of two-qubit gate operating signals is controlled based on a functional representation of an operating signal characteristic as a function of an input signal to a modulator configured to adjust the at least one operating signal, the at least one characteristic being at least one of a power level, a frequency, and a duration.

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