Using a microwave dressing field to control the frequency dependence of the frequency of the 0 Gaussian clock state on Bz.

Abstract

The controller of the quantum system causes a dressing field circuit to generate a dressing field at a target location where one or more target qubits are located. The dressing field modifies the initial set of states into a set of superposition states. The first (second) dressing state of the set of superposition states includes a non-zero contribution from the first (second) qubit state of the initial set of states. The dressing frequency difference between the first and second dressing states and the qubit frequency difference between the first and second qubit states are different. The dressing field is configured to generate first and second dressing states that have a desired level of sensitivity (e.g., energy / frequency dependence) to the components of an external magnetic field in the quantization direction of the quantum system.

Description

TECHNICAL FIELD

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Application No. 18 / 806,881 filed on August 16, 2024, which claims priority to U.S. Application No. 63 / 581,017 filed on September 7, 2023, the entire contents of which are incorporated herein by reference in their entirety.

[0002] Various embodiments relate to controlling the frequency dependence of the 0 Gauss clock state frequency with respect to an external magnetic field using a microwave dressing field. Various embodiments relate to multi-qubit quantum logic gates that use a microwave dressing field to cause target qubits to be sensitively responsive to an external magnetic field, and use a non-zero magnetic field gradient to mediate entanglement of the target qubits. Various embodiments relate to increasing the coherence time of qubits by applying a microwave dressing field that results in a superposition state that effectively behaves as a clock state at non-zero magnetic field amplitudes. BACKGROUND ART

[0003] In large quantum charge-coupled device (QCCD) based quantum computers using hyperfine splitting qubits, operating at low magnetic field amplitudes (e.g., less than 10G) allows for the provision of a reasonably uniform magnetic field. In addition, to enable energy splitting of the hyperfine states, the quantum processor is operated at magnetic field amplitudes greater than 0G. Generally, a set of low F (e.g., F=0, 1, and / or 2), m=0 states is used to define the qubit subspace of the qubit. However, these m=0 states function only as clock states at a magnetic field amplitude of 0G. Therefore, when operating in a magnetic field with amplitudes in the range of 2-5G, the m=0 states are not clock states (e.g., they have energy / frequency that responds sensitively in proportion to changes in the magnetic field). This can lead to a significant increase in memory errors and / or a reduction in memory coherence time. Through effort, ingenuity, and innovation, many of the shortcomings of such conventional quantum computers have been overcome by developing structured solutions according to embodiments of the present invention, many examples of which are described in detail herein. [Prior art documents] [Patent Documents]

[0004] [Patent Document 1] U.S. Patent Application No. 63 / 509,098 [Patent Document 2] U.S. Patent Application No. 63 / 504,808 [Patent Document 3] U.S. Patent Application No. 63 / 476,226 [Overview of the project] [Problems that the invention aims to solve]

[0005] Exemplary embodiments provide quantum systems, controllers for quantum systems, and corresponding methods for controlling the sensitivity of a 0-Gauss clock state to an external magnetic field (e.g., a hyperfine state that functions as a clock state with a magnetic field amplitude / magnitude of 0 Gauss). For example, various embodiments provide QCCD quantum computers using hyperfine split qubits, controllers for QCCD-based quantum computers, and corresponding methods for controlling the sensitivity of qubits to an external magnetic field. For example, in exemplary embodiments, a quantum system, a controller for a quantum system, and a corresponding method are provided for controlling (e.g., decreasing) the sensitivity of qubits to an external magnetic field to increase the coherence time of one or more qubits. In exemplary embodiments, a quantum system, a controller for a quantum system, and a corresponding method are provided for performing a multi-qubit gate by controlling (e.g., increasing) the sensitivity of qubits to an external magnetic field to allow a non-zero magnetic field gradient to mediate the entanglement of two or more qubits. [Means for solving the problem]

[0006] In various embodiments, a qubit has an initial set of quantum states. The initial set of quantum states includes a first qubit state and a second qubit state in the qubit subspace of the initial set of quantum states. The initial set of states is defined, at least in part, by the hyperfine splitting of the quantum states of the quantum object that functions as a qubit. In various embodiments, controlling the sensitivity of the qubit to an external magnetic field involves causing a dressing field to exist at a target location defined, at least in part, by a confinement device. The dressing field interacts with the qubit located at the target location, causing the quantum states of the qubit to be dressed and / or modified to provide a set of superposition states. The dressing states of the set of superposition states are superpositions of two or more quantum states of the initial set of quantum states. The set of superposition states includes a first dressing state containing a non-zero contribution from the first qubit state and a second dressing state containing a non-zero contribution from the second qubit state.

[0007] By controlling various aspects of the dressing field (e.g., magnitude, frequency, and / or polarization), the coupling of a set of initial states resulting in a first dressing state and a set of initial states resulting in a second dressing state can be controlled to provide a first and second dressing state with desired magnetic field sensitivity. For example, in one exemplary embodiment, various aspects of the dressing field are controlled so that the first and second dressing states do not respond sensitively to changes in the external magnetic field in the magnetic field operating region of the system. In another example, in one exemplary embodiment, various aspects of the dressing field are controlled so that the first and second dressing states respond sensitively to the external magnetic field, thereby allowing a non-zero magnetic field gradient to be used to mediate entanglement and / or other interactions between two or more qubits.

[0008] According to one embodiment, a method is provided for executing a multi-qubit gate on two or more qubits confined by a confinement device. In an exemplary embodiment, the method includes controlling the operation of a dressing field circuit by a controller to cause the dressing field circuit to generate a dressing field at a target location defined at least partly by the confinement device. The dressing field is configured to modify the energy structure of each of the two or more qubits arranged at the target location by causing the initial set of each qubit to form a set of superposition states. The first dressing state of the superposition state set includes a non-zero contribution from the first qubit state of the initial set, and the second dressing state of the superposition state set includes a non-zero contribution from the second qubit state of the initial set. The first and second dressing states are more sensitive to a magnetic field than the first and second qubit states. A non-zero magnetic field gradient is present at the target location and mediates the entanglement of the two or more qubits arranged at the target location. This method further includes, after the gate time has elapsed, controlling the operation of the dressing field circuit by a controller to cause the dressing field circuit to stop generating a dressing field at a target position so that the energy structure of each of the two or more qubits returns to its respective initial energy structure, which includes a set of initial states.

[0009] In one exemplary embodiment, the dressing field circuit stops generating the dressing field at the target location, and the energy structure of each of the two or more target qubits returns to its initial energy structure, which includes the initial set of qubits.

[0010] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that, when the dressing field circuit initiates the generation of a dressing field, the amplitude of the dressing field increases from zero to the gate amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0011] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the gate amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0012] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

[0013] In one exemplary embodiment, controlling the operation of a dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

[0014] In one exemplary embodiment, the dressing field is a microwave field.

[0015] In one exemplary embodiment, the dressing field circuit is arranged on the confinement device.

[0016] In an exemplary embodiment, the dressing field circuit is lithographically printed onto the surface of the confinement device.

[0017] In another embodiment, a method is provided for performing a clock state generation procedure for one or more target qubits confined by a confinement device. In an exemplary embodiment, the method includes controlling the operation of a dressing field circuit by a controller to cause the dressing field circuit to generate a dressing field at a target location defined at least partly by the confinement device. The dressing field is configured to modify the energy structure of each of the one or more target qubits arranged at the target location by causing each set of initial states of the one or more target qubits to form each set of superposition states. The first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states. A substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states behave effectively as clock states at the operable magnetic field amplitude.

[0018] In one exemplary embodiment, a first dressing state is formed by combining two or more first states from an initial set of states, and a second dressing state is formed by combining two or more second states from an initial set of states.

[0019] In an exemplary embodiment, the coupling of two or more first states and two or more second states in the initial set of states causes an AC Zeeman shift that has a linear dependence on a magnetic field having the same magnitude and opposite sign as the energy dependence of the first and second qubit states on an external magnetic field.

[0020] In one exemplary embodiment, the method further includes controlling the operation of a dressing field circuit to cause the generation of a dressing field at a target location to cease, such that the energy structure of the qubit returns to an initial energy structure containing the initial set of the qubit's states, before transporting the qubit.

[0021] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that, when the dressing field circuit initiates the generation of a dressing field, the amplitude of the dressing field increases from zero to the dressing amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0022] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

[0023] In one exemplary embodiment, controlling the operation of a dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

[0024] In one exemplary embodiment, the dressing field is a microwave field.

[0025] In one exemplary embodiment, the dressing field circuit is arranged on the confinement device.

[0026] In an exemplary embodiment, the dressing field circuit is lithographically printed onto the surface of the confinement device.

[0027] In an exemplary embodiment, the method further includes a controller controlling the operation of one or more manipulators to generate and provide each manipulator signal such that each manipulator signal is incident on one or more target qubits positioned at a target location, each manipulator signal causing a single-qubit gate or a multi-qubit gate to be executed on one or more target qubits, and at least one of the frequencies of each manipulator signal or the frequency difference between each manipulator signal corresponds to the frequency difference between a first dressing state and a second dressing state.

[0028] In one exemplary embodiment, the clock state generation procedure is performed to extend the qubit coherence time of one or more target qubits.

[0029] In another embodiment, a system is provided configured to execute a multi-qubit gate on two or more target qubits. In an exemplary embodiment, the system comprises a confinement device configured to confine a plurality of qubits, the plurality of qubits including two or more target qubits; a dressing field circuit, the dressing field circuit and the confinement device defining a target position in at least part of it; a magnetic field source configured to generate a non-zero magnetic field gradient at the target position; and a controller configured to control the operation of the dressing field circuit. The controller is configured to control the operation of the dressing field circuit, thereby causing the dressing field circuit to generate a dressing field at the target position defined in at least part of it by the confinement device, and thereby causing the multi-qubit gate to be executed on two or more target qubits located at the target position. The dressing field is configured to modify the energy structure of each of the two or more qubits located at the target position by causing the initial set of each of the two or more qubits to form a set of superposition states. The first dressing state of the superposition state set includes a non-zero contribution from the first qubit state of the initial state set, and the second dressing state of the superposition state set includes a non-zero contribution from the second qubit state of the initial state set. The first and second dressing states are more sensitive to magnetic fields than the first and second qubit states. A non-zero magnetic field gradient is present at the target location and mediates the entanglement of two or more qubits located at the target location. The controller is further configured to control the operation of the dressing field circuit after the gate time has elapsed, causing the dressing field circuit to stop generating a dressing field at the target location so that the energy structure of each of the two or more qubits returns to its respective initial energy structure, which includes the initial state set.

[0030] In one exemplary embodiment, when the dressing field circuit stops generating the dressing field at the target location, the energy structure of each of the two or more target qubits returns to its initial energy structure, which includes the initial set of states of the qubits.

[0031] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that, when the dressing field circuit initiates the generation of a dressing field, the amplitude of the dressing field increases from zero to the gate amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0032] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the gate amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0033] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

[0034] In one exemplary embodiment, controlling the operation of a dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

[0035] In one exemplary embodiment, the dressing field is a microwave field.

[0036] In one exemplary embodiment, the dressing field circuit is arranged on the confinement device.

[0037] In an exemplary embodiment, the dressing field circuit is lithographically printed onto the surface of the confinement device.

[0038] In another embodiment, a system is provided configured to perform a clock state generation procedure on one or more target qubits. In an exemplary embodiment, the system comprises a confinement device configured to confine a plurality of qubits, the plurality of qubits including two or more target qubits; a dressing field circuit, the dressing field circuit and the confinement device defining a target location in at least part; and a controller configured to control the operation of the dressing field circuit. The controller is configured to control the operation of the dressing field circuit, thereby causing the clock state generation procedure to be performed on one or more target qubits located at the target location by controlling the operation of the dressing field circuit to cause the dressing field circuit to generate a dressing field at the target location defined in at least part by the confinement device. The dressing field is configured to modify the energy structure of each of the one or more target qubits located at the target location by causing each set of initial states of the one or more target qubits to form each set of superposition states. The first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states. A substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states effectively behave as clock states at the operable magnetic field amplitude.

[0039] In one exemplary embodiment, a first dressing state is formed by combining two or more first states from an initial set of states, and a second dressing state is formed by combining two or more second states from an initial set of states.

[0040] In an exemplary embodiment, the coupling of two or more first states and two or more second states in the initial set of states causes an AC Zeeman shift that has a linear dependence on a magnetic field having the same magnitude and opposite sign as the energy dependence of the first and second qubit states on an external magnetic field.

[0041] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that, when the dressing field circuit initiates the generation of a dressing field, the amplitude of the dressing field increases from zero to the dressing amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0042] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the dressing amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

[0043] In an exemplary embodiment, the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

[0044] In one exemplary embodiment, controlling the operation of a dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

[0045] In one exemplary embodiment, the dressing field is a microwave field.

[0046] In one exemplary embodiment, the dressing field circuit is arranged on the confinement device.

[0047] In an exemplary embodiment, the dressing field circuit is lithographically printed onto the surface of the confinement device.

[0048] In an exemplary embodiment, the controller is further configured to control the operation of one or more manipulators to generate and provide each manipulator signal so that each manipulator signal is incident on one or more target qubits positioned at a target location, each manipulator signal causing a single-qubit gate or a multi-qubit gate to be executed on one or more target qubits, and at least one of the frequencies of each manipulator signal or the frequency difference between each manipulator signal corresponds to the frequency difference between a first dressing state and a second dressing state.

[0049] In one exemplary embodiment, the clock state generation procedure is performed to extend the qubit coherence time of one or more target qubits.

[0050] In another embodiment, a controller is provided which is configured to control one or more components of a quantum system and to cause the quantum system to execute a multi-qubit gate. In an exemplary embodiment, the controller comprises a processing device, a memory for storing executable instructions, and a driver controller element. The executable instructions are configured, when executed by the processing device, to cause the controller to use the driver controller element to control the operation of a dressing field circuit, causing the dressing field circuit to generate a dressing field at a target location defined at least partly by a confinement device. The dressing field is configured to modify the energy structure of each of the two or more qubits arranged at the target location by causing the initial set of each qubit of two or more qubits to form a set of superposition states. The first dressing state of the set of superposition states includes a non-zero contribution from the first qubit state of the set of initial states, and the second dressing state of the set of superposition states includes a non-zero contribution from the second qubit state of the set of initial states. The first and second dressing states are more sensitive to magnetic fields than the first and second qubit states. A non-zero magnetic field gradient exists at the target location and mediates the entanglement of two or more qubits located at the target location. The executable instruction, when executed by the processing device, uses a driver controller element and, after the gate time has elapsed, causes the controller to control the operation of the dressing field circuit so that the dressing field circuit stops generating a dressing field at the target location, so that the energy structure of each of the two or more qubits returns to their respective initial energy structures, which include a set of initial states.

[0051] In yet another embodiment, a controller is provided which is configured to control one or more components of a quantum system and to cause the quantum system to perform a clock state generation procedure. The controller comprises a processing device, a memory for storing executable instructions, and a driver controller element. The executable instructions are configured such that, when executed by the processing device, the controller uses the driver controller element to control the operation of a dressing field circuit, causing the dressing field circuit to generate a dressing field at a target location defined at least in part by a confinement device. The dressing field is configured to modify the energy structure of each of the one or more target qubits disposed at the target location by causing each set of initial states of one or more target qubits to form each set of superposition states. The first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states. A substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states effectively behave as clock states at the operable magnetic field amplitude.

[0052] In yet another embodiment, a computer program product is provided. The computer program product comprises a non-temporary computer storage medium for storing computer executable instructions. The computer executable instructions are configured, when executed by the controller's processing device, to cause the controller to use the controller's driver controller element to control the operation of a dressing field circuit, causing the dressing field circuit to generate a dressing field at a target location defined at least in part by a confinement device. The dressing field is configured to modify the energy structure of each of the two or more qubits arranged at the target location by causing the initial set of each qubit to form a set of superposition states. The first dressing state of the superposition state set includes a non-zero contribution from the first qubit state of the initial set, and the second dressing state of the superposition state set includes a non-zero contribution from the second qubit state of the initial set. The first and second dressing states are more sensitive to a magnetic field than the first and second qubit states. A non-zero magnetic field gradient exists at the target location and mediates the entanglement of two or more qubits positioned at the target location. The executable instruction, when executed by the processing device, uses a driver controller element and, after the gate time has elapsed, causes the controller to control the operation of the dressing field circuit so that the dressing field circuit stops generating a dressing field at the target location, so that the energy structure of each of the two or more qubits returns to their respective initial energy structures, which include a set of initial states.

[0053] In yet another embodiment, a computer program product is provided. The computer program product comprises a non-temporary computer storage medium for storing computer executable instructions. The computer executable instructions are configured, when executed by the controller's processing device, to cause the controller to use the controller's driver controller element to control the operation of a dressing field circuit, causing the dressing field circuit to generate a dressing field at a target location defined at least in part by a confinement device. The dressing field is configured to modify the energy structure of each of the one or more target qubits disposed at the target location by causing each set of initial states of one or more target qubits to form each set of superposition states. The first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states. A substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states effectively behave as clock states at the operable magnetic field amplitude.

[0054] This invention is described using general terminology, and while the accompanying drawings are provided for reference, they are not necessarily to scale. [Brief explanation of the drawing]

[0055] [Figure 1] This is a block diagram presenting an exemplary quantum system based on an exemplary quantum charge-coupled device (QCCD) according to one exemplary embodiment. [Figure 2] This is a schematic diagram showing a top view of an exemplary confinement region of a confinement device including a target position, according to an exemplary embodiment. [Figure 3] This is a schematic diagram showing an exemplary set of initial states and an exemplary set of superimposed states according to an exemplary embodiment. [Figure 4A] This is a flowchart illustrating the process and / or operation for executing a multi-qubit gate according to one exemplary embodiment. [Figure 4B] This figure illustrates the qubit sensitivity to the amplitude or intensity of the dressing field and the magnetic field, which change over time during the execution of a multi-qubit gate, according to one exemplary embodiment. [Figure 5A] This flowchart illustrates a process and / or operation for performing a clock state generation procedure according to an exemplary embodiment. [Figure 5B] This figure illustrates the qubit sensitivity to the amplitude or intensity of the dressing field and the magnetic field, which change over time during the execution of a clock state generation procedure, according to one exemplary embodiment. [Figure 6] This is a schematic diagram of an exemplary controller for a quantum system according to one exemplary embodiment. [Figure 7] This is a schematic diagram of an exemplary computing entity of a quantum system that may be used in one exemplary embodiment. [Modes for carrying out the invention]

[0056] Next, the present invention will be described in more detail below with reference to the accompanying drawings, which illustrate 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 described herein, but rather these embodiments are provided to satisfy the legal requirements to which this disclosure is applicable. The phrase "or" (also written as " / ") is used herein in both an alternative and a conjunctive sense unless otherwise noted. The phrases "exemplify" and "exemplary" are used as examples that do not indicate a level of quality. The phrases "generally" and "about" refer unless otherwise noted to being within the limits of appropriate engineering and / or manufacturing and / or within the user's measuring ability. Throughout, similar numbers refer to similar elements.

[0057] Exemplary embodiments provide a quantum system, a controller for the quantum system, and a corresponding method for controlling the sensitivity of a 0-Gauss clock state to an external magnetic field (e.g., a hyperfine state that functions as a clock state with a magnetic field amplitude / magnitude of 0 Gauss). For example, various embodiments provide a QCCD quantum computer using hyperfine split qubits, a controller for a QCCD-based quantum computer, and a corresponding method for controlling the sensitivity of qubits to an external magnetic field.

[0058] In various embodiments, quantum objects having a hyperfine splitting level are used as qubits in QCCD-based quantum computers. The hyperfine splitting level is a result of the nuclear magnetic dipole moment of a quantum object (e.g., an ion in one exemplary embodiment) interacting with the magnetic field generated by the electrons of the quantum object, and the nuclear electric quadrupole moment of the quantum object interacting with the electric field gradient caused by the charge distribution within the quantum object.

[0059] A pair of hyperfine splitting levels is a clock state at its respective magnetic field amplitude / magnitude. For example, at 0 Gauss, the F=2, m=0 and F=1, m=0 states of monovalent ionized Ba 137 are clock states. A clock state is a state that has the same energy / frequency dependence on an external magnetic field of a particular amplitude / magnitude (particularly the external magnetic field in the quantization direction of the quantized bit). For example, the energy difference between two clock states is constant at a particular magnetic field amplitude / magnitude for small changes or perturbations in the magnetic field. The term external magnetic field is used to identify a magnetic field that is independent of the qubit and / or quantum object. In this specification, the hyperfine structure of Ba 137 is used as an example, but in various embodiments, more than zero ions of various nuclear spins may be used as quantum objects, if appropriate for the application.

[0060] It should be understood that the magnetic quantum number m identifies the component of the orbital angular momentum of a quantum object, such as an atom or ion, positioned along a given axis. The given axis aligns with and / or defines the quantization direction of a qubit, and is commonly referred to as the z-axis within the reference frame of the qubit.

[0061] In exemplary embodiments, a quantum system, a controller for the quantum system, and a corresponding method are provided for controlling the sensitivity of qubits to an external magnetic field to increase the coherence time of one or more qubits.

[0062] In exemplary embodiments, a quantum system, a controller for the quantum system, and a corresponding method are provided for performing a multi-qubit gate by controlling the sensitivity of qubits to an external magnetic field to allow a non-zero magnetic field gradient to mediate the entanglement of two or more qubits.

[0063] In various embodiments, a qubit has an initial set of quantum states. The initial set of quantum states includes a first qubit state and a second qubit state in the qubit subspace of the initial set of quantum states. The initial set of states is defined, at least in part, by the hyperfine splitting of the quantum states of the quantum object that functions as a qubit. In various embodiments, controlling the sensitivity of the qubit to an external magnetic field involves causing a dressing field to exist at a target location defined, at least in part, by a confinement device. The dressing field interacts with the qubit located at the target location, causing the quantum states of the qubit to be dressed and / or modified to provide a set of superposition states. The dressing states of the set of superposition states are superpositions of two or more quantum states of the initial set of quantum states. The set of superposition states includes a first dressing state containing a non-zero contribution from the first qubit state and a second dressing state containing a non-zero contribution from the second qubit state.

[0064] By controlling various aspects of the dressing field (e.g., magnitude, frequency, and / or polarization), the coupling of a set of initial states resulting in a first dressing state and the coupling of a set of initial states resulting in a second dressing state can be controlled to provide a first dressing state and a second dressing state having a desired magnetic field sensitivity.

[0065] For example, in one exemplary embodiment, various aspects of the dressing field are controlled such that the first and second dressing states do not respond sensitively to changes in the external magnetic field in the system's magnetic field operating region.

[0066] In another example, in one exemplary embodiment, various aspects of the dressing field are controlled such that the first and second dressing states are sensitive to an external magnetic field, thereby allowing the non-zero magnetic field gradient to be used to mediate entanglement and / or other interactions between two or more qubits.

[0067] With respect to one or more target qubits positioned at the target location, the dressing field is slowly turned on and off so that the energy structure of each of the one or more target qubits is adiabatically dressed and / or modified from a set of initial states to a set of superposition states. As used herein, the phrase “slowly” refers to the dressing field being turned on and / or turned off on a slow timescale compared to the frequency difference between the first dressing state and the second dressing state and / or the frequency difference between the first qubit state and the second qubit state. For example, the time elapsed while the dressing field is turned on from zero amplitude to a set amplitude (e.g., the dressing amplitude and / or gate amplitude), and the time elapsed while the dressing field is turned off from the set amplitude (e.g., the dressing amplitude and / or gate amplitude) to zero amplitude, are, respectively, longer than 1 of the frequency difference between the first dressing state and the second dressing state (e.g., greater than the reciprocal of the frequency difference between the first dressing state and the second dressing state) and / or longer than 1 of the frequency difference between the first qubit state and the second qubit state (e.g., greater than the reciprocal of the frequency difference between the first qubit state and the second qubit state).

[0068] In large quantum charge-coupled device (QCCD) based quantum computers using hyperfine split qubits, operating at low magnetic field amplitudes (e.g., less than 10G) allows for the provision of a uniform magnetic field. In addition, to enable energy splitting of the hyperfine states, the quantum processor is made to operate at magnetic field amplitudes greater than 0G. Generally, a set of low F (e.g., F=0, 1, and / or 2), m=0 states is used to define the qubit subspace of the qubit. However, these m=0 states only function as clock states at a magnetic field amplitude of 0G. Therefore, when operating in a magnetic field with amplitudes in the range of 2-5G, the m=0 states are not clock states (e.g., they have energies / frequencies that are sensitive to changes in the magnetic field). This results in memory errors and / or reduced memory coherence time in conventional QCCD-based quantum computers using hyperfine split qubits. Thus, there is a technical problem regarding extending the coherence time of the hyperfine split qubits in QCCD-based quantum computers.

[0069] Various embodiments provide technical solutions to these technical problems. For example, various embodiments provide control over the sensitivity of a qubit to an external magnetic field. For example, in various embodiments, a dressing field is generated at the target location. The dressing field causes the energy structure of the qubit located at the target location to be modified such that the initial set of states of the qubit located at the target location is made to form a set of superposition states. The set of superposition states includes a first dressing state of the set of superposition states, which includes a non-zero contribution from a first qubit state of the initial set of states, and a second dressing state of the set of superposition states, which includes a non-zero contribution from a second qubit state of the initial set of states. The first and second dressing states effectively behave as clock states at the magnetic field amplitude / magnitude in which the system is operating. When the first and second dressing states effectively behave as clock states, the coherence time of the qubit is virtually infinite while the qubit is in the first and / or second dressing states. Therefore, various embodiments result in an extension of the qubit coherence time, which reduces memory errors and enables the execution of deeper quantum circuits. Thus, various embodiments offer improvements over conventional QCCD-based quantum computers.

[0070] Furthermore, executing conventional quantum logic gates requires a radiating field, such as a laser beam, microwave, and / or similar, to realize, mediate, and / or induce entanglement of qubits. However, these radiating fields can introduce various gate errors, such as affecting transitions in the spectator qubit, which can lead to photon scattering and / or crosstalk problems, phase noise, and / or similar. These gate errors can result in low-fidelity logic gates and noisy computations. Moreover, quantum logic gates that use radiating fields are highly sensitive to the state of one or more motion modes of the qubit. Thus, spin-motion coupling can introduce additional gate errors, and / or require significant time to cool the qubit to a state close to its motion ground state before executing the quantum logic gate. Consequently, various technical problems exist regarding the execution of quantum logic gates.

[0071] One possible technical solution to these technical problems is to use a non-zero magnetic field gradient to realize, mediate, and / or induce qubit entanglement. However, for such an interaction to be performed within a reasonable time, this requires the qubit to be sensitive to the magnetic field. Conventionally, causing a qubit to be sensitive to a magnetic field involves performing a shelving process in which the qubit state of the qubit is shelved to a state outside the qubit subspace that is sensitive to the magnetic field. However, this shelving is performed by driving the transition from the qubit state to the shelved state with a laser, and thus can introduce crosstalk problems, phase noise, and / or similar. Thus, technical problems exist regarding the implementation of quantum logic gates.

[0072] Various embodiments provide technical solutions to these technical problems. In particular, a dressing field may be applied to two or more qubits rather than shelving the qubits to allow a non-zero magnetic field gradient to realize, mediate, and / or induce entanglement of two or more qubits. The dressing field causes the energy structure of each qubit placed at the target position to be modified such that each set of initial states of the qubits placed at the target position is made to form each set of superposition states. The set of superposition states includes a first dressing state of the set of superposition states, which includes a non-zero contribution from a first qubit state of the set of initial states, and a second dressing state of the set of superposition states, which includes a non-zero contribution from a second qubit state of the set of initial states. The first and second dressing states are more sensitive to the magnetic field than these qubit states. A non-zero magnetic field gradient present at the target position can realize, mediate, and / or induce entanglement of two or more qubits. Therefore, various embodiments enable the execution of multi-qubit gates without the use of lasers and without the introduction of various errors (such as crosstalk, phase noise, and / or similar) that may be induced by the use of lasers in such systems. Thus, various embodiments offer improvements over conventional QCCD-based quantum computers.

[0073] Examples of QCCD-based quantum systems An exemplary system that can be configured to perform qubit magnetic field sensitivity control in various embodiments is a quantum charge-coupled device (QCCD) based quantum system using hyperfine split qubits. Figure 1 presents a schematic diagram of an exemplary QCCD-based quantum system 100 that can be used to perform qubit magnetic field sensitivity control in various embodiments. The exemplary QCCD-based quantum system 100 shown in Figure 1 is at least part a quantum computer system comprising a confinement device 50 that defines at least one target position 55. For example, the confinement device 50 is configured to confine one or more qubits. In one exemplary embodiment, the confinement device 50 is an ion trap (e.g., a surface ion trap and / or pole trap), and the qubits are ions. In various embodiments, the confinement device 50 comprises or is physically associated with a dressing field circuit 70 that is operable to generate a dressing field at the target position 55.

[0074] In various embodiments, the dressing field circuit 70 is either part of the confinement device 50 (for example, disposed on and / or embedded on the same substrate and / or chip as the confinement device 50) or a circuit (e.g., a printed circuit) disposed in physical proximity to the confinement device 50 so that the qubits disposed at and / or confined at the target position 55 are subject to the action of the dressing field when the dressing field circuit 70 is operated. For example, in one exemplary embodiment, the dressing field circuit 70 is lithographically printed on the confinement device 50. In various embodiments, the dressing field is a microwave field.

[0075] In various embodiments, the confinement device 50 is configured to confine a qubit within one or more confinement regions defined by the confinement device 50. In various embodiments, the qubit is a neutral or charged atom, a neutral, charged, or multipolar molecule, a quantum particle, a quantum dot, or any other object that can be confined by the confinement device and has an energy structure that can be manipulated through one or more dressing fields, and / or is embodied as such. For example, in one exemplary embodiment, the confinement device 50 is an ion trap (e.g., a surface ion trap and / or a pole ion trap), and the qubit is an ion with a non-zero nuclear spin.

[0076] In various embodiments, the QCCD-based quantum system 100 comprises a computing entity 10 and a quantum computer 110. In various embodiments, the quantum computer 110 comprises a controller 30 and a quantum processor 115. In various embodiments, the quantum processor 115 comprises a cryogenic and / or vacuum chamber 40 surrounding a confinement device 50 and associated dressing field circuit 70, one or more operating sources (e.g., a laser 60, a microwave source 62), and a magnetic field source 90. In one exemplary embodiment, the one or more operating sources include one or more light sources such as a laser 60, one or more microwave sources 62, and / or similar.

[0077] In various embodiments, one or more lasers 60 are configured to generate and / or provide an operation signal (e.g., a light beam) configured to manipulate and / or induce the development of a controlled quantum state of one or more quantum objects confined by the confinement device 50. In various embodiments, one or more microwave sources 62 are configured to generate and / or provide a gate microwave signal configured to cause the execution of a single qubit gate on a target qubit having a dressed and / or modified energy structure (e.g., an energy structure comprising a set of superposition states including a first dressing state and a second dressing state). For example, in one exemplary embodiment, one or more operation sources are configured to deliver the operation signal (e.g., a light / laser beam in the case of lasers 60 and / or a microwave gate signal in the case of microwave sources 62) to respective target locations defined at least in part by the confinement device 50 in the cryogenic and / or vacuum chamber 40 via their respective beam delivery systems 66 (e.g., 66A, 66B). In various embodiments, the beam delivery system 66 includes one or more optical elements, photonic integrated circuits (PICs), optical fibers, free-space optical elements, waveguides, and / or similar. In an exemplary embodiment, the microwave source 62 is a circuit formed on a substrate housing the confinement device 50, and / or on another substrate disposed within the cryogenic and / or vacuum chamber 40, mounted on the confinement device 50, and / or fixed with respect to the confinement device 50. For example, in an exemplary embodiment, the microwave source 62 is an integrated circuit configured to carry an alternating current (AC) current of GHz frequency.

[0078] In various embodiments, the quantum processor 115 includes one or more magnetic field sources 90 (see Figure 2). In various embodiments, the magnetic field sources 90 may be permanent magnets (e.g., made from ferromagnetic material) and / or electromagnets. One or more magnetic field sources 90 may be fixed to a substrate housing the confinement device 50 and / or otherwise mounted in some way within the cryogenic and / or vacuum chamber 40. For example, the magnetic field sources 90 may be similar to those described in U.S. Patent Application No. 63 / 509,098 filed June 20, 2023, the entire contents of which are incorporated herein by reference. In various embodiments, one or more magnetic field sources 90 are configured to generate a non-zero magnetic field gradient at each target position 55 of the confinement device 50 (e.g., each target position configured to perform a multi-qubit gate therein). In one exemplary embodiment, a target position 55 configured for performing a clock state generation procedure may not have a magnetic field source 90 disposed therein.

[0079] In various embodiments, the quantum processor 115 further comprises a plurality of voltage and / or current sources 80. The voltage and / or current sources 80 are operable (for example, by a controller 30) to generate and supply voltage or current signals to electrical elements (e.g., electrodes) of the confinement device 50, one or more dressing field circuits 70, one or more magnetic field sources 90 (in an example, one or more magnetic field sources 90 being electromagnets), and / or similar.

[0080] In various embodiments, the computing entity 10 is configured to allow a user to supply input to the quantum computer 110 (for example, through the user interface of the computing entity 10), receive and display outputs from the quantum computer 110, and / or perform similar operations on them. The computing entity 10 may communicate with the controller 30 of the quantum computer 110 via one or more wired or wireless networks 20 and / or via direct wired and / or wireless communication. In exemplary embodiments, the computing entity 10 may translate, configure, format, and / or perform similar operations on information / data, quantum computing algorithms and / or similar into computing languages, executable instructions, command sets and / or similar that the controller 30 can understand and / or implement.

[0081] In various embodiments, the controller 30 is configured to control a voltage and / or current source 80, a cryogenic system and / or vacuum system that controls the temperature and pressure within the cryogenic and / or vacuum chamber 40, an operating source (e.g., a laser 60, a microwave source 62, and / or similar), and / or other systems that control environmental conditions within the cryogenic and / or vacuum chamber 40 (e.g., temperature, humidity, pressure, and / or similar), or confinement device 50 (magnetic field source 90 in embodiments where the magnetic field source includes an electromagnet) and operate and / or induce a controlled evolution of the quantum state of one or more qubits confined by the confinement device.

[0082] Figure 2 illustrates a top view of a portion of the confinement device 50. The illustrated portion of the confinement device 50 includes radio frequency (RF) rails 210A, 210B and three rows of control electrodes 212A, 212B, 212C. Each row of control electrodes 212 includes a plurality of control electrodes 214. For example, the illustrated portion of the row of control electrodes 212A includes control electrodes 214A, 214B, ..., 214N.

[0083] In various embodiments, the RF voltage source of the voltage and / or current source 80 is applied to the RF rails 210A and 210B to generate and provide RF voltage signals that create pseudopotentials defining one or more linear confinement regions 200 of the confinement device 50. The null points of the pseudopotentials generated by the RF voltage signals applied to the RF rails 210A and 210B define an RF null axis 216 that substantially extends along the centerline of the linear confinement region 200. Quantum objects confined by the confinement device 50 are confined within one or more linear confinement regions 200.

[0084] In various embodiments, the confinement device 50 and the dressing field circuit 70 define a target position 55. The qubit is subject to the dressing field when it is confined within the target position 55 by the confinement device 50 (and the dressing field circuit 70 operates to generate the dressing field). In various embodiments, the dressing field is a microwave field (for example, oscillating at a frequency in the range of 100 MHz to 500 GHz).

[0085] In various embodiments, the dressing field circuit 70 is either part of the confinement device 50 (for example, disposed and / or embedded on the same substrate and / or chip as the confinement device 50) or a circuit (e.g., a printed circuit) disposed in physical proximity to the confinement device 50 so that the qubits disposed and / or confined at the target position 55 are subject to the action of the dressing field when the dressing field circuit 70 is operated. For example, in one exemplary embodiment, the dressing field circuit 70 is lithographically printed on the confinement device 50. In various embodiments, the controller 30 is configured to control the operation of the dressing field circuit 70 by controlling the operation of a voltage and / or current source 80 configured to supply voltage and / or current signals to the dressing field circuit 70.

[0086] In various embodiments, the dressing field circuit 70 is configured to generate a dressing field, which is a microwave field having polarization in a plane perpendicular to the quantization field of the confinement device 50. The quantization field of the confinement device 50 defines the quantization direction of the qubits confined by the confinement device 50. In various embodiments, the quantization field is a substantially static magnetic field that is generally uniform on the confinement device 50. In one exemplary embodiment, the quantization field enters or exits the page in Figure 2, and the polarization of the dressing field lies in the plane of the page in Figure 2.

[0087] In various embodiments, the dressing field circuit 70 is configured to generate a dressing field having an amplitude that decays significantly and / or rapidly outside the target position 55. For example, the dressing field circuit 70 is configured to generate a dressing field that decays and / or decreases outside the target position 55, so as to cause a trackable AC Zeeman shift on one or more additional qubits confined by the confinement device and located outside the target position. The trackable AC Zeeman shift may be accounted for by the quantum system 100 so as not to lead to errors or gate infidelity.

[0088] For example, target qubits 5A and 5B, located and / or confined at target position 55, are subjected to the action of the dressing field (e.g., while the dressing field circuit 70 is operating), which causes the energy structures of each target qubit 5A and 5B to be modified and / or dressed to include their respective sets of superposition states. An additional qubit 5C is located and / or confined outside of target position 55. The additional qubit 5C has an energy structure that includes its initial set of states. For example, the energy structure of the additional qubit 5C is not dressed and / or modified to include its set of superposition states. The additional qubit 5C may undergo a trackable and / or computable AC Zeeman shift. For example, the AC Zeeman shift that the additional qubit 5C undergoes may be determined and tracked (e.g., by the controller 30) so that the AC Zeeman shift that the additional qubit 5C undergoes is tracked and / or considered by the quantum system 100. For example, the AC Zeeman shift experienced by the additional qubit 5C is tracked and / or taken into consideration so as not to cause errors in the computations and / or controlled quantum state evolution performed by the quantum system 100. For example, a trackable AC Zeeman shift could cause the phase of the additional qubit 5C to evolve at a different rate than if the additional qubit 5C were located further away from the target position 55 and / or if the dressing field was not turned on.

[0089] Figure 3 illustrates at least a portion of the set of initial states 310 of a qubit. The set of initial states 310 includes the qubit subspace 312 of the energy structure of the qubit. The qubit subspace 312 includes a first qubit state 314A and a second qubit state 314B. The energy difference between the first qubit state 314A and the second qubit state 314B is the qubit frequency difference Δf qcorresponds to. For example, the energy difference ΔE between the first qubit state 314A and the second qubit state 314B q is equal to the qubit frequency difference Δf multiplied by Planck's constant h (e.g., ΔE q =hΔf q ) q .

[0090] In the illustrated embodiment, corresponding to the exemplary use of singly ionized Ba137 as the qubit 5, the set of initial states 310 includes the F=2, m=1, F=2, m=0, F=2, m=-1, F=1, m=1, F=1, m=0, F=1, m=-1 states. The qubit subspace 312 includes the F=2, m=0 and F=1, m=0 states. For example, in the illustrated embodiment, the first qubit state 314A is the F=2, m=0 state, and the second qubit state 314B is the F=1, m=0 state. In various other embodiments where various other quantum objects are used as qubits, various other sets of initial states are present, along with corresponding selections of the qubit subspace and the first and second qubit states, as appropriate for the application. In the illustrated embodiment, the dressing field, illustrated by the two-dot chain line, couples the first qubit state 314A (e.g., the F=2, m=0 state) with one or more states that are sensitive to magnetic fields (e.g., the F=1, m=±1 states), and couples the second qubit state 314B (e.g., the F=1, m=0 state) with one or more different states that are sensitive to magnetic fields (e.g., the F=2, m=±1 states).

[0091] Figure 3 also illustrates at least a portion of the set of superposition states 320. The set of superposition states 320 includes at least two dressing states that are each a superposition of a respective state of the set of initial states 310. For example, the dressing state ψ d is a superposition of multiple initial states ψ of the set of initial states 310 i (e.g., with coefficients α and initial states ψ i denoted with a superscript j, using Einstein's summation convention, ψ d =α j ψi j It is formed by a combination of ) and / or receives contributions from them.

[0092] The set of superposition states 320 includes a first dressing state 324A. The first dressing state 324A includes a non-zero contribution from the first qubit state 314A. For example, the coefficient α corresponding to the first qubit state 314A in the mathematical representation of the first dressing state 324A is non-zero. In one exemplary embodiment, the first dressing state 324A does not include a contribution from the second qubit state 314B. For example, the coefficient α corresponding to the second qubit state 314B in the mathematical representation of the first dressing state 324A is zero. In the exemplary embodiment illustrated, the first dressing state 324A includes non-zero contributions from the F=1, m=±1 states and F=2, m=0 states (e.g., the first qubit state 314A) of the initial set of states 310.

[0093] The set of superposition states 320 further includes a second dressing state 324B. The second dressing state 324B includes a non-zero contribution from a second qubit state 314B. For example, the coefficient α corresponding to the second qubit state 314B in the mathematical representation of the second dressing state 324B is non-zero. In one exemplary embodiment, the second dressing state 324B does not include a contribution from the first qubit state 314A. For example, the coefficient α corresponding to the first qubit state 314A in the mathematical representation of the second dressing state 324B is zero. In the exemplary embodiment illustrated, the second dressing state 324B includes non-zero contributions from the F=2, m=±1 states and F=1, m=0 states (e.g., the second qubit state 314B) of the initial set of states 310.

[0094] Notably, the first dressing state 324A and the second dressing state 324B include non-zero contributions from different and / or non-overlapping groups of states from the set of initial states 310.

[0095] The energy difference between the first dressing state 324A and the second dressing state 324B is the dressing frequency difference Δf d This corresponds to the energy difference ΔE between the first dressing state 324A and the second dressing state 324B. d This is the dressing frequency difference Δf multiplied by Planck's constant h. d Equal to (for example, ΔE d =hΔf d ).

[0096] In various embodiments, the dressing frequency difference Δf d This is the qubit frequency difference Δf q This is different. For example, in various embodiments, the dressing frequency difference Δf d and the qubit frequency difference Δf q The difference between them is in the range of 0.1 to 20 MHz (for example, 0.1 MHz ≤ |Δf d -Δf q (≤20MHz).

[0097] Due to the contribution of quantum states having non-zero magnetic quantum numbers m to the first dressing state 324A and the second dressing state 324B, the first dressing state 324A and the second dressing state 324B have different sensitivities to the external magnetic field than the first qubit state 314A and the second qubit state 314B. For example, by combining multiple states from the set of initial states 310 to form each dressing state, a dressing state is obtained that is a hybrid of each of the combined states and / or has properties influenced by them. The combination of various states from the set of initial states 310 can therefore be tuned to produce a dressing state with desired properties, such as a desired dependence on the external magnetic field (e.g., at least a component of the external magnetic field aligned with the quantization axis of the confinement device 50).

[0098] For example, based on the desired characteristics of the dressing state and the known characteristics of the set of initial states 310, a desired coupling that gives the desired characteristics of the dressing state can be determined. The dressing field circuit 70 is then engineered and / or designed to be capable of operating to generate a dressing field that achieves the desired coupling.

[0099] For example, in various embodiments, the first dressing state 324A and the second dressing state 324B may be more sensitive to an external magnetic field than the first qubit state 314A and the second qubit state 314B. For example, in one exemplary embodiment, a small change in the external magnetic field may cause a larger change in the respective energy / frequency of the first dressing state 324A and the second dressing state 324B compared to the first qubit state 314A and the second qubit state 314B. In another example, in one exemplary embodiment, a small change in the external magnetic field may cause a qubit frequency difference Δf between the first qubit state 314A and the second qubit state 314B. q In comparison, the dressing frequency difference Δf between the first dressing state 324A and the second dressing state 324B d This can lead to larger changes. For example, the combination of the set of initial states 310 resulting in the first dressing state 324A and the second dressing state 324B can be tuned to be sufficiently sensitive to an external magnetic field (and / or a component of the external magnetic field aligned with the quantization direction of the confinement device 50) that the first dressing state 324A and the second dressing state 324B can realize, mediate, and / or cause the entanglement of two or more qubits located within the target position 55 within a set length of time (e.g., gate time) of a non-zero magnetic field gradient.

[0100] In another example, in various embodiments, the first dressing state 324A and the second dressing state 324B may not be as sensitive to an external magnetic field as the first qubit state 314A and the second qubit state 314B. For example, in one exemplary embodiment, a small change in the external magnetic field may cause a smaller change in the respective energy / frequency of the first dressing state 324A and the second dressing state 324B compared to the first qubit state 314A and the second qubit state 314B. In another example, in one exemplary embodiment, a small change in the external magnetic field may cause a qubit frequency difference Δf between the first qubit state 314A and the second qubit state 314B. q In comparison, the dressing frequency difference Δf between the first dressing state 324A and the second dressing state 324B d This can cause smaller changes.

[0101] For example, in one exemplary embodiment, the first qubit state 314A and the second qubit state 314B, which are nearly clock states, have a specific energy dependence on the external magnetic field in the operable magnetic field amplitude / magnitude of the quantum system 100. The dressing field is tuned so that the coupling of the set of initial states 310 results in an AC Zeeman shift that has a linear dependence on the quantization-direction component of the external magnetic field, which is of the same magnitude as the energy dependence of the qubit states on the external magnetic field but with the opposite sign. This causes the resulting first dressing state 324A and the second dressing state 324B, caused by the coupling introduced by the dressing field, to effectively behave as clock states in the non-zero operable magnetic field amplitude / magnitude used when the quantum system 100 (e.g., a QCCD-based quantum computer) operates. In other words, the dressing field is tuned so that the respective energies / frequencies of the first dressing state 324A and the second dressing state 324B have the same dependence on the change in the external magnetic field (quantization-direction component). As a result, even if the target qubit is subjected to small changes in the external magnetic field (e.g., noise and / or perturbations), the dressing frequency difference Δf remains unchanged. d It is constant.

[0102] A qubit confined by the confinement device 50 can be transported between different locations within the confinement device 50 through the application of a set of voltage signal sequences (e.g., generated by a voltage and / or current source 80) to the control electrode 212. For example, one qubit (or more qubits) can be transported into and / or out of the target location 55 and / or other locations defined by the confinement device 50. For example, the controller 30 is configured to control the voltage and / or current source 80 to trigger the execution of transport operations for a qubit (or group of qubits) between various locations defined by the confinement device 50.

[0103] In one exemplary embodiment, the confinement device 50 includes and / or defines a single linear confinement region 200. In various embodiments, the confinement device 50 includes and / or defines a plurality of linear confinement regions 200 and / or an array of linear confinement regions 200. For example, in one exemplary embodiment, the confinement device 50 includes a two-dimensional array of linear confinement regions 200.

[0104] Exemplary behavior of a quantum system for executing multi-qubit gates In various systems, quantum systems, such as QCCD-based quantum system 100, are capable of operating to perform single-qubit gates. In various embodiments, performing a single-qubit gate includes modifying and / or dressing the energy structure of a target qubit by adiabatically applying a dressing field to the target qubit, and applying a gate microwave signal to the target qubit that is tuned and / or resonates with a dressing frequency difference corresponding to the modified and / or dressed energy structure of the target qubit.

[0105] Figure 4A presents a flowchart of the processes, procedures, operations, and / or similar actions performed by the controller 30 of the quantum system 100 to execute a multi-qubit gate, according to an exemplary embodiment. In various embodiments, a multi-qubit gate is executed as part of executing a quantum circuit and / or algorithm. For example, a multi-qubit gate may be executed to entangle two or more qubits.

[0106] In various embodiments, the qubits 5 (e.g., 5A, 5B, 5C) confined by the confinement device 50 can be transported between various locations defined by the confinement device 50. For example, the qubits 5 can be transported into or out of a target location 55. In various embodiments, starting from step 402, the controller 30 causes two or more target qubits 5A, 5B, which are to be entangled via the execution of a multi-qubit gate, to be located within the target location 55. For example, in cases where one or more of the target qubits 5A, 5B are located outside the target location 55, the controller 30 controls the operation of one or more voltage and / or current sources 80 (e.g., via one or more driver controller elements 615, see Figure 6) to cause the target qubits 5A, 5B to be transported within the range of the target location 55. In an example where at least one of the target qubits 5A, 5B is positioned within the target position 55, the controller 30 controls the operation of one or more voltage and / or current sources (for example, via one or more driver controller elements 615, see Figure 6) to ensure that at least one of the target qubits 5A, 5B remains positioned within the target position 55.

[0107] In step 404, while the target qubits 5A and 5B are positioned, placed, and / or confined within the target position 55, the controller 30 controls the operation of the dressing field circuit 70 to cause the generation of a dressing field at the target position 55. For example, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70, causing the dressing field circuit to generate a dressing field. For example, in an exemplary embodiment, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70 that increase (for example, from zero amplitude towards a non-zero amplitude of the target).

[0108] From the perspective of target qubits 5A and 5B, the dressing field is slowly turned on so that the energy structure of each target qubit is adiabatically dressed and / or modified from each set of initial states 310 to the set of superposition states 320. The phrase “slowly” as used herein relates to the dressing field being turned on on a slow timescale (for the execution of a multi-qubit gate) compared to the qubit frequency difference and / or dressing frequency difference. For example, the time elapsed while the dressing field is turned on from zero amplitude to gate amplitude is longer than 1 of the dressing frequency difference (e.g., the dressing frequency difference Δf d (greater than the reciprocal of Δf) and / or longer than 1 of the qubit frequency difference (for example, qubit frequency difference Δf q (Greater than the reciprocal of ).

[0109] For example, FIG. 4B presents a plot illustrating the evolution of the amplitude of the dressing field 420 with respect to time during execution of the multi-qubit gate. FIG. 4B also illustrates the sensitivity 430 of the target qubits 5A, 5B to the (quantization direction component) of the external magnetic field with respect to time during execution of the multi-qubit gate.

[0110] For example, at the initial time t0, the amplitude of the dressing field is zero. During the turn-on time period 422 spanning from the initial time t0 to the first time t1 (t0<t1), the amplitude of the dressing field increases from zero to the gate amplitude A g . In the illustrated embodiment, the increase in the amplitude of the dressing field is linear over the turn-on time period 422. Various other functional forms may be used to increase the amplitude of the dressing field in a manner that increases monotonically starting from the initial time t0 up to the first time t1.

[0111] In various embodiments, the turn-on time period is longer than the reciprocal of the dressing frequency difference (for example, t1-t0>1 / Δf d ), and / or longer than the reciprocal of the qubit frequency difference (for example, t1-t0>1 / Δf q ). The slow turn-on of the dressing field and / or the increase in amplitude causes the respective energy structures of the target qubits 5A, 5B to be adiabatically dressed and / or modified, whereby the quantum information preserved by the target qubits 5A, 5B is maintained (for example, not destroyed) by the turn-on of the dressing field.

[0112] As the amplitude of the dressing field increases (slowly), the strength of the coupling caused by the dressing field increases. Since the first dressing state 324A and the second dressing state 324B are more sensitive to the magnetic field than the first qubit state 314A and the second qubit state 314B, increasing the amplitude of the dressing field causes the target qubits 5A and 5B to be more sensitive to at least the quantization-direction component of the external magnetic field. For example, at initial time, the target qubits 5A and 5B have an initial sensitivity level S to the quantization-direction component of the external magnetic field. i It has the following characteristics. At the first time t1, the target qubits 5A and 5B have a gate sensitivity level S with respect to the component of the external magnetic field in the quantization direction. g It holds.

[0113] In various embodiments, the sensitivity of target qubits 5A and 5B to the components of an external magnetic field in the quantization direction corresponds to the derivative of the energy level of target qubits 5A and 5B with respect to the components of an external magnetic field in the quantization direction. In an exemplary embodiment, the sensitivity of target qubits 5A and 5B to the components of an external magnetic field in the quantization direction corresponds to the derivative of the energy difference between a first state of the instantaneous energy structure of the qubit having a non-zero contribution from the first qubit state 314A and a second state of the instantaneous energy structure of the qubit having a non-zero contribution from the second qubit state 314B. For example, the initial sensitivity of the target qubit to the components of an external magnetic field in the quantization direction (e.g., sensitivity at initial time t0) is the derivative of the qubit frequency difference with respect to the components of the external magnetic field in the quantization direction, and the gate sensitivity of the target qubit to the components of an external magnetic field in the quantization direction (e.g., sensitivity at first time t1) is the derivative of the dressing frequency difference with respect to the components of the external magnetic field in the quantization direction.

[0114] In step 406, the controller 30 enables the target qubits 5A and 5B to be affected by a non-zero magnetic field gradient present at the target position 55 between a first time t1 and a second time t2. The time between the first time t1 and the second time t2 is a gate time period 424 configured to give the two or more target qubits 5A and 5B sufficient time to interact (mediated by the non-zero magnetic field gradient present at the target position 55) and to cause entanglement of the two or more target qubits 5A and 5B. For example, the length of the gate time period 424 (e.g., t2-t1) is determined based at least in part on the length of time required for the non-zero magnetic field gradient to mediate / realize / cause entanglement of the two or more target qubits located at the target position 55, taking into account the sensitivity of the first dressing state 324A and the second dressing state 324B to the external magnetic field (and / or its component in the quantization direction).

[0115] In one exemplary embodiment, the magnetic field gradient has an amplitude / magnitude greater than 100 T / m, and the gate time period is 10 4 The duration is less than μs. In an exemplary embodiment, the magnetic field gradient has an amplitude / magnitude greater than 200 T / m, and the gate time period is 3 × 10⁻⁶. 3 It is less than μs. In an exemplary embodiment, the magnetic field gradient has an amplitude / magnitude greater than 300 T / m, and the gate time period is 10 3 It is less than μs. For example, in various embodiments, the gate time period is determined at least in part as a function of the magnetic field gradient amplitude / magnitude, the sensitivity of the target qubit to an external magnetic field, and / or the like, and / or the like.

[0116] In an exemplary embodiment, the magnetic field source 90 may be a permanent magnet (for example, including a ferromagnetic material), and the controller 30 may run a timer to ensure that the target qubits 5A, 5B are acted upon by a non-zero magnetic field gradient generated by the magnetic field source 90 over a gate time period 424. In another example, the magnetic field source 90 may be an electromagnet, and the controller 30 may cause a voltage and / or current source 80 (for example, via a driver controller element 615) to supply an appropriate voltage and / or current signal to the electromagnet, causing the electromagnet to generate a non-zero magnetic field gradient for a duration of at least a gate time period 424. In an exemplary embodiment where the magnetic field source 90 is an electromagnet, the controller 30 may run a timer to ensure that the target qubits 5A, 5B are acted upon by a non-zero magnetic field gradient generated by the magnetic field source 90 over a gate time period 424.

[0117] In one exemplary embodiment, the non-zero magnetic field gradient is a static magnetic field gradient and is generally constant over the gate time period 424. In one exemplary embodiment, the magnetic field gradient is an oscillating magnetic field gradient that oscillates at a frequency lower than the motion frequency of one or more motion modes of the target qubits 5A, 5B. For example, the magnetic field gradient may oscillate so that the spin-motion coupling of the target qubits is reduced and / or eliminated through the interaction of the target qubits with the magnetic field gradient during the execution of a multi-qubit gate.

[0118] In response to the controller 30 determining that the target qubits 5A and 5B have been subjected to a non-zero magnetic field gradient over a gate time period of 424, the process proceeds to step 408. For example, in response to the controller determining that the time has reached a second time t2, the controller 30 proceeds to step 408.

[0119] In step 408, the controller 30 controls the operation of the dressing field circuit 70 to cause the generation of the dressing field at the target position 55 to stop. For example, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70, which causes the dressing field circuit to stop generating the dressing field. For example, in an exemplary embodiment, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70 that decrease (for example, from a previous amplitude toward zero amplitude).

[0120] From the perspective of two or more target qubits 5A, 5B, the dressing field is slowly turned off so that the energy structure of each target qubit is adiabatically dedressed and / or returned to its original energy structure. For example, the energy structure of each target qubit is dedressed and / or modified so that the set of superposition states is adiabatically returned to the set of initial states. As used herein, the phrase “slowly” refers to the dressing frequency difference Δf d and / or qubit frequency difference Δf q This relates to the dressing field being turned off at slower timescales (after the execution of a multi-qubit gate) compared to [the previous timescale]. For example, if the dressing field is gate amplitude A g The time elapsed between turning off from zero amplitude is longer than 1 of the dressing frequency difference (e.g., greater than the reciprocal of the dressing frequency difference) and / or longer than 1 of the qubit frequency difference (e.g., greater than the reciprocal of the qubit frequency difference).

[0121] For example, at a second time t2 (t1<t2), the amplitude of the dressing field is the gate amplitude A g . During a turn-off time period 426 extending from the second time t2 to a third time t3 (t2<t3), the amplitude of the dressing field is the gate amplitude A g decreasing to zero. In the illustrated embodiment, the decrease in the amplitude of the dressing field is linear over the turn-off time period 426. Various other functional forms may be used to decrease the amplitude of the dressing field in a manner that monotonically decreases from the second time t2 to the third time t3.

[0122] In various embodiments, the turn-off time period is longer than the reciprocal of the dressing frequency difference (for example, t3-t2>1 / Δf d ), and / or longer than the reciprocal of the qubit frequency difference (for example, t3-t2>1 / Δf q ). The slow turn-off and / or amplitude decrease of the dressing field causes the respective energy structures of the target qubits 5A, 5B to be adiabatically undressed and / or modified, whereby the quantum information preserved by the respective target qubits 5A, 5B is maintained (for example, not destroyed) by the turn-off of the dressing field.

[0123] As the amplitude of the dressing field (slowly) decreases, the strength of the coupling induced by the dressing field decreases. Since the first qubit state 314A and the second qubit state 314B are less sensitive to magnetic fields than the first dressed state 324A and the second dressed state 324B, the decrease in the amplitude of the dressing field causes the target qubits 5A, 5B to become less sensitive to the external magnetic field (at least its component in the quantization direction). For example, at the second time t2, the target qubits 5A, 5B have a gate sensitivity level S to the component of the external magnetic field in the quantization direction gIt has the following characteristics. At the third time t3, the target qubits 5A and 5B have an initial sensitivity level S to the component of the external magnetic field in the quantization direction. i (Si <Sg)。

[0124] In various embodiments, the controller 30 determines information regarding the AC Zeeman shifts given to one or more additional qubits 5C located and / or positioned outside the target position 55 as a result of a dressing field being generated at the target position 55 (for example, between the initial time t0 and the third time t3). For example, the amplitude of the dressing field decays rapidly with distance from the target position 55, but additional qubits 5C located and / or positioned outside the target position 55 may be affected by the dressing field at a low amplitude / intensity. For example, additional qubits 5C located and / or positioned outside the target position 55 are not affected by a dressing field of sufficiently high amplitude / intensity so that the energy structure of the additional qubits 5C is dressed and / or modified in the same way as the target qubits 5A, 5B. Furthermore, the non-zero magnetic field gradient decays rapidly with distance from the target position 55. Therefore, the additional qubits 5C are not affected by any adjacent additional qubits in such a manner that the target qubits 5A, 5B are located within the range of the target position 55. Therefore, the additional qubit 5C is unaffected by dressing fields beyond the traceable AC Zeeman shift.

[0125] A low-amplitude / intensity dressing field acting on the additional qubit 5C causes the additional qubit 5C to be subjected to an AC Zeeman shift, which is the magnetic counterpart or version of the AC Stark shift. In particular, the oscillating magnetic field of the dressing field interacting with the additional qubit 5C can change the rate or percentage at which the additional qubit 5C accumulates phase. As such, a phase accumulator corresponding to the additional qubit 5C and stored in the classical memory of the controller 30 (e.g., memory 610, see Figure 6) can be updated based on the AC Zeeman shift acting on the additional qubit 5C.

[0126] For example, the classical memory 610 of the controller 30 may store a phase accumulator corresponding to each qubit confined by the confinement device 50. The phase accumulator corresponding to each qubit may be updated periodically, regularly, and / or continuously, or triggered, to reflect the phase accumulated by each qubit. In various embodiments, the memory 610 stores executable instructions for calculating and / or determining information corresponding to the AC Zeeman shift experienced by each qubit, based on the distance of each qubit from the target position 55 (controlling the amplitude / intensity of the dressing field experienced by each qubit), the gate time period (e.g., the elapsed time between a first time t1 and a second time t2) or the elapsed time between an initial time and a third time (e.g., t3-t0), and / or other information corresponding to the AC Zeeman shift experienced by each qubit. In an exemplary embodiment, the memory 610 stores executable instructions for using information regarding the AC Zeeman shift experienced by each qubit to update the phase accumulator corresponding to each qubit. The processing device 605 of the controller 30, in various embodiments, determines information corresponding to each AC Zeeman shift assigned to one or more additional qubits, stores information corresponding to each AC Zeeman shift assigned to one or more additional qubits, and executes executable instructions to cause the controller to update the phase accumulators corresponding to one or more additional qubits based on the information corresponding to each AC Zeeman shift assigned to one or more additional qubits, and / or similarly.

[0127] In various embodiments, a phase accumulator corresponding to each qubit may be used to perform one or more quantum error correction tasks corresponding to each qubit, to adjust and / or control the phase of one or more laser beams injected into each qubit, and / or similarly.

[0128] In step 410, the controller 30 may cause at least one of the two or more target qubits 5A, 5B to be transported away from the target position 55. For example, the controller 30 may control the operation of one or more voltage and / or current sources 80 (e.g., via one or more driver controller elements 615) to cause at least one of the target qubits 5A, 5B to be transported away from the target position 55. In an example where at least one of the target qubits 5A, 5B should remain at the target position 55 (e.g., be gated and / or interact with a different target qubit), the controller 30 may control the operation of one or more voltage and / or current sources (e.g., via one or more driver controller elements 615) to cause at least one of the target qubits 5A, 5B to remain at the target position 55.

[0129] Exemplary operation of a quantum system for performing a clock state generation procedure In various systems, a quantum system, such as a QCCD-based quantum system 100, is operable to perform a clock state generation procedure. In various embodiments, performing a clock state generation procedure involves modifying and / or dressing the energy structure of one or more target qubits by adiabatically applying a dressing field to one or more target qubits. One or more target qubits are located at a target position 55, which may be a storage location configured to store qubits. For example, the target position may be a storage section and / or sort section, as described in U.S. Application No. 63 / 504,808 filed May 30, 2023, the entire contents of which are incorporated herein by reference. In another example, the target position may be a cache confinement site and / or storage area, as described in U.S. Application No. 63 / 476,226 filed December 20, 2022, the entire contents of which are incorporated herein by reference. In another example, the target location may be a quantum operation location / section (e.g., an area of ​​the confinement device where single and / or multi-qubit gates and / or qubit readout operations are performed), a gate zone (e.g., an area of ​​the confinement device where single and / or multi-qubit gates are performed), a location along the data bus confinement corridor, and / or similar locations.

[0130] Figure 5A presents a flowchart of a process, procedure, operation, and / or similar performed by the controller 30 of the quantum system 100 to perform a clock state generation procedure according to an exemplary embodiment. In various embodiments, the clock state generation procedure is performed as part of executing a quantum circuit and / or algorithm. For example, if a qubit should be stored for a certain period of time during the execution of a quantum circuit and / or algorithm (e.g., if the quantum information stored by the qubit is needed at some point in the future but not now), the clock state generation procedure is performed on the qubit to cause the quantum information to be held by the qubit for a longer period of time. For example, the clock state generation procedure may be used to extend and / or lengthen the coherence time of a target qubit. In another example, the clock state generation procedure may be performed on one or more target qubits that are the target of a single-qubit gate and / or a multi-qubit gate (e.g., using one or more laser beams to realize, mediate, and / or cause the execution of a gate). For example, a clock state generation procedure may be used to induce a known stable frequency difference between a first dressing state and a second dressing state so that noise and / or fluctuations in the external magnetic field (e.g., in the component of the external magnetic field in the quantization direction) do not adversely affect the gate fidelity of the gate being operated on.

[0131] In various embodiments, the qubits 5 (e.g., 5A, 5B, 5C) confined by the confinement device 50 can be transported between various locations defined by the confinement device 50. For example, the qubit 5 can be transported into or out of the target location 55. In various embodiments, starting from step 502, the controller 30 causes the target qubit 5A for the clock state generation procedure to be positioned within the range of the target location 55. For example, in the case where the target qubit 5A is positioned outside the target location 55, the controller 30 controls the operation of one or more voltage and / or current sources 80 (e.g., via one or more driver controller elements 615) to cause the target qubit 5A to be transported within the range of the target location 55. For example, in the case where the target qubit 5A is positioned within the range of the target location 55, the controller 30 controls the operation of one or more voltage and / or current sources 80 (e.g., via one or more driver controller elements 615) to cause the target qubit 5A to remain positioned at the target location 55.

[0132] In step 504, while the target qubit 5A is positioned, placed, and / or confined within the target position 55, the controller 30 controls the operation of the dressing field circuit 70 to cause the generation of a dressing field at the target position 55. For example, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70, causing the dressing field circuit to generate a dressing field. For example, in an exemplary embodiment, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70 increasing (for example, from zero amplitude towards a non-zero amplitude of the target).

[0133] As noted above, the first qubit state 314A and the second qubit state 314B are nearly clock states at the operable magnetic field amplitude / magnitude of the quantum system 100 (e.g., greater than 0G and less than 10G). Therefore, the qubit frequency difference Δf q The operable magnetic field amplitude / magnitude of quantum system 100 depends on the external magnetic field. In other words, the energy E of the first qubit state is related to the magnitude / amplitude of the component of the external magnetic field in the quantization direction. q1 The derivative of is a first function of the magnitude / amplitude of the components of the external magnetic field in the quantization direction (e.g., δE q1 / δB z =F1(B z ) and the first function F1 depends on the (initial and / or unmodified) energy structure of the qubit. The second qubit state energy E is related to the magnitude / amplitude of the component of the external magnetic field in the quantization direction. q2The derivative of is a second function of the magnitude / amplitude of the external magnetic field component in the quantization direction (e.g., δE q2 / δB z =F2(B z ) and the second function F2 depends on the (initial and / or unmodified) energy structure of the qubit). Since the first function F1 and the second function F2 are not the same, E q1 -E q2 =hΔf q This is the component B of the external magnetic field in the quantization direction. z It is not constant due to changes and / or fluctuations.

[0134] The dressing field is a component of the external magnetic field in the quantization direction, where the coupling of the initial set of states 310 results in the same magnitude as the energy dependence of the qubit state on the external magnetic field, but with the opposite sign. z It is tuned to produce an AC Zeeman shift with a linear dependence on . For example, as a result of the coupling of the set of initial states 310, the energy difference ΔE between the first dressing state 324A and the second dressing state 324B with respect to the component of the external magnetic field in the quantization direction is d The derivative of is zero, at least for the first-order approximation of the external magnetic field component in the quantization direction. For example, at least for the first-order approximation, δΔE d / δB z =hδΔf d / δB z =[F1(B z )-F2(B z )]-[F1(B z )-F2(B z )] ≈ 0. This causes the first dressing state 324A and the second dressing state 324B, which result from the coupling introduced by the dressing field, to effectively behave as clock states in the non-zero operable magnetic field amplitude / magnitude used when the quantum system 100 (e.g., a QCCD-based quantum computer) operates.

[0135] In other words, the dressing field is tuned such that the respective energies / frequencies of the first dressed state 324A and the second dressed state 324B have the same dependence on changes to the (component in the quantization direction) of the external magnetic field. As a result, even if the target qubit is subjected to small changes in the external magnetic field (e.g., noise and / or perturbations), the dressing frequency difference Δf d remains constant.

[0136] From the perspective of the one or more target qubits 5A, 5B, the dressing field is slowly turned on such that the respective energy structures of the one or more target qubits are adiabatically dressed and / or modified from their respective sets of initial states to their respective sets of superposition states. As used herein, the phrase "slowly" relates to the dressing field being turned on (for performing the clock state generation procedure) on a time scale that is slow compared to the dressing frequency difference and / or the qubit frequency difference. For example, the time that elapses while the dressing field is turned on from zero amplitude to the dressing amplitude is longer than 1 over the dressing frequency difference (e.g., greater than the reciprocal of the dressing frequency difference), and / or longer than 1 over the qubit frequency difference (e.g., greater than the reciprocal of the qubit frequency difference).

[0137] For example, FIG. 5B presents a plot illustrating the evolution of the amplitude of the dressing field 520 with respect to time during execution of the clock state generation procedure. FIG. 5B also illustrates the sensitivity 530 of the one or more target qubits 5A, 5B to the (component in the quantization direction) of the external magnetic field with respect to time during execution of the clock state generation procedure.

[0138] For example, at the initial time t0, the amplitude of the dressing field is zero. During the turn-on time period 522 spanning from the initial time t0 to a first time t1 (t0<t1), the amplitude of the dressing field goes from zero to the dressing amplitude A dIt increases up to . In the embodiment illustrated, the increase in the amplitude of the dressing field is linear over the turn-on time period 522. Various other functional forms may be used to increase the amplitude of the dressing field in a manner that increases monotonically from the initial time t0 to the first time t1.

[0139] In various embodiments, the turn-on time period is longer than the reciprocal of the dressing frequency difference (for example, t1-t0>1 / Δf d ), and / or longer than the reciprocal of the qubit frequency difference (e.g., t1-t0>1 / Δf q The slow turn-on and / or amplitude increase of the dressing field causes the energy structure of one or more target qubits 5A, 5B to be adiabatically dressed and / or modified, thereby preserving (e.g., not destroying) the quantum information stored by one or more target qubits 5A, 5B through the turn-on of the dressing field.

[0140] As the amplitude of the dressing field increases (slowly), the strength of the coupling caused by the dressing field increases. Since the first dressing state 324A and the second dressing state 324B are less sensitive to the magnetic field than the first qubit state 314A and the second qubit state 314B, increasing the amplitude of the dressing field causes the target qubits 5A and 5B to become less sensitive to the component of the external magnetic field at least in the quantization direction. For example, at initial time, one or more target qubits 5A and 5B have an initial sensitivity level S to the component of the external magnetic field in the quantization direction. i It has the following characteristics. At the first time t1, one or more target qubits 5A, 5B have a clock state sensitivity level S with respect to the component of the external magnetic field in the quantization direction. c (S i >S c ).

[0141] In various embodiments, the dressing field has a dressing amplitude A over a clock state time period 524 (for example, the time between a first time t1 and a second time t2). d It is maintained in this state. In various embodiments, the clock state time period 524 is used to extend and / or lengthen the coherence time of one or more target qubits 5A, 5B. In various embodiments, the clock state time period 524 is used for the execution of one or more single-qubit gates and / or multi-qubit gates in which the frequency difference between the occupied states of the qubits has a stable energy and / or frequency difference even when noise is present in the components of the external magnetic field in the quantization direction.

[0142] In step 506, the controller 30 tracks the extension of the coherence time of one or more target qubits 5A, 5B as a result of one or more target qubits undergoing a clock state generation procedure. For example, the coherence time of a qubit whose qubit subspace contains a pair of clock states is approximately infinite. Therefore, in one exemplary embodiment, while one or more target qubits 5A, 5B are undergoing the clock state generation procedure, the controller 30 suspends the accumulation of time on the respective coherence time timers corresponding to one or more target qubits 5A, 5B. In another example, in one exemplary embodiment, the controller 30 tracks the time while one or more target qubits 5A, 5B are undergoing the clock state generation procedure, thereby extending the respective coherence time timers corresponding to one or more target qubits 5A, 5B by the amount of time one or more target qubits have undergone the clock state generation procedure.

[0143] In step 508, the controller 30 causes the quantum computer 110 to execute one or more single-qubit gates and / or multi-qubit gates on one or more target qubits 5A, 5B while one or more target qubits 5A, 5B are undergoing a clock state generation procedure. For example, the controller 30 controls the operation of one or more operating sources (e.g., laser 60, microwave source 62) (e.g., via one or more driver controller elements 615) and causes one or more operating sources to generate and provide their respective operating signals. Each operating signal is supplied to the target position 55 via their respective beam delivery systems 66. One or more operating signals are tuned to the transition between a first dressing state 324A and a second dressing state 324B and / or characterized by their corresponding respective frequencies and / or frequency differences. For example, the controller 30 causes a single-qubit gate or a multi-qubit gate to be executed where the frequencies characterizing each operation signal correspond to the first dressing state 324A and the second dressing state 324B, rather than the first qubit state 314A and the second qubit state 314B.

[0144] In step 510, the controller 30 controls the operation of the dressing field circuit 70 to cause the generation of the dressing field at the target position 55 to stop. For example, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70, which causes the dressing field circuit to stop generating the dressing field. For example, in an exemplary embodiment, the controller 30 controls the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause one or more voltage and / or current sources 80 to supply voltage signals and / or current signals to the dressing field circuit 70 that decrease (for example, from a previous amplitude toward zero amplitude).

[0145] From the perspective of one or more target qubits 5A, 5B, the dressing field is slowly turned off so that the energy structure of each of the one or more target qubits is adiabatically dedressed and / or returned to its original energy structure. For example, the energy structure of a target qubit is dedressed and / or modified so that the set of superposition states is adiabatically returned to the set of initial states. As used herein, the phrase “slowly” refers to the dressing frequency difference Δf d and / or qubit frequency difference Δf q This relates to the dressing field being turned off at a slower timescale (after the execution of the clock state generation procedure) compared to [the previous timescale]. For example, if the dressing field has a dressing amplitude A d The time elapsed between turning off from zero amplitude is longer than 1 of the dressing frequency difference (e.g., greater than the reciprocal of the dressing frequency difference) and / or longer than 1 of the qubit frequency difference (e.g., greater than the reciprocal of the qubit frequency difference).

[0146] For example, at a second time t2 (t1<t2), the amplitude of the dressing field is the dressing amplitude A d . During a turn-off time period 526 spanning from the second time t2 to a third time t3 (t2<t3), the amplitude of the dressing field is the dressing amplitude A d decreasing to zero. In the illustrated embodiment, the decrease in the amplitude of the dressing field is linear over the turn-off time period 526. Various other functional forms may be used to decrease the amplitude of the dressing field in a manner that decreases monotonically starting from the second time t2 until the third time t3.

[0147] In various embodiments, the turn-off time period 526 is longer than the reciprocal of the dressing frequency difference (for example, t3-t2>1 / Δf d ), and / or longer than the reciprocal of the qubit frequency difference (for example, t3-t2>1 / Δf q ). The slow turn-off and / or amplitude decrease of the dressing field causes the respective energy structures of the target qubits 5A, 5B to be adiabatically undressed and / or modified, whereby the quantum information preserved by the respective target qubits 5A, 5B is maintained (for example, not destroyed) by the turn-off of the dressing field.

[0148] As the amplitude of the dressing field decreases (slowly), the strength of the coupling induced by the dressing field becomes smaller. Since the first qubit state 314A and the second qubit state 314B are more sensitive to magnetic fields than the first dressing state 324A and the second dressing state 324B, the decrease in the amplitude of the dressing field causes the target qubits 5A, 5B to become sensitive to the external magnetic field (at least its component in the quantization direction). For example, at the second time t2, the target qubits 5A, 5B have a clock state sensitivity level S for the component of the external magnetic field in the quantization direction chas. At the third time t3, the target qubits 5A, 5B have an initial sensitivity level S with respect to the component of the external magnetic field in the quantization direction i have( c <S i ).

[0149] In various embodiments, the controller 30 determines information about the AC Zeeman shift imparted to one or more additional qubits 5C positioned and / or arranged outside the target location 55 as a result of the dressing field being generated at the target location 55 (e.g., between the initial time t0 and the third time t3). For example, although the amplitude of the dressing field decays rapidly with distance from the target location 55, the additional qubits 5C positioned and / or arranged outside the target location 55 may be subjected to the action of the dressing field at a low amplitude / intensity. For example, the additional qubits 5C positioned and / or arranged outside the target location 55 are not subjected to the action of a dressing field of sufficiently high amplitude / intensity such that the energy structure of the additional qubits 5C is dressed and / or modified in the same manner as the target qubits 5A, 5B. Accordingly, the additional qubits 5C are not affected by the dressing field beyond a traceable AC Zeeman shift (and are likely not affected by any gates performed during the time period 524 of the clock state).

[0150] The low-amplitude / intensity dressing field acting on the additional qubits 5C causes the additional qubits 5C to be subjected to the action of the AC Zeeman shift. The AC Zeeman shift is the magnetic counterpart or version of the AC Stark shift. In particular, the oscillating magnetic field of the dressing field that interacts with the additional qubits 5C can change the speed or rate at which the additional qubits 5C accumulate phase. As such, the phase accumulator corresponding to the additional qubits 5C and stored in the classical memory (e.g., memory 610, see FIG. 6) of the controller 30 may be updated based on the AC Zeeman shift acting on the additional qubits 5C.

[0151] For example, the classical memory 610 of the controller 30 may store a phase accumulator corresponding to each qubit confined by the confinement device 50. The phase accumulator corresponding to each qubit may be updated periodically, regularly, and / or continuously, or triggered, to reflect the phase accumulated by each qubit. In various embodiments, the memory 610 stores executable instructions for calculating and / or determining information corresponding to the AC Zeeman shift experienced by each qubit, based on the distance of each qubit from the target position 55 (controlling the amplitude / intensity of the dressing field experienced by each qubit), the gate time period (e.g., the elapsed time between a first time t1 and a second time t2) or the elapsed time between an initial time and a third time (e.g., t3-t0), and / or other information corresponding to the AC Zeeman shift experienced by each qubit. In an exemplary embodiment, the memory 610 stores executable instructions for using information regarding the AC Zeeman shift experienced by each qubit to update the phase accumulator corresponding to each qubit. The processing device 605 of the controller 30, in various embodiments, determines information corresponding to each AC Zeeman shift assigned to one or more additional qubits, stores information corresponding to each AC Zeeman shift assigned to one or more additional qubits, and executes executable instructions to cause the controller to update the phase accumulators corresponding to one or more additional qubits based on the information corresponding to each AC Zeeman shift assigned to one or more additional qubits, and / or similarly.

[0152] In various embodiments, a phase accumulator corresponding to each qubit may be used to perform one or more quantum error correction tasks corresponding to each qubit, to adjust and / or control the phase of one or more laser beams injected into each qubit, and / or similarly.

[0153] In step 512, the controller 30 may cause at least one of the two or more target qubits 5A, 5B to be transported out of the target position 55. For example, the controller 30 may control the operation of one or more voltage and / or current sources 80 (for example, via one or more driver controller elements 615) to cause at least one of the target qubits 5A, 5B to be transported out of the target position 55. For example, if target qubit 5A was stored in the target position 55 but is now to undergo one or more quantum logic operations, target qubit 5A may be transported out of the target position 55 to a quantum operation section, gate zone, and / or similar, which is at least partially defined by the confinement device 50. In an example where at least one of the target qubits 5A, 5B should remain at target position 55 (for example, by being gated and / or interacting with a different target qubit and / or undergoing another clock state generation procedure), the controller 30 controls the operation of one or more voltage and / or current sources (for example, via one or more driver controller elements 615) to cause at least one of the target qubits 5A, 5B to remain at target position 55.

[0154] Technical advantages In large quantum charge-coupled device (QCCD) based quantum computers using hyperfine split qubits, operating at low magnetic field amplitudes (e.g., less than 10G) allows for the provision of a uniform magnetic field. In addition, to enable energy splitting of the hyperfine states, the quantum processor is made to operate at magnetic field amplitudes greater than 0G. Generally, a set of low F (e.g., F=0, 1, and / or 2), m=0 states is used to define the qubit subspace of the qubit. However, these m=0 states only function as clock states at a magnetic field amplitude of 0G. Therefore, when operating in a magnetic field with amplitudes in the range of 2-5G, the m=0 states are not clock states (e.g., they have energies / frequencies that are sensitive to changes in the magnetic field). This results in memory errors and / or reduced memory coherence time in conventional QCCD-based quantum computers using hyperfine split qubits. Thus, there is a technical problem regarding extending the coherence time of the hyperfine split qubits in QCCD-based quantum computers.

[0155] Various embodiments provide technical solutions to these technical problems. For example, various embodiments provide control over the sensitivity of a qubit to an external magnetic field. For example, in various embodiments, a dressing field is generated at the target location. The dressing field causes the energy structure of the qubit located at the target location to be modified such that the initial set of states of the qubit located at the target location is made to form a set of superposition states. The set of superposition states includes a first dressing state of the set of superposition states, which includes a non-zero contribution from a first qubit state of the initial set, and a second dressing state of the set of superposition states, which includes a non-zero contribution from a second qubit state of the initial set. The first and second dressing states effectively behave as clock states at the amplitude / magnitude of the magnetic field on which the system is operating. When the first and second dressing states effectively behave as clock states, the coherence time of the qubit is virtually infinite while the qubit is in the first and / or second dressing states. Therefore, various embodiments result in an extension of the qubit coherence time, which reduces memory errors and enables the execution of deeper quantum circuits. Thus, various embodiments offer improvements over conventional QCCD-based quantum computers.

[0156] Furthermore, executing conventional quantum logic gates requires a radiating field, such as a laser beam, microwave, and / or similar, to realize, mediate, and / or induce entanglement of qubits. However, these radiating fields can introduce various gate errors, such as affecting transitions in the spectator qubit, which can lead to photon scattering and / or crosstalk problems, phase noise, and / or similar. These gate errors can result in low-fidelity logic gates and noisy computations. Moreover, quantum logic gates that use radiating fields are highly sensitive to the state of one or more motion modes of the qubit. Thus, spin-motion coupling can introduce additional gate errors, and / or require significant time to cool the qubit to a state close to its motion ground state before executing the quantum logic gate. Consequently, various technical problems exist regarding the execution of quantum logic gates.

[0157] One possible technical solution to these technical problems is to use a non-zero magnetic field gradient to realize, mediate, and / or induce qubit entanglement. However, for such an interaction to be performed within a reasonable time, this requires the qubit to be sensitive to the magnetic field. Conventionally, causing a qubit to be sensitive to a magnetic field involves performing a shelving process in which the qubit state of the qubit is shelved to a state outside the qubit subspace that is sensitive to the magnetic field. However, this shelving is performed by driving the transition from the qubit state to the shelved state with a laser, and thus can introduce crosstalk problems, phase noise, and / or similar. Thus, technical problems exist regarding the implementation of quantum logic gates.

[0158] Various embodiments provide technical solutions to these technical problems. In particular, a dressing field may be applied to two or more qubits rather than shelving the qubits to allow a non-zero magnetic field gradient to realize, mediate, and / or induce entanglement of two or more qubits. The dressing field causes the energy structure of each qubit placed at the target position to be modified such that each set of initial states of the qubits placed at the target position is made to form each set of superposition states. The set of superposition states includes a first dressing state of the set of superposition states, which includes a non-zero contribution from a first qubit state of the set of initial states, and a second dressing state of the set of superposition states, which includes a non-zero contribution from a second qubit state of the set of initial states. The first and second dressing states are more sensitive to the magnetic field than these qubit states. A non-zero magnetic field gradient present at the target position can realize, mediate, and / or induce entanglement of two or more qubits. Therefore, various embodiments enable the execution of multi-qubit gates without the use of lasers and without the introduction of various errors (such as crosstalk, phase noise, and / or similar) that may be induced by the use of lasers in such systems. Thus, various embodiments offer improvements over conventional QCCD-based quantum computers.

[0159] Example Controller In various embodiments, the controller 30 is configured to control one or more components of the quantum system 100 that are configured to execute multi-qubit gates and / or clock state generation procedures using a dressing field and a non-zero magnetic field gradient. For example, in various embodiments, the controller 30 is configured to control one or more components of the quantum system 100 so that the quantum system executes multi-qubit gates and / or clock state generation procedures using a dressing field and a non-zero magnetic field gradient.

[0160] For example, in various embodiments, at least part of a confinement device 50 defining at least one target position 55 and associated at least one dressing field circuit 70 are part of the QCCD-based quantum system 100. In one exemplary embodiment, at least one target position 55 is associated with a magnetic field source 90. In various embodiments, the QCCD-based quantum system 100 includes, for example, a controller 30 configured to control the operation of various components of a quantum processor 115.

[0161] For example, the controller 30 is configured to control a voltage and / or current source 80 configured to supply voltage and / or current signals to the row of control electrodes 212 of the confinement device 50 and / or the dressing field circuit 70 (and optionally one or more magnetic field sources 90 including electromagnets). For example, the controller 30 is configured to control one or more operating sources (e.g., a laser 60, a microwave source 62) configured to generate and / or provide their respective operating signals (e.g., a laser beam, a microwave signal). The controller 30 may be further configured to control a cryogenic system and / or vacuum system that controls the temperature and pressure within the cryogenic and / or vacuum chamber 40, as well as other systems that control environmental conditions (e.g., temperature, humidity, pressure, and / or similar) within the cryogenic and / or vacuum chamber 40. In various embodiments, the controller 30 may be further configured to manipulate and / or induce a controlled evolution of the quantum state of one or more qubits confined by the confinement device 50.

[0162] As shown in Figure 6, in various embodiments, the controller 30 includes various controller elements, including a processing device 605, memory 610, driver controller element 615, communication interface 620, analog-to-digital converter element 625, and / or similar elements. For example, the processing device 605 may include processing elements, programmable logic devices (CPLDs), microprocessors, coprocessing 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, controllers, and / or similar. The term "circuit" may refer to embodiments consisting solely of hardware, or combinations of hardware and computer program products. In one exemplary embodiment, the processing device 605 of the controller 30 includes and / or communicates with a clock. In various embodiments, the processing device 605 of the controller 30 is configured to execute executable instructions compiled according to a quantum assembly (QASM) and / or another quantum intermediate representation (QIR) compilation process.

[0163] For example, memory 610 may include non-temporary memory such as volatile and / or non-volatile memory storage, such as one or more of the following: hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, and / or similar. In various embodiments, memory 610 may store qubit records (e.g., in a qubit record datastore, qubit record database, qubit record table, and / or similar), calibration tables, executable queues, computer program code (e.g., one or more computer languages, dedicated controller languages, and / or similar), and / or similar. In an exemplary embodiment, the execution of at least a portion of computer program code stored in memory 610 (e.g., by processing device 605) causes controller 30 to perform one or more steps, operations, processes, procedures, and / or similar as described herein to execute a multi-qubit gate and / or a clock state generation procedure using a dressing field and a non-zero magnetic field gradient (e.g., without using a laser beam).

[0164] In various embodiments, the driver controller element 615 may include one or more driver and / or controller elements, each configured to control one or more drivers. In various embodiments, the driver controller element 615 may comprise drivers and / or driver controllers. For example, a driver controller may be configured to cause one or more corresponding drivers to be operated according to executable instructions, commands, and / or similar, scheduled and executed by the controller 30 (e.g., by the processing device 605). In various embodiments, the driver controller element 615 may allow the controller 30 to operate one or more operating sources (e.g., a laser 60 and / or a microwave source 62) to provide a light beam or microwave signal, and respectively cause a voltage and / or current source 80 to provide its respective voltage signal and / or current signal to its respective control electrode 214 and / or dressing field circuit 70 (and optionally a magnetic field source 90 including an electromagnet), and / or similar operation. In various embodiments, the driver controller element 615 enables the controller 30 to control and / or operate various drivers (e.g., laser drivers, microwave source drivers, AWGs, DACs, vacuum component drivers, cryogenic and / or vacuum system component drivers, and / or similar).

[0165] In various embodiments, the controller 30 includes means for transmitting and / or receiving signals from one or more photodetector components and / or photodetectors, such as cameras, MEMS cameras, CCD cameras, photodiodes, photomultiplier tubes, and / or similar devices. For example, the controller 30 may include one or more analog-to-digital converter elements 625 configured to receive signals from one or more photodetector components, calibration sensors, and / or similar devices.

[0166] In various embodiments, the controller 30 may include a communication interface 620 for interfaceing with and / or communicating with the computing entity 10. For example, the controller 30 may include a communication interface 620 for receiving executable instructions, command sets, and / or similar from the computing entity 10 and for providing the computing entity 10 with outputs received from the quantum computer 110 (e.g., from the optical focusing system) and / or the results of processing those outputs. In various embodiments, the computing entity 10 and the controller 30 may communicate via direct wired and / or wireless connections and / or one or more wired and / or wireless networks 20.

[0167] Exemplary Computing Entity Figure 7 shows an exemplary schematic diagram of an exemplary computing entity 10 that can be used in combination with embodiments of the present invention. In various embodiments, the computing entity 10 is configured to enable a user to provide input to a quantum computer 110 (for example, through a user interface of the computing entity 10), receive, display, analyze, and / or perform similar operations on outputs from the quantum computer 110.

[0168] As shown in Figure 7, the computing entity 10 may include an antenna 712, a transmitter 704 (e.g., wireless), a receiver 706 (e.g., wireless), and a processing device 708 that provides and receives signals to the transmitter 704 and receiver 706, respectively. The signals provided to and received from the transmitter 704 and receiver 706 may include signaling information / data according to applicable wireless system air interface standards for communication with various entities such as the controller 30, other computing entities 10, and / or similar. In this regard, the computing entity 10 may be able to operate with one or more air interface standards, communication protocols, modulation types, and access types. In various embodiments, the computing entity 10 includes a network interface 720 configured to enable communication between the computing entity 10 and the controller 30 and / or various other computing devices.

[0169] For example, computing entity 10 may be configured to receive and / or provide communications using wired data transmission protocols such as Fiber Distributed Data Interface (FDDI), Digital Subscriber Line (DSL), Ethernet, Asynchronous Transfer Mode (ATM), Frame Relay, Data Over Cable Service Interface Specification (DOCSIS), or any other wired transmission protocol. Similarly, Computing Entity 10 supports General-Purpose Packet Radio System (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA®), Global System for Mobile Communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), Time Division Synchronous Code Division Multiple Access (TD-SCDMA), Long-Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized (EVDO), High Speed ​​Packet Access (HSPA), High Speed ​​Downlink Packet Access (HSDPA), IEEE 802.11 (Wi-Fi), and Wi-Fi. It can be configured to communicate over a wireless external communication network using any of the following protocols: Direct, 802.16 (WiMAX), Ultra Wideband (UWB), Infrared (IR) protocol, Near Field Communication (NFC) protocol, Wibree, Bluetooth protocol, Wireless Universal Serial Bus (USB) protocol, and / or any other wireless protocol.Computing entity 10 may communicate using such protocols and standards as 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 (HTML), and / or similar.

[0170] Through these communication standards and protocols, computing entity 10 can communicate with various other entities using concepts such as unstructured supplemental service information / data (USSD), short message service (SMS), multimedia messaging service (MMS), dual-tone multi-frequency signaling (DTMF), and / or subscriber identification module dialer (SIM dialer). Computing entity 10 can also download changes, add-ons, and updates to its firmware, software (including, for example, executable instructions, applications, and program modules), and operating system.

[0171] The computing entity 10 may also include user interface devices, including one or more user input / output interfaces (for example, a display 716 and / or speaker / speaker driver coupled to the processing device 708, and a touchscreen, keyboard, mouse, and / or microphone coupled to the processing device 708). For example, a user output interface may be configured to provide applications, browsers, user interfaces, interfaces, dashboards, screens, web pages, pages, and similar words used interchangeably herein, which run on and / or are accessible through the computing entity 10, for displaying or audibly presenting information / data, and for interactive operation via one or more user input interfaces. A user input interface may comprise any of a number of devices that enable the computing entity 10 to receive data, such as a keypad 718 (hard or soft), a touch display, a voice / speech or motion interface, a scanner, a reader, or other input device. In embodiments including a keypad 718, the keypad 718 may include (or trigger) a set of keys that can be activated to provide a full set of alphabetic keys or a full set of alphanumeric keys, and may include conventional numeric keys (0-9) and related keys (#, *), and other keys used to operate the computing entity 10. In addition to providing input, the user input interface can be used to activate or deactivate several functions, such as a screen saver and / or sleep mode. Through such input, the computing entity 10 can collect information / data, user interactions / inputs, and / or the like.

[0172] Computing entity 10 may also include volatile storage or memory 722 and / or non-volatile storage or memory 724, which may be embedded and / or removable. For example, non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, and / or similar. 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, register memory, and / or similar. 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, bytecode, compiled code, interpreter code, machine code, executable instructions, and / or similar to implement the functionality of computing entity 10.

[0173] conclusion Many modifications and other embodiments of the invention described herein will be conceivable to those skilled in the art who benefit from the teachings presented in the foregoing description and the accompanying drawings. It will be understood that the invention is not to be limited to the specific embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the accompanying claims. Certain terms are used herein, but these are used only in a general and descriptive sense and are not intended to be limiting. [Explanation of Symbols]

[0174] 5A, 5B, 5C Target Qubits 10 Computing Entities 20. Wired or wireless network 30 controllers 40 Vacuum Chamber 50 Confinement device 55 Target location 60 lasers 62 Microwave Sources 66 Beam Delivery System 70 Dressing area circuit 80 Voltage and / or current sources 90 Magnetic field source 100 QCCD-based quantum systems 110 Quantum Computers 115 Quantum Processors 200 Linear confinement region 210A, 210B Radio Frequency (RF) Rail 212 Control electrodes 212A, 212B, 212C control electrodes 214 Control electrodes 214A, 214B, ..., 214N control electrodes 216 RF Null Axis 310 Initial state 312-qubit subspace 314A First qubit state 314B Second qubit state 320 Superposition state 324A First dressing state 324B Second dressing state 422 Turn-on time cycle 424 Gate Time Period 426 Turn-off time cycle 430 Sensitivity 520 Dressing room 524 Clock state time period 526 Turn-off time cycle 530 Sensitivity 605 Processing Devices 610 Classic Memory 615 Driver Controller Element 620 Communication Interfaces 625 Analog / Digital Converter Elements 704 Transmitter 706 Receiver 708 Processing Devices 712 Antenna 716 displays 718 Keypad 720 Network Interfaces 722 Volatile storage or memory 724 Non-volatile storage or memory

Claims

1. A method for executing a multi-qubit gate on two or more qubits confined by a confinement device, A controller controls the operation of a dressing field circuit to cause the dressing field circuit to generate a dressing field at a target location defined at least in part by the confinement device, wherein the dressing field is configured to modify the energy structure of each of the two or more qubits disposed at the target location by causing the initial set of each of the two or more qubits to form a set of superposition states, wherein the first dressing state of the set of superposition states includes a non-zero contribution from the first qubit state of the set of initial states, the second dressing state of the set of superposition states includes a non-zero contribution from the second qubit state of the set of initial states, the first and second dressing states are more sensitive to a magnetic field than the first and second qubit states, a non-zero magnetic field gradient exists at the target location and mediates the entanglement of the two or more qubits disposed at the target location, After the gate time has elapsed, the controller controls the operation of the dressing field circuit to cause the dressing field circuit to stop generating the dressing field at the target position so that the respective energy structures of the two or more qubits return to their respective initial energy structures, including the set of initial states. Methods that include...

2. The method according to claim 1, wherein the dressing field circuit stops generating the dressing field at the target position, and the energy structure of each of the two or more target qubits returns to the initial energy structure including the set of initial states of the qubits.

3. The method according to claim 1, wherein the operation of the dressing field circuit is controlled such that, when the dressing field circuit starts generating the dressing field, the amplitude of the dressing field increases from zero to the gate amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

4. The method according to claim 1, wherein the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the gate amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

5. The method according to claim 1, wherein the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

6. The method according to claim 1, wherein the step of controlling the operation of the dressing field circuit includes the step of controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

7. The method according to claim 1, wherein the dressing field is a microwave field.

8. A method for performing a clock state generation procedure on one or more target qubits confined by a confinement device, A controller controls the operation of a dressing field circuit to cause the dressing field circuit to generate a dressing field at a target location defined at least in part by the confinement device, wherein the dressing field is configured to modify the energy structure of each of the one or more target qubits disposed at the target location by causing each set of initial states of the one or more target qubits to form each set of superposition states, wherein the first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states, and the substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states behave effectively as clock states at the operable magnetic field amplitude. Methods that include...

9. The method according to claim 8, wherein the first dressing state is formed by combining two or more first states of the initial set of states, and the second dressing state is formed by combining two or more second states of the initial set of states.

10. The method according to claim 9, wherein the combinations of the first two or more states and the second two or more states of the initial set of states cause an AC Zeeman shift having a linear dependence on a magnetic field having the same magnitude and opposite sign as the energy dependence of the first qubit state and the second qubit state on an external magnetic field.

11. The method of claim 8, further comprising the step of controlling the operation of the dressing field circuit so that, before transporting the one or more target qubits, the energy structure of each of the one or more target qubits returns to an initial energy structure including the respective set of initial states of the one or more target qubits, thereby causing the dressing field circuit to cease generating the dressing field at the target location.

12. The method according to claim 8, wherein the operation of the dressing field circuit is controlled such that, when the dressing field circuit starts generating the dressing field, the amplitude of the dressing field increases from zero to the dressing amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

13. The method according to claim 8, wherein the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

14. The method according to claim 8, wherein the step of controlling the operation of the dressing field circuit includes the step of controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

15. The method according to claim 8, wherein the dressing field is a microwave field.

16. The method according to claim 8, further comprising the step of controlling the operation of one or more manipulators to generate and provide each manipulator signal such that each manipulator signal is incident on the one or more target qubits positioned at the target location, wherein each manipulator signal causes a single-qubit gate or a multi-qubit gate to be executed on the one or more target qubits, and at least one of the respective frequencies of each manipulator signal or the frequency difference between each manipulator signal corresponds to the frequency difference between the first dressing state and the second dressing state.

17. The method according to claim 8, wherein the clock state generation procedure is performed to extend the qubit coherence time of one or more target qubits.

18. A system configured to perform a multi-qubit gate on two or more target qubits, A confinement device configured to confine multiple qubits, wherein the multiple qubits include two or more target qubits, A dressing field circuit, wherein at least a portion of the dressing field circuit and the confinement device define a target position, A magnetic field source configured to generate a non-zero magnetic field gradient at the target position, A controller configured to control the operation of the dressing field circuit, wherein the controller controls the operation of the dressing field circuit so that the multi-qubit gate is executed on the two or more target qubits located at the target positions. The operation of the dressing field circuit is controlled to cause the dressing field circuit to generate a dressing field at the target location defined at least in part by the confinement device, wherein the dressing field is configured to modify the energy structure of each of the two or more target qubits disposed at the target location by causing the initial set of each qubit of the two or more target qubits to form a set of superposition states, wherein the first dressing state of the set of superposition states includes a non-zero contribution from the first qubit state of the set of initial states, the second dressing state of the set of superposition states includes a non-zero contribution from the second qubit state of the set of initial states, the first and second dressing states are more sensitive to a magnetic field than the first and second qubit states, the non-zero magnetic field gradient is present at the target location and mediates, causes, entanglement of the two or more target qubits disposed at the target location. After the gate time has elapsed, the operation of the dressing field circuit is controlled to cause the dressing field circuit to stop generating the dressing field at the target position so that the respective energy structures of the two or more qubits return to their respective initial energy structures, including the set of initial states. The controller and A system equipped with these features.

19. The system according to claim 18, wherein when the dressing field circuit stops generating the dressing field at the target position, the energy structure of each of the two or more target qubits returns to the initial energy structure including the set of initial states of the qubits.

20. The system according to claim 18, wherein the operation of the dressing field circuit is controlled such that when the dressing field circuit starts generating the dressing field, the amplitude of the dressing field increases from zero to the gate amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

21. The system according to claim 18, wherein the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the gate amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

22. The system according to claim 18, wherein the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

23. The system according to claim 18, wherein controlling the operation of the dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

24. The system according to claim 18, wherein the dressing field is a microwave field.

25. The dressing area circuit is arranged on the confinement device, according to claim 18.

26. The system according to claim 25, wherein the dressing field circuit is lithographically printed on the surface of the confinement device.

27. A system configured to perform a clock state generation procedure for one or more target qubits, A confinement device configured to confine a plurality of qubits, wherein the plurality of qubits include one or more target qubits, A dressing field circuit, wherein at least a portion of the dressing field circuit and the confinement device define a target position, A controller configured to control the operation of the dressing field circuit, wherein the controller controls the operation of the dressing field circuit so that the clock state generation procedure is performed for one or more target qubits located at the target position. Controlling the operation of the dressing field circuit to cause the dressing field circuit to generate a dressing field at the target location defined at least in part by the confinement device, wherein the dressing field is configured to modify the energy structure of each of the one or more target qubits disposed at the target location by causing each set of initial states of the one or more target qubits to form each set of superposition states, wherein the first dressing state of each set of superposition states includes a non-zero contribution from the first qubit state of each set of initial states, and the second dressing state of each set of superposition states includes a non-zero contribution from the second qubit state of each set of initial states, wherein the substantially uniform magnetic field has an operable magnetic field amplitude across the confinement device, and the first and second dressing states behave effectively as clock states at the operable magnetic field amplitude. The controller and A system equipped with these features.

28. The system according to claim 27, wherein the first dressing state is formed by combining two or more first states of the initial set of states, and the second dressing state is formed by combining two or more second states of the initial set of states.

29. The system according to claim 28, wherein the combinations of the first two or more states and the second two or more states of the initial set of states cause an AC Zeeman shift having a linear dependence on a magnetic field having the same magnitude and opposite sign as the energy dependence of the first qubit state and the second qubit state on an external magnetic field.

30. The system according to claim 27, wherein the operation of the dressing field circuit is controlled such that when the dressing field circuit starts generating the dressing field, the amplitude of the dressing field increases from zero to the dressing amplitude over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

31. The system according to claim 27, wherein the operation of the dressing field circuit is controlled such that when the dressing field circuit stops generating the dressing field, the amplitude of the dressing field decreases from the dressing amplitude to zero over a time period longer than the reciprocal of the frequency difference between the first dressing state and the second dressing state.

32. The system according to claim 27, wherein the operation of the dressing field circuit is controlled such that the turn-on and turn-off of the dressing field occur adiabatically.

33. The system according to claim 27, wherein controlling the operation of the dressing field circuit includes controlling the operation of a current source or a voltage source configured to supply either current or voltage to the dressing field circuit.

34. The system according to claim 27, wherein the dressing field is a microwave field.

35. The dressing area circuit is arranged on the confinement device, according to claim 27.

36. The system according to claim 35, wherein the dressing field circuit is lithographically printed on the surface of the confinement device.

37. The system according to claim 27, wherein the controller is further configured to control the operation of one or more operating sources to generate and provide each operating signal such that each operating signal is incident on the one or more target qubits positioned at the target location, each operating signal causing a single-qubit gate or a multi-qubit gate to be executed on the one or more target qubits, and at least one of the respective frequencies of each operating signal or the frequency difference between each operating signal corresponds to the frequency difference between the first dressing state and the second dressing state.

38. The system according to claim 27, wherein the clock state generation procedure is performed to extend the qubit coherence time of one or more target qubits.

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