Geometric phase gate using magnetic field gradients

Abstract

A controller of the quantum system causes two or more qubits of the quantum system to be subjected to a (near-field and / or non-radiative) magnetic field gradient, and, in response to determining that a gate time period has elapsed since the two or more qubits of the quantum system began to be subjected to the magnetic field gradient, prevents the two or more qubits from further being subjected to the magnetic field gradient, thereby causing a geometric phase gate to be performed on the two or more qubits. Entanglement of the two or more qubits corresponding to the performance of the gate is realized, mediated, and / or caused by the magnetic field gradient.

Description

[Technical Field]

[0001] CROSS-REFERENCE TO RELATED APPLICATIONS This application claims priority to U.S. Patent Application No. 18 / 449,967, filed August 15, 2023, which claims priority to U.S. Patent Application No. 63 / 374,811, filed September 7, 2022, and U.S. Patent Application No. 63 / 514,621, filed July 20, 2023, the contents of which are incorporated herein by reference in their entireties.

[0002] Various embodiments relate to quantum logic gates using magnetic field gradients.Various embodiments relate to quantum logic gates that use magnetic field gradients to achieve entanglement between quantum objects. [Background technology]

[0003] Quantum computing uses quantum interactions to perform quantum calculations. An exemplary quantum interaction is the implementation of a quantum logic gate on a pair of qubits. For example, a quantum logic gate can be used to entangle two qubits. Traditionally, the implementation of a quantum logic gate involves the application of a laser beam or microwaves to two qubits that are being gated together. However, laser beams can lead to photon scattering during the implementation of conventional quantum logic gates and / or introduce phase noise, leading to reduced gate fidelity. Microwaves are sensitive to motional error and require the qubits to be cooled to a motional ground state. Through hard work, ingenuity, and innovation, many of the shortcomings of such conventional quantum logic gates have been overcome by developing solutions constructed in accordance with embodiments of the present invention. Many examples of these embodiments are described in detail herein. Summary of the Invention [Means for solving the problem]

[0004] Exemplary embodiments provide methods for realizing quantum logic gates that use (near-field) magnetic field gradients to entangle two or more qubits, systems configured to implement such quantum logic gates, etc. In various embodiments, the quantum logic gates do not use any radiation fields (e.g., laser beams, microwave signals, etc.) to cause entanglement of the two or more qubits. Rather, entanglement of the two or more qubits is realized, mediated, and / or caused by (near-field) magnetic field gradients.

[0005] In various embodiments, implementing a quantum logic gate comprises subjecting two or more qubits to a (near-field) magnetic field gradient, and after and / or in response to determining that a gate period has elapsed since the two or more qubits began to be subjected to the magnetic field gradient, the two or more qubits are no longer subjected to the magnetic field gradient.

[0006] For example, in an exemplary embodiment, implementing a quantum logic gate comprises controlling operation of a confinement device that confines two or more quantum objects to cause the two or more quantum objects to be transported into a magnetic field gradient region defined by the confinement device and a magnetic field gradient source (e.g., a permanent magnet, an array of permanent magnets, an electromagnet, an array of electromagnets, a combined array of permanent magnets and electromagnets, etc.). While the two or more qubits are disposed within the magnetic field gradient region, they are subjected to a (near-field) magnetic field gradient. After and / or in response to the two or more qubits being disposed in the magnetic field gradient region for a gate period, the two or more qubits are transported out of the magnetic field gradient region. In an exemplary embodiment, the gate period is determined at least in part based on the time it takes for the magnetic field gradient to realize, mediate, and / or cause entanglement of quantum states of the two or more quantum objects.

[0007] In another exemplary embodiment, two or more qubits are transported to a magnetic field gradient region while in a substantially magnetic field-independent quantum state or a superposition of substantially magnetic field-independent states. The substantially magnetic field-independent quantum states are then associated with and / or coupled to respective magnetic field-dependent quantum states (e.g., via one or more single qubit gates), thereby subjecting the two or more qubits to the (near-field) magnetic field gradient present in the magnetic field gradient region. After and / or in response to the two or more qubits being subjected to the (near-field) magnetic field of the magnetic field gradient region for the gate period, the quantum states of the two or more qubits are again associated with or coupled to the respective magnetic field-independent quantum states.

[0008] According to one aspect, a method for implementing a geometric phase gate is provided. In an exemplary embodiment, the method includes controlling, by a controller, operation of the confinement device to transport two or more quantum objects confined by the confinement device into a magnetic field gradient region of the confinement device. While disposed in the magnetic field gradient region, the two or more quantum objects are subjected to a (near-field) magnetic field gradient. In response to determining that a gate period has elapsed with at least one of (a) the two or more quantum objects disposed in the magnetic field gradient region, or (b) the two or more quantum objects subjected to the magnetic field gradient, controlling, by the controller, operation of the confinement device such that the two or more quantum objects are no longer subjected to the (near-field) magnetic field gradient.

[0009] In an exemplary embodiment, two or more quantum objects are entangled within a magnetic field gradient region during a gate period without using any radiation field to achieve / mediate the entanglement of the two or more quantum objects.

[0010] In an exemplary embodiment, a (near-field) magnetic field gradient enables / mediates the entanglement of two or more quantum objects within the magnetic field gradient region.

[0011] In an exemplary embodiment, the gate period is determined at least in part based on the time it takes for a (near-field) magnetic field gradient to mediate / achieve / cause entanglement of two or more quantum objects.

[0012] In an exemplary embodiment, the method further comprises, before transporting the two or more quantum objects into the magnetic field gradient region, allowing the quantum states of each of the two or more quantum objects to evolve into a respective gate subspace state.

[0013] In one exemplary embodiment, each quantum state extends out of the memory subspace and into the gate subspace, and each gate subspace state is a respective state of the gate subspace.

[0014] In one exemplary embodiment, the memory subspace comprises two or more memory states, each a respective clock state, and the gate subspace comprises two or more gate subspace states, each a Zeeman state.

[0015] In an exemplary embodiment, evolving each quantum state into a respective gate subspace state comprises causing an operating signal, characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state, to be incident on at least one of the two or more quantum objects.

[0016] In an exemplary embodiment, the method further comprises transporting the two or more quantum objects out of the magnetic field gradient region after determining that the gating period has elapsed, and evolving the quantum states of each of the two or more quantum objects from the gate subspace to a respective memory state.

[0017] In an exemplary embodiment, evolving the quantum states of each of the two or more quantum objects from the gate subspace to a respective memory state comprises causing an operating signal to be incident on at least one of the two or more quantum objects, the operating signal being characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state.

[0018] In an exemplary embodiment, the method further comprises performing one or more dynamic decoupling sequences on at least one quantum object of the two or more quantum objects between a start of the gate period and a completion of the gate period.

[0019] In an exemplary embodiment, performing one or more dynamic decoupling sequences on at least one quantum object of the two or more quantum objects comprises causing a dynamic decoupling manipulation signal to be incident on the at least one quantum object.

[0020] In an exemplary embodiment, the at least one quantum object is transported out of the magnetic field gradient region, a dynamic decoupling operating signal is incident on the at least one quantum object outside the magnetic field gradient region, and the at least one quantum object is transported back into the magnetic field gradient region. In an exemplary embodiment, the dynamic decoupling operating signal is incident on the at least one quantum object while the at least one quantum object is disposed within the magnetic field gradient region.

[0021] In an exemplary embodiment, the (near-field) magnetic field gradient is turned on in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported into the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, and the (near-field) magnetic field gradient is turned off in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported out of the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, or (c) after two or more quantum objects have been transported out of the magnetic field gradient section.

[0022] In an exemplary embodiment, the magnetic field gradient is a static magnetic field gradient and is substantially constant over the gate period.

[0023] In an exemplary embodiment, the magnetic field gradient oscillates during the gate period at a frequency that is lower than a motional mode frequency of the motional mode of each of the two or more quantum objects.

[0024] According to another aspect, a system configured to implement a geometric phase gate is provided. In an exemplary embodiment, the system includes a confinement device that defines (at least in part) at least one magnetic field gradient section and is operable to confine two or more quantum objects. The system further includes a controller configured to control operation of the confinement device. The controller is configured to control operation of the confinement device to cause two or more quantum objects confined by the confinement device to be transported into the at least one magnetic field gradient section of the confinement device. The two or more quantum objects are subjected to a (near-field) magnetic field gradient while disposed within the magnetic field gradient section. The controller is further configured to control operation of the confinement device such that the two or more quantum objects are no longer subjected to the at least one (near-field) magnetic field gradient in response to determining that a gate period has elapsed with at least one of (a) the two or more quantum objects disposed within the magnetic field gradient section or (b) the two or more quantum objects subjected to the magnetic field gradient.

[0025] In an exemplary embodiment, the containment device comprises or is associated with at least one of: (a) at least one permanent magnet; or (b) at least one electromagnet configured such that a (near-field) magnetic field gradient is present in at least one magnetic field gradient region.

[0026] In an exemplary embodiment, the containment device defines a plurality of magnetic field gradient sections comprising at least one magnetic field gradient section, the two or more quantum objects comprise a plurality of pairs of quantum objects, and the controller is configured to cause each of the plurality of pairs of quantum objects to be transported into and out of a respective magnetic field gradient section of the plurality of magnetic field gradient sections substantially simultaneously.

[0027] In an exemplary embodiment, the plurality of magnetic field gradient sections form a periodic arrangement of magnetic field gradient sections.

[0028] In an exemplary embodiment, the containment device defines at least one radiation field region spatially separate from the at least one magnetic field gradient region, and the controller is further configured to, prior to causing transport of the two or more quantum objects into the at least one magnetic field gradient region, evolve a respective quantum state of at least one of the two or more quantum objects into a respective gate subspace state while the quantum object is disposed within the at least one radiation field region.

[0029] In an exemplary embodiment, two or more quantum objects are entangled within a magnetic field gradient region during a gate period without using any radiation field to achieve / mediate the entanglement of the two or more quantum objects.

[0030] In an exemplary embodiment, the magnetic field gradient enables / mediates entanglement of two or more quantum objects within the magnetic field gradient region.

[0031] In an exemplary embodiment, the gate period is determined at least in part based on the time it takes for the magnetic field gradient to mediate / achieve / cause entanglement of two or more quantum objects.

[0032] In an exemplary embodiment, the controller is further configured to evolve the quantum states of each of the two or more quantum objects into a respective gate subspace state before transporting the two or more quantum objects into the magnetic field gradient region.

[0033] In one exemplary embodiment, each quantum state extends out of the memory subspace and into the gate subspace, and each gate subspace state is a respective state of the gate subspace.

[0034] In one exemplary embodiment, the memory subspace comprises two or more memory states, each a respective clock state, and the gate subspace comprises two or more gate subspace states, each a Zeeman state.

[0035] In an exemplary embodiment, evolving each quantum state into a respective gate subspace state comprises causing an operating signal, characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state, to be incident on at least one of the two or more quantum objects.

[0036] In an exemplary embodiment, the controller is further configured, after determining that the gate period has elapsed, to transport the two or more quantum objects out of the magnetic field gradient region and cause the quantum states of each of the two or more quantum objects to evolve from the gate subspace to a respective memory state.

[0037] In an exemplary embodiment, evolving the quantum states of each of the two or more quantum objects from the gate subspace to a respective memory state comprises causing an operating signal to be incident on at least one of the two or more quantum objects, the operating signal being characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state.

[0038] In an exemplary embodiment, the controller is further configured to cause implementation of one or more dynamic decoupling sequences for at least one quantum object of the two or more quantum objects between the start of the gate period and the completion of the gate period.

[0039] In an exemplary embodiment, performing one or more dynamic decoupling sequences on at least one quantum object of the two or more quantum objects comprises causing a dynamic decoupling manipulation signal to be incident on the at least one quantum object.

[0040] In an exemplary embodiment, the at least one quantum object is transported out of the magnetic field gradient region, a dynamic decoupling operating signal is incident on the at least one quantum object outside the magnetic field gradient region, and the at least one quantum object is transported back into the magnetic field gradient region. In an exemplary embodiment, the dynamic decoupling operating signal is incident on the at least one quantum object while the at least one quantum object is disposed within the magnetic field gradient region.

[0041] In an exemplary embodiment, the magnetic field gradient is turned on in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported into the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, and the magnetic field gradient is turned off in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported out of the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, or (c) after the two or more quantum objects have been transported out of the magnetic field gradient section.

[0042] In an exemplary embodiment, the magnetic field gradient is a static magnetic field gradient and is substantially constant over the gate period.

[0043] In an exemplary embodiment, the magnetic field gradient oscillates during the gate period at a frequency that is lower than a motional mode frequency of the motional mode of each of the two or more quantum objects.

[0044] According to another aspect, a controller is provided that is configured to control one or more components of a quantum system and that is configured to cause the quantum system to implement a geometric phase gate. In an exemplary embodiment, the controller comprises a processing device, a memory that stores executable instructions, and a driver controller element. The executable instructions, when executed by the processing device, are configured to cause the controller to use the driver controller element to control operation of the confinement device to transport two or more quantum objects confined by the confinement device into a magnetic field gradient region of the confinement device. The two or more quantum objects are subjected to a (near-field) magnetic field gradient while disposed in the magnetic field gradient region. The executable instructions, when executed by the processing device, are further configured to cause the controller to use the driver controller element to control operation of the confinement device such that the two or more quantum objects are no longer subjected to the magnetic field gradient in response to determining (by the controller) that a gating period has elapsed with at least one of (a) the two or more quantum objects disposed in the magnetic field gradient region or (b) the two or more quantum objects subjected to the magnetic field gradient.

[0045] In an exemplary embodiment, two or more quantum objects are entangled within a magnetic field gradient region during a gate period without using any radiation field to achieve / mediate the entanglement of the two or more quantum objects.

[0046] In an exemplary embodiment, the magnetic field gradient enables / mediates entanglement of two or more quantum objects within the magnetic field gradient region.

[0047] In an exemplary embodiment, the gate period is determined at least in part based on the time it takes for the magnetic field gradient to mediate / achieve / cause entanglement of two or more quantum objects.

[0048] In an exemplary embodiment, the executable instructions, when executed by the processing device, are further configured to cause the controller to use the driver controller element to cause each quantum state of the two or more quantum objects to evolve into a respective gate subspace state before transporting the two or more quantum objects into the magnetic field gradient region.

[0049] In one exemplary embodiment, each quantum state extends out of the memory subspace and into the gate subspace, and each gate subspace state is a respective state of the gate subspace.

[0050] In one exemplary embodiment, the memory subspace comprises two or more memory states, each a respective clock state, and the gate subspace comprises two or more gate subspace states, each a Zeeman state.

[0051] In an exemplary embodiment, evolving each quantum state into a respective gate subspace state comprises causing an operating signal, characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state, to be incident on at least one of the two or more quantum objects.

[0052] In an example embodiment, the executable instructions, when executed by the processing device, are further configured to cause the controller to use the driver controller element to transport the two or more quantum objects out of the magnetic field gradient region and evolve the quantum states of each of the two or more quantum objects from the gate subspace to a respective memory state after determining that the gate period has elapsed.

[0053] In an exemplary embodiment, evolving the quantum states of each of the two or more quantum objects from the gate subspace to a respective memory state comprises causing an operating signal to be incident on at least one of the two or more quantum objects, the operating signal being characterized by a frequency that is substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state.

[0054] In an example embodiment, the executable instructions, when executed by the processing device, are further configured to cause the controller to use the driver controller element to cause implementation of one or more dynamic decoupling sequences for at least one quantum object of the two or more quantum objects between a start of a gate period and a completion of the gate period.

[0055] In an exemplary embodiment, performing one or more dynamic decoupling sequences on at least one quantum object of the two or more quantum objects comprises causing a dynamic decoupling manipulation signal to be incident on the at least one quantum object.

[0056] In an exemplary embodiment, the at least one quantum object is transported out of the magnetic field gradient region, a dynamic decoupling operating signal is incident on the at least one quantum object outside the magnetic field gradient region, and the at least one quantum object is transported back into the magnetic field gradient region. In an exemplary embodiment, the dynamic decoupling operating signal is incident on the at least one quantum object while the at least one quantum object is disposed within the magnetic field gradient region.

[0057] In an exemplary embodiment, the magnetic field gradient is turned on in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported into the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, and the magnetic field gradient is turned off in the magnetic field gradient section during at least one of (a) while two or more quantum objects are being transported out of the magnetic field gradient section, or (b) while two or more quantum objects are disposed within the magnetic field gradient section, or (c) after the two or more quantum objects have been transported out of the magnetic field gradient section.

[0058] In an exemplary embodiment, the magnetic field gradient is a static magnetic field gradient and is substantially constant over the gate period.

[0059] In an exemplary embodiment, the magnetic field gradient oscillates during the gate period at a frequency that is lower than a motional mode frequency of the motional mode of each of the two or more quantum objects.

[0060] According to another aspect, a method for implementing a geometric phase gate is provided. In an exemplary embodiment, the method comprises the steps of: causing, by a controller of a quantum system, two or more qubits of the quantum system to be subjected to a (near-field) magnetic field gradient; and, in response to determining that a gate time period has elapsed since the two or more qubits of the quantum system began to be subjected to the magnetic field gradient, causing, by the controller, the two or more qubits to no longer be subjected to the magnetic field gradient.

[0061] In one exemplary embodiment, the gate period is determined based at least in part on the time it takes for the magnetic field gradient to mediate / achieve / cause entanglement of two or more qubits.

[0062] In an exemplary embodiment, two or more qubits are entangled within a magnetic field gradient region during a gate period without using any radiation field to achieve / mediate entanglement of the two or more qubits.

[0063] In an exemplary embodiment, a (near-field) magnetic field gradient enables / mediates entanglement of two or more qubits within the magnetic field gradient region.

[0064] In an exemplary embodiment, the magnetic field gradient is a static magnetic field gradient and is substantially constant over the gate period.

[0065] In an exemplary embodiment, the magnetic field gradient oscillates during the gate period at a frequency that is lower than a motional mode frequency of the motional mode of each of the two or more quantum objects.

[0066] Having described the invention in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale. [Brief explanation of the drawings]

[0067] [Figure 1] FIG. 1 is a block diagram of an exemplary quantum charge-coupled device (QCCD)-based quantum system, according to an exemplary embodiment. [Figure 2] 2 is a schematic diagram of a top view of an exemplary containment region of a containment device including a magnetic field gradient section, according to an exemplary embodiment. [Figure 3] 1 is a schematic diagram of a top view of at least a portion of a containment device, according to an example embodiment; [Figure 4] 1 is a flowchart illustrating a process, procedure, and / or operation for implementing a geometric phase gate, in accordance with an example embodiment. [Figure 5] 1 is a flowchart illustrating processes, procedures, and / or operations for implementing a geometric phase gate, in accordance with various embodiments. [Figure 6] FIG. 1 is an exemplary partial quantum state diagram illustrating a memory subspace and a gate subspace, according to an example embodiment. [Figure 7] FIG. 1 is a schematic diagram of an exemplary controller for a quantum system, according to an exemplary embodiment. [Figure 8]FIG. 1 is a schematic diagram of an example computational entity of a quantum system that may be used in accordance with certain example embodiments. DETAILED DESCRIPTION OF THE INVENTION

[0068] The present invention will now be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments of the invention are shown. Indeed, the present invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term "or" (also written " / ") is used herein in both the alternative and connective sense, unless otherwise indicated. The terms "exemplary" and "exemplary" are used as examples without denoting a level of quality. The terms "generally" and "about" refer to within the limits of reasonable processing and / or manufacturing and / or the capabilities of the user, unless otherwise indicated. Like numbers refer to like elements throughout.

[0069] Various embodiments provide methods, quantum systems, controllers, computer program products, etc. for implementing quantum logic gates. As used herein, a quantum logic gate is implemented on two or more quantum objects by gating two or more quantum objects with one another and / or by causing an interaction between the two or more quantum objects such that the logical function of the quantum logic gate is realized through the interaction of the two or more quantum objects. In various embodiments, the quantum logic gate is a geometric phase gate that includes entanglement of two or more qubits. The entanglement of two or more qubits is realized, mediated, and / or caused by a (near-field) magnetic field gradient. Specifically, the entanglement of two or more qubits does not require any radiation field (e.g., laser beam, microwave, etc.). For example, in various embodiments of a quantum logic gate, a radiation field is not used to realize, mediate, and / or cause the entanglement of two or more qubits. Rather, the magnetic field gradient is used to remove spin-motion entanglement of quantum objects embodying qubits and to realize, mediate, and / or induce entanglement between the quantum objects' respective quantum states.

[0070] Moreover, from the perspective of the quantum object, the magnetic field gradient is turned on and off slowly such that the spin entanglement of the quantum object is adiabatically removed for the implementation of a quantum logic gate. As used herein, the term “slowly” refers to the magnetic field gradient being turned on (for the implementation of a quantum logic gate) and / or turned off (after the implementation of a quantum logic gate) on a time scale that is slow compared to the motion frequency of the qubit defined by the trap confinement (e.g., operation of the confinement device).

[0071] As used herein, a near-field magnetic field gradient is the gradient of the near-field portion of the magnetic field generated by a respective magnetic field gradient source. For example, the near-field portion of the magnetic field may be such that the amplitude of the magnetic field at a distance r from the magnetic field gradient source is 1 / r 2For example, the near-field portion of a magnetic field is the portion of the magnetic field within a distance c / f from a magnetic field gradient source, where f is the frequency of any oscillation of the magnetic field and c is the speed of light. In an exemplary embodiment, the near-field portion of a magnetic field is the portion of the magnetic field within a distance c / (2πf) from the magnetic field gradient source. For example, the near-field magnetic field gradient is the gradient of a non-radial magnetic field.

[0072] In various embodiments, implementing a quantum logic gate comprises subjecting two or more qubits to a magnetic field gradient, and after and / or in response to determining that a gate period has elapsed since the two or more qubits began to be subjected to the (near-field) magnetic field gradient, the two or more qubits are no longer subjected to the (near-field) magnetic field gradient.

[0073] For example, in an exemplary embodiment, implementing a quantum logic gate comprises controlling operation of a confinement device that confines two or more quantum objects to cause the two or more quantum objects to be transported into a magnetic field gradient region defined by the confinement device and a magnetic field gradient source (e.g., a permanent magnet, an array of permanent magnets, an electromagnet, an array of electromagnets, a combined array of permanent magnets and electromagnets, etc.). While the two or more qubits are disposed within the magnetic field gradient region, they are subjected to a magnetic field gradient. After and / or in response to the two or more qubits being disposed in the magnetic field gradient region for a gate period, the two or more qubits are transported out of the magnetic field gradient region. In an exemplary embodiment, the gate period is determined at least in part based on the time it takes for the magnetic field gradient to realize, mediate, and / or cause entanglement of quantum states of the two or more quantum objects.

[0074] Conventional quantum logic gate implementations require radiation fields, such as laser beams or microwaves, to achieve, mediate, and / or induce entanglement of qubits. However, these radiation fields can lead to various gate errors, such as photon scattering, and / or affect the transitions of observer qubits, which can lead to crosstalk issues, phase noise, and the like. These gate errors can lead to low-fidelity logic gates and noisy computations. Furthermore, quantum logic gates using radiation fields are highly sensitive to the state of one or more qubit motional modes. Thus, spin-motion coupling can lead to additional gate errors, and / or long periods of time are required to cool qubits to near their motional ground states before quantum logic gate implementation. Therefore, various technical challenges exist for the implementation of quantum logic gates.

[0075] Various embodiments provide technical solutions to these technical problems. In various embodiments, quantum logic gates are implemented by using (near-field) magnetic field gradients to realize, mediate, and / or induce entanglement of two or more quantum bits. Because the (near-field) magnetic field gradient is a gradient of at least a portion of a magnetic field that is a non-radiative field, the quantum logic gates disclosed herein are immune to phase noise and key mechanisms that lead to crosstalk-related errors. Additionally, the quantum logic gates of various embodiments are insensitive to the motional modes and / or temperature of the quantum bits. Thus, time-consuming cooling operations can be avoided and / or reduced. Accordingly, various embodiments provide improved quantum logic gates, methods for implementing improved quantum logic gates, quantum systems configured to implement improved quantum logic gates, controllers configured to cause quantum systems to implement improved quantum logic gates, and the like.

[0076] Various embodiments of exemplary quantum logic gates will now be described with reference to exemplary QCCD-based quantum systems.

[0077] An exemplary QCCD-based quantum system 1 provides a schematic diagram of an exemplary QCCD-based quantum system 100 that can be used to implement quantum logic gates of various embodiments. The exemplary QCCD-based quantum system 100 shown in FIG. 1 is a quantum computer system that includes, at least in part, a quantum object confinement device 50 (e.g., an ion trap) that defines at least one magnetic field gradient region. For example, the confinement device 50 includes, or is physically associated with, a magnetic field gradient source 70.

[0078] In various embodiments, magnetic field gradient source 70 is a permanent magnet (e.g., a ferromagnetic material) and / or an array of permanent magnets that is part of confinement device 50 (e.g., located and / or incorporated in the same substrate and / or chip as confinement device 50) or is positioned in physical proximity to confinement device 50, such that quantum objects confined within the magnetic field gradient region of the confinement device are subjected to a magnetic field gradient. In an exemplary embodiment, magnetic field gradient source 70 is an electromagnet, an array of electromagnets, and / or an array of magnets comprising at least one electromagnet and at least one permanent magnet that is part of confinement device 50 (e.g., located and / or incorporated in the same substrate and / or chip as confinement device 50) or is positioned in physical proximity to confinement device 50, such that quantum objects confined within the magnetic field gradient region of the confinement device are subjected to a magnetic field gradient.

[0079] In various embodiments, magnetic field gradient source 70 is configured to generate a static magnetic field gradient, such that the magnetic field gradient is substantially constant and / or does not change over time (e.g., over a gate period). In various embodiments, magnetic field gradient source 70 is configured to generate an oscillating magnetic field gradient, where the magnetic field gradient oscillates over time at a frequency that is slower and / or lower than the motional frequency of the motional modes of the quantum object embodying the qubit. For example, in an exemplary embodiment, the magnetic field gradient oscillates at a frequency of about 100 kHz or at a frequency that is more detuned from the motional frequency of one or more motional modes of the quantum object embodying the qubit. For example, the magnetic field gradient may oscillate such that spin motional coupling of the quantum object is reduced and / or eliminated via the quantum object's interaction with the magnetic field gradient during implementation of a quantum logic gate.

[0080] In various embodiments, confinement device 50 is configured to confine quantum objects in one or more confinement regions defined by confinement device 50. In various embodiments, the quantum objects are neutral or charged atoms, neutral, charged, or multipolar molecules, quantum particles, quantum dots, or other objects that can be confined by the confinement device and have quantum states that can be manipulated via interaction with one or more manipulation signals and / or electric and / or magnetic fields. In various embodiments, the quantum objects embody qubits of QCCD-based quantum system 100. In one exemplary embodiment, confinement device 50 is an ion trap and the quantum objects are ions.

[0081] In various embodiments, QCCD-based quantum system 100 comprises computational entity 10 and quantum computer 110. In various embodiments, quantum computer 110 comprises controller 30 and quantum processor 115. In various embodiments, quantum processor 115 comprises cryogenic and / or vacuum chamber 40 enclosing confinement device 50 and magnetic field gradient source 70, and one or more manipulation sources 60. In an exemplary embodiment, one or more manipulation sources 60 comprise one or more light sources, such as lasers, microwave sources, or the like.

[0082] In various embodiments, one or more manipulation sources 60 are configured to generate and / or provide manipulation signals (e.g., light beams) configured to manipulate and / or cause the controlled evolution of quantum states of one or more quantum objects confined by confinement device 50. For example, in certain exemplary embodiments in which one or more manipulation sources 60 comprise one or more lasers, the lasers may provide one or more light beams and / or laser beams (e.g., π pulses) to confinement device 50 within cryogenic and / or vacuum chamber 40 via respective beam delivery systems 66. In various embodiments, beam delivery systems 66 comprise one or more optical elements, photonic integrated circuits (PICs), optical fibers, free-space optics, waveguides, etc.

[0083] In various embodiments, quantum processor 115 further comprises a plurality of voltage sources 80. Voltage sources 80 are operable (e.g., by controller 30) to generate and provide voltage signals to electrical elements (e.g., electrodes) of containment device 50, any electromagnets of magnetic field gradient source 70, etc.

[0084] In various embodiments, computational entity 10 is configured to allow a user to provide input to quantum computer 110 (e.g., via a user interface of computational entity 10) and receive, view, etc. output from quantum computer 110. Computational entity 10 may be in communication with a controller 30 of quantum computer 110 via one or more wired or wireless networks 20 and / or via direct wired and / or wireless communication. In an exemplary embodiment, computational entity 10 may convert, organize, format, etc., information / data, quantum computing algorithms, etc., into a computational language, executable instructions, instruction set, etc. that can be understood and / or implemented by controller 30.

[0085] In various embodiments, controller 30 is configured to control voltage source 80, a cryogenic system and / or vacuum system that controls the temperature and pressure within cryogenic and / or vacuum chamber 40, manipulation source 60, and / or other systems configured to control the environmental conditions (e.g., temperature, humidity, pressure, etc.) within cryogenic and / or vacuum chamber 40 and / or manipulate and / or cause the controlled evolution of the quantum states of one or more quantum objects (e.g., ions) confined by confinement device 50 (e.g., ion trap). In various embodiments, the quantum objects confined by confinement device 50 are used as qubits in quantum computer 110.

[0086] 2 shows a top view of a portion of containment device 50. The depicted portion of containment device 50 includes radio frequency (RF) rails 210A, 210B and three series of control electrodes 212A, 212B, 212C. Each series of control electrodes 212 includes multiple control electrodes 214. For example, the depicted portion of series of control electrodes 212A includes control electrodes 214A, 214B, ..., 214N.

[0087] In various embodiments, the RF voltage sources of voltage source 80 generate and provide RF voltage signals that are applied to RF rails 210A, 210B to generate pseudopotentials that define one or more linear confinement regions 200 of confinement device 50. A zero point of the pseudopotential generated by the RF voltage signals applied to RF rails 210A, 210B defines an RF null axis 216 that extends substantially along the centerline of linear confinement region 200. Quantum objects confined by confinement device 50 are confined to one or more linear confinement regions 200.

[0088] In various embodiments, confinement device 50 and magnetic field gradient source 70 define magnetic field gradient region 230. When quantum objects are confined by confinement device 50 within magnetic field gradient region 230, the quantum objects are subjected to a (near-field) magnetic field gradient. For example, magnetic field gradient region 230 is located within and / or corresponds to the near-field region of the magnetic field generated by magnetic field gradient source 70.

[0089] In various embodiments, confinement device 50 and one or more beam delivery systems 66 define radiation field zone 220. In various embodiments, radiation field zone 220 is configured such that a manipulation signal may be incident on the quantum objects when the quantum objects are disposed within radiation field zone 220. For example, beam delivery system 66 is configured such that a manipulation signal generated by manipulation source 60 is applied to confinement device 50 within radiation field zone 220 such that the manipulation signal may be incident on the quantum objects disposed within radiation field zone 220.

[0090] Quantum objects confined by confinement device 50 may be transported between different locations of confinement device 120 through application of a set of voltage signal sequences to control electrodes 212. For example, a quantum object (or multiple quantum objects) may be repeatedly transported between radiation field region 220 and magnetic field gradient region 230 and / or other locations defined by confinement device 50. For example, controller 30 is configured to control voltage source 80 to cause the performance of transport operations on the quantum object (or group of quantum objects) between the various locations defined by confinement device 50.

[0091] In certain exemplary embodiments, confinement device 50 comprises and / or defines a single linear confinement region 200. In various embodiments, confinement device 50 comprises and / or defines multiple confinement regions 200 and / or an array of confinement regions 200. Figure 3 provides a top view of a portion of confinement device 50 showing a two-dimensional array of confinement regions 200 (e.g., 200A, 200B, 200C, 200D, 200E, 200F, 200G, 200H). In the illustrated embodiment, multiple radiation field zones 220 (e.g., 220A, 220B, 220C, 220D, 220E, 220F) and / or multiple magnetic field gradient zones 230 (e.g., 230A, 230B, 230C, 230D, 230E, 230F) are defined along the array of confinement regions. For example, in the embodiment shown, multiple of the plurality of radiation field sections 220 (e.g., 220A, 220B, 220C, 220D, 220E, 220F) and / or multiple magnetic field gradient sections 230 (e.g., 230A, 230B, 230C, 230D, 230E, 230F) each provide a periodic arrangement of radiation field sections 220 and / or magnetic field gradient sections.

[0092] Exemplary Operation of a Quantum System for Implementing a Quantum Logic Gate In various systems, quantum systems such as the QCCD-based quantum system 100 may utilize (near-field) magnetic field gradients to achieve, mediate, and / or induce entanglement of two or more qubits corresponding to quantum logic gates. 4 provides a flowchart illustrating various processes, procedures, operations, etc. that may be performed (e.g., by controller 30) to cause a quantum logic gate to be implemented in accordance with various embodiments.

[0093] In various embodiments, quantum logic gates implemented through the processes, procedures, operations, etc. of Figure 4 cause entanglement of two or more qubits using entanglement realized, mediated, and / or caused by (near-field) magnetic field gradients. In various embodiments, radiation fields are not used to realize, mediate, and / or cause entanglement of two or more qubits when quantum logic gates are implemented.

[0094] In various embodiments, a quantum bit (e.g., quantum bit) is embodied as a quantum object. For example, the quantum state of the quantum object is used to encode information that is the result of a quantum computation. For example, controlled evolution of the quantum states of each of multiple quantum objects results in the performance of a quantum computation. The terms quantum object and qubit are used interchangeably herein.

[0095] In response to determining that two or more quantum objects should interact with one another via a quantum logic gate, controller 30 causes the transport of the two or more quantum objects to a common location. In an exemplary embodiment, the common location is within magnetic field gradient region 230. In an exemplary embodiment, the common location is outside magnetic field gradient region 230.

[0096] In step / operation 402, controller 30 causes two or more quantum objects that are to interact with each other via a quantum logic gate to begin experiencing a (near-field) magnetic field gradient. In an exemplary embodiment, the two or more quantum objects begin experiencing a (near-field) magnetic field gradient as a result of being transported into magnetic field gradient region 230. For example, controller 30 controls operation of voltage source 80 and / or confinement device 50 to cause two or more quantum objects to be transported into magnetic field gradient region 230 such that the two or more quantum objects begin experiencing a (near-field) magnetic field gradient. In an exemplary embodiment, magnetic field gradient source 70 comprises one or more electromagnets, which are operated such that a (near-field) magnetic field gradient is present in magnetic field gradient region 230 such that the two or more quantum objects begin experiencing a (near-field) magnetic field gradient.

[0097] In various embodiments, two or more quantum objects are subjected to a magnetic field gradient that is slowly turned on (by the quantum objects being moved into magnetic field gradient section 230 or by turning on a magnetic field generating circuit). Specifically, the quantum objects are subjected to a magnetic field gradient that is turned on and / or ramped up over a time axis that is slow compared to the frequency of motion of the qubits as defined by the trapping confinement (e.g., operation of the confinement device).

[0098] In step / operation 404, controller 30 determines that a gate period has elapsed with two or more quantum objects subjected to the (near-field) magnetic field gradient. For example, controller 30 may determine that a gate period has elapsed because two or more quantum objects have been transported into (near-field) magnetic field gradient region 230.

[0099] In various embodiments, the gate period is determined based at least in part on the time it takes for the (near-field) magnetic field gradient to realize, mediate, and / or cause entanglement of two or more quantum objects. In one exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 100 T / m, and the gate period is 10 4In an exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 200 T / m and the gate period is less than 3×10 3 In an exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 300 T / m and the gate period is less than 10 μs. 3 For example, in various embodiments, the gate period is determined at least in part based on a function of the magnetic field strength and / or amplitude of the magnetic field gradient, the motional frequency of one or more motional modes of the quantum object, etc.

[0100] In an exemplary embodiment, the magnetic field gradient is a static magnetic field gradient and is generally constant during the gate period. In an exemplary embodiment, the magnetic field gradient is an oscillating magnetic field gradient that oscillates at a frequency lower than the motional frequency of one or more motional modes of the quantum object. For example, the magnetic field gradient may oscillate such that spin motional coupling of the quantum object is reduced and / or eliminated via the interaction of the quantum object with the magnetic field gradient during implementation of a quantum logic gate.

[0101] In step / operation 406, after determining that the gate period has elapsed with the two or more quantum objects subjected to the (near-field) magnetic field gradient, and / or in response thereto, controller 30 causes the two or more quantum objects to no longer be subjected to the (near-field) magnetic field gradient. For example, after determining that the two or more quantum objects have been disposed in magnetic field gradient region 230 for the gate period, and / or in response thereto, controller 30 may control operation of voltage source 80 and / or confinement device 50 to cause the two or more quantum objects to be transported out of magnetic field gradient region 230. As a result of being transported out of magnetic field gradient region 230, the two or more quantum objects are no longer subjected to the magnetic field gradient. In an exemplary embodiment in which magnetic field gradient source 70 comprises at least one electromagnet, controller 30 may turn off the at least one electromagnet such that the two or more quantum objects are no longer subjected to the (near-field) magnetic field gradient.

[0102] In various embodiments, two or more quantum objects are subjected to a magnetic field gradient that is slowly turned off (by the quantum objects being moved out of magnetic field gradient region 230 or by the magnetic field generating circuitry being turned off). Specifically, the quantum objects are subjected to a magnetic field gradient that is turned off and / or reduced on a time scale that is slow compared to the frequency of motion of the qubits as defined by the trap confinement (e.g., operation of the confinement device).

[0103] 5 provides a flowchart illustrating various processes, procedures, operations, etc. that may be performed (e.g., by controller 30) to cause a quantum logic gate to be implemented according to various embodiments. In various embodiments, the quantum logic gate implemented through the processes, procedures, operations, etc. of FIG. 5 causes entanglement of the quantum states of two or more quantum objects using entanglement realized, mediated, and / or caused by a (near-field) magnetic field gradient. In various embodiments, a radiation field is not used to realize, mediate, and / or cause entanglement of the quantum states of two or more quantum objects when a quantum logic gate is implemented.

[0104] In various embodiments, controller 30 determines (e.g., based on the quantum circuit and / or algorithm being executed by quantum processor 115) that a quantum logic gate should be implemented for two or more quantum objects confined by confinement device 50. In response, controller 30 may initiate implementation of the quantum logic gate in step / operation 502.

[0105] In step / operation 502, each quantum state of two or more quantum objects is mapped to, expanded into, and / or transformed into a respective and / or corresponding gate subspace state in a gate subspace. For example, a memory subspace is defined as a subset of the quantum states of a quantum object. FIG. 6 shows a partial energy diagram illustrating a portion of the quantum states of a quantum object. Memory subspace 610 is defined in a ground state manifold 605 (e.g., an S-manifold) of the quantum object. In the illustrated embodiment, memory subspace 610 comprises two quantum states: a first memory state 612A and a second memory state 612B. In the illustrated embodiment, first memory state 612A and second memory state 612B are clock states (e.g., magnetic quantum number m=0).

[0106] In various embodiments, a gate subspace 620 is defined. Specifically, the gate subspace 620 is defined to include a first gate subspace state 622A and a second gate subspace state 622B. The first gate subspace state 622A is chosen and / or selected such that the first memory state 612A can be coupled to the first gate subspace state 622A via a first operating signal 630A. For example, in one exemplary embodiment, the first operating signal 630A is a π pulse of a laser beam characterized by a frequency that is resonant with or close enough to resonate with the energy difference between the first memory state 612A and the first gate subspace state 622A.

[0107] The second gate subspace state 622B is chosen and / or selected such that the second memory state 612B can be coupled to the second gate subspace state 622B via the second operating signal 630B. For example, the second operating signal 630B is a π pulse of a laser beam characterized by a frequency that resonates with or is close enough to resonate with the energy difference between the second memory state 612B and the second gate subspace state 622B. In an exemplary embodiment, the first operating signal and the second operating signal are characterized by the same frequency (e.g., the frequency difference between the first memory state 612A and the first gate subspace state 622A and the frequency difference between the second memory state 612B and the second gate subspace state 622B may be substantially equal). In an exemplary embodiment, the first operating signal and the second operating signal are characterized by different frequencies.

[0108] In an exemplary embodiment in which the first memory state 612A and the second memory state 612B are clock states, the memory states are relatively unaffected by magnetic fields. However, the gate subspace states 622A, 622B are chosen or selected to be Zeeman states with quantum number m≠0 such that the gate subspace states are affected by magnetic fields.

[0109] Returning to FIG. 5 , in step / operation 502, controller 30 causes a single qubit gate to be applied to each of two or more quantum objects on which a quantum logic gate is to be performed to map and / or transform the respective quantum states of each of the two or more quantum objects to a respective corresponding gate subspace state 622. For example, controller 30 may cause each of the two or more quantum objects on which a quantum logic gate is to be performed to be transported to radiation field zone 220. In various embodiments, the two or more quantum objects may be transported to the same radiation field zone 220 or different radiation field zones. In various embodiments, the two or more quantum objects may be transported to radiation field zone 220 in series or in parallel. Controller 30 then controls operation of one or more manipulation sources 60 and / or beam delivery system 66 to cause first manipulation signal 630A and / or second manipulation signal 630B to be incident on at least a portion of radiation field zone 220 (and thus incident on at least one of the two or more quantum objects). As a result of the first manipulation signal and / or the second manipulation signal being incident on at least one of the two or more quantum objects, the quantum state of the quantum object is mapped to and / or transformed from a respective memory state 612 (or a superposition of memory states 612) to a respective gate subspace state 622 (or a superposition of gate subspace states 622).

[0110] In step / operation 504, if the two or more quantum objects on which the quantum logic gate is to be implemented are not positioned within the same potential well of the confinement device 50, the controller 30 causes a transport operation to be performed so that the two or more quantum objects on which the quantum logic gate is to be implemented are positioned within the same potential well of the confinement device 50.

[0111] In step / operation 506, controller 30 causes two or more quantum objects in which a quantum logic gate is to be implemented to be transported into magnetic field gradient region 230. For example, controller 30 may control the operation of voltage source 80 and / or confinement device 50 such that a potential well in which the two or more quantum objects are disposed is transported into magnetic field gradient region 230. Thus, the two or more quantum objects begin and / or start to be subjected to a (near-field) magnetic field gradient while disposed within magnetic field gradient region 230.

[0112] In an exemplary embodiment, a (near-field) magnetic field gradient is present in magnetic field gradient region 230 before two or more quantum objects are transported into magnetic field gradient region 230. In various embodiments, magnetic field gradient source 70 comprises one or more electromagnets, and the magnetic field gradient region is turned on and / or brought into existence (e.g., the current to the electromagnets is increased to a steady-state current having an absolute value greater than zero) as two or more quantum objects are transported into magnetic field gradient region 230 and / or once two or more quantum objects are disposed within magnetic field gradient region 230.

[0113] In step / operation 508, controller 30 causes one or more dynamic decoupling sequences to be performed on at least one of the two or more quantum objects in which the quantum logic gate is implemented. In various embodiments, one or more dynamic decoupling sequences are performed to prevent and / or mitigate the effects of spin decoherence of at least one of the two or more quantum objects. In various embodiments, the dynamic decoupling sequence comprises applying a π pulse to at least one of the two or more qubits to cause a spin flip of the qubit. In certain exemplary embodiments, the one or more dynamic decoupling sequences comprise one or more Walsh sequences. Various other dynamic decoupling sequences are used in various other embodiments.

[0114] In various embodiments, one or more dynamic decoupling sequences are respectively performed on one or more of the two or more quantum objects during a gate period. For example, in one exemplary embodiment, g For each, one or more dynamic decoupling sequences are <t≦t g may be performed for each quantum object at time t=0, where time t=0 is when transport of two or more quantum objects into magnetic field gradient region 230 is complete. In various embodiments, the timing of the performance of the dynamic decoupling sequence is determined in part based on the dynamic decoupling sequence utilized.

[0115] In various embodiments, controller 30 is configured to implement a dynamic decoupling sequence on the quantum objects by controlling operation of one or more manipulation sources 60 to cause one or more dynamic decoupling manipulation signals to be incident on each quantum object of two or more quantum objects. In one exemplary embodiment, the dynamic decoupling manipulation signals are π pulses configured to correct and / or prevent errors caused by energy splitting of chaotic qubit drift during implementation of a quantum logic gate.

[0116] In various embodiments, one or more dynamic decoupling operating signals are incident on each quantum object while the quantum object is disposed within magnetic field gradient region 230. For example, in an exemplary embodiment, when performing a dynamic decoupling sequence, the (near-field) magnetic field gradient is turned off (e.g., when magnetic field gradient source 70 comprises one or more electromagnets, the current to the electromagnets is reduced to nominally zero), a dynamic decoupling operating signal is applied to each quantum object, and the (near-field) magnetic field gradient is turned on again (e.g., the current to the electromagnets is increased to a steady-state current having an absolute value greater than zero). In an exemplary embodiment, when performing a dynamic decoupling sequence on a quantum object, the quantum object is transported outside magnetic field gradient region 230 (e.g., possibly into radiation field region 220), a dynamic decoupling operating signal is incident on the quantum object, and the quantum object is transported back into magnetic field gradient region 230.

[0117] In various embodiments, the clock used to determine that a gating period has elapsed since two or more quantum objects began to experience the (near-field) magnetic field gradient and / or since the (initial) transport of two or more quantum objects into magnetic field gradient section 230 was completed is paused during the performance of one or more dynamic decoupling sequences. In an exemplary embodiment, the gating period is determined and / or defined to include the time that one or more dynamic decoupling sequences are to be performed during the gating period, and the clock is not paused for the performance of the one or more dynamic decoupling sequences.

[0118] In step / operation 510, after determining that a gating period has elapsed since two or more quantum objects began to be subjected to the (near-field) magnetic field gradient and / or since the (initial) transport of two or more quantum objects into magnetic field gradient region 230 was completed, and / or in response thereto, controller 30 controls the operation of voltage source 80 and / or confinement device 50 to cause the two or more quantum objects to be transported out of magnetic field gradient region 230. For example, after determining that two or more quantum objects have been disposed in magnetic field gradient region 230 during the gating period, and / or in response thereto, controller 30 may control the operation of voltage source 80 and / or confinement device 50 to cause the two or more quantum objects to be transported out of magnetic field gradient region 230. In an exemplary embodiment, as a result of being transported out of magnetic field gradient region 230, the two or more quantum objects are no longer subjected to the (near-field) magnetic field gradient. For example, in various embodiments in which the magnetic field gradient source 70 comprises one or more electromagnets, the (near-field) magnetic field gradient is turned off (e.g., the current to the electromagnets is reduced to nominally zero) before, during, or after two or more quantum objects are transported out of the magnetic field gradient region 230.

[0119] In various embodiments, the gate period is determined based at least in part on the time it takes for the (near-field) magnetic field gradient to realize, mediate, and / or cause entanglement of two or more quantum objects. In one exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 100 T / m, and the gate period is 10 4 In an exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 200 T / m and the gate period is less than 3×10 3 In an exemplary embodiment, the (near-field) magnetic field gradient has a field strength and / or amplitude greater than 300 T / m and the gate period is less than 10 μs. 3For example, in various embodiments, the gate period is determined based at least in part on a function of the magnetic field strength and / or amplitude of the (near-field) magnetic field gradient, the motional frequency of one or more motional modes of the quantum object, etc. In an exemplary embodiment, the gate period is determined based at least in part on the length of time required to perform one or more dynamic decoupling sequences performed as part of step / operation 508.

[0120] In step / operation 512, controller 30 causes a single qubit gate to be applied to each of two or more quantum objects implemented with a quantum logic gate to remap and / or convert the respective quantum states of each of the two or more quantum objects from respective gate subspace states 622 to corresponding states in memory subspace 610. For example, the quantum states of each of the two or more quantum objects are mapped to, evolve into, and / or converted to respective and / or corresponding memory states 612 in memory subspace 610. For example, controller 30 may cause each of two or more quantum objects implemented with a quantum logic gate to be transported to radiation field zone 220. In various embodiments, the two or more quantum objects may be transported to the same radiation field zone 220 or different radiation field zones. In various embodiments, the two or more quantum objects may be transported to radiation field zone 220 in series or in parallel. Controller 30 then controls operation of one or more manipulation sources 60 and / or beam delivery system 66 to cause first manipulation signal 630A and / or second manipulation signal 630B to be incident on at least a portion of radiation field region 220 (and thus on at least one of the two or more quantum objects). As a result of the first manipulation signal and / or second manipulation signal being incident on at least one of the two or more quantum objects, the quantum state of the quantum object is mapped to and / or transformed from a respective gate subspace state 622 (or superposition of gate subspace states 622) to a respective memory state 612 (or superposition of memory states 612).

[0121] After the implementation of the quantum logic gate is complete, controller 30 may continue to control the operation of various components of quantum processor 115 to cause quantum processor 115 to continue and / or terminate implementation of the quantum circuit and / or algorithm that includes the quantum logic gate. For example, each quantum object of the two or more quantum objects may be transported, have one or more single qubit gates implemented thereon, have one or more qubit gates implemented thereon, have one or more read operations implemented thereon, etc., in accordance with the quantum circuit and / or algorithm.

[0122] As will be understood, the first and second manipulation signals used to map the respective quantum states of two or more quantum objects from memory subspace states to gate subspace states, and vice versa, and the dynamic decoupling manipulation signals used to implement one or more dynamic decoupling sequences each act independently on a single quantum object. In other words, the first and second manipulation signals and the dynamic decoupling manipulation signals do not realize, mediate, and / or cause interaction and / or entanglement between the two or more quantum objects. The interaction and / or entanglement between the two or more quantum objects is realized, mediated, and / or caused solely by (near-field) magnetic field gradients.

[0123] Technical Advantages Conventional quantum logic gate implementations require radiation fields, such as laser beams or microwaves, to achieve, mediate, and / or induce entanglement of qubits. However, these radiation fields can lead to various gate errors, such as photon scattering, and / or affect the transitions of observer qubits, which can lead to crosstalk issues, phase noise, and the like. These gate errors can lead to low-fidelity logic gates and noisy computations. Furthermore, quantum logic gates using radiation fields are highly sensitive to the state of one or more qubit motional modes. Thus, spin-motion coupling can lead to additional gate errors, and / or long periods of time are required to cool qubits to near their motional ground states before quantum logic gate implementation. Therefore, various technical challenges exist for the implementation of quantum logic gates.

[0124] Various embodiments provide technical solutions to these technical problems. In various embodiments, quantum logic gates are implemented by using a (near-field) magnetic field gradient (e.g., a gradient of a non-radiative magnetic field) to realize, mediate, and / or induce entanglement of two or more quantum bits. Because the (near-field) magnetic field gradient oscillates (or is static) at a frequency lower than one of the motional frequencies of the quantum objects embodying the quantum bits, the quantum logic gates disclosed herein are immune to phase noise and major mechanisms that lead to crosstalk-related errors. Because no optical beam is used to realize, mediate, or induce entanglement of two or more quantum objects, sources of photon scattering errors are reduced. Additionally, the quantum logic gates of various embodiments are insensitive to the motional modes and / or temperature of the quantum bits. Thus, time-consuming cooling operations can be avoided and / or reduced. Accordingly, various embodiments provide improved quantum logic gates, methods for implementing improved quantum logic gates, quantum systems configured to implement improved quantum logic gates, controllers configured to cause quantum systems to implement improved quantum logic gates, and the like.

[0125] Exemplary Controller In various embodiments, confinement device 50 and at least one associated magnetic field gradient source 70 defining at least one magnetic field gradient region 230 are part of QCCD-based quantum system 100. In various embodiments, QCCD-based quantum system 100 comprises a controller 30 configured to control the operation of various components of quantum processor 115, for example. For example, controller 30 is configured to control voltage source 80 configured to provide electrical control signals to a series of control electrodes 212 of confinement device 50. Controller 30 may be further configured to control a cryogenic and / or vacuum system that controls the temperature and pressure within cryogenic and / or vacuum chamber 40, manipulation source 60, and / or other systems configured to control environmental conditions (e.g., temperature, humidity, pressure, etc.) within cryogenic and / or vacuum chamber 40 and / or manipulate and / or cause the controlled evolution of the quantum states of one or more quantum objects confined by quantum object confinement device 50.

[0126] As shown in FIG. 7 , in various embodiments, the controller 30 may comprise various controller elements, including a processing element 705, a memory 710, a driver controller element 715, a communication interface 720, an analog-to-digital converter element 725, etc. For example, the processing element 705 may comprise a programmable logic device (CPLD), a microprocessor, a coprocessing entity, an application-specific instruction set processor (ASIP), an integrated circuit, an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices and / or circuits, etc. and / or a controller. The term circuit may refer to an entirely hardware embodiment or a combination of hardware and a computer program product. In an exemplary embodiment, the processing element 705 of the controller 30 comprises and / or is in communication with a clock. In various embodiments, the processing element 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.

[0127] For example, memory 710 may comprise non-transitory memory, such as volatile and / or non-volatile memory storage, such as one or more of a hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. In various embodiments, memory 710 may store qubit records (e.g., in a qubit record data store, qubit record database, qubit record table, etc.) corresponding to qubits of the quantum computer, calibration tables, executable cues, computer program code (e.g., one or more computer languages, dedicated controller languages, etc.), etc. In an exemplary embodiment, execution of at least a portion of the computer program code stored in memory 710 (e.g., by processing element 705) causes controller 30 to perform one or more steps, operations, processes, procedures, etc. described herein for tracking the phase of atomic objects in an atomic system and causing adjustments to the phase of one or more manipulation sources and / or signals generated thereby.

[0128] In various embodiments, the driver controller element 715 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 715 may comprise a driver and / or a driver controller. For example, a driver controller may be configured to cause one or more corresponding drivers to operate according to executable instructions, commands, etc. scheduled and executed by the controller 30 (e.g., by the processing element 705). In various embodiments, the driver controller element 715 may enable the controller 30 to operate the operation source 60 to provide an input light beam, operate the voltage source 80 to provide respective electrical control signals to respective control electrodes 214, operate any electromagnets of the magnetic field gradient source 70, etc. In various embodiments, the driver controller element 715 enables the controller 30 to control and / or operate various drivers (e.g., laser drivers, vacuum component drivers, cryogenic and / or vacuum system component drivers, etc.).

[0129] In various embodiments, the controller 30 comprises means for communicating and / or receiving signals from one or more optical receiving components, such as a camera, a MEMs camera, a CCD camera, a photodiode, a photomultiplier tube, etc. For example, the controller 30 may comprise one or more analog-to-digital converter elements 725 configured to receive signals from one or more optical receiving components, calibration sensors, etc.

[0130] In various embodiments, controller 30 may comprise a communications interface 720 for interfacing and / or communicating with computational entity 10. For example, controller 30 may comprise a communications interface 720 for receiving executable instructions, command sets, etc. from computational entity 10 and for providing results of processing outputs received from quantum computer 110 (e.g., from a light collection system) and / or outputs to computational entity 10. In various embodiments, computational entity 10 and controller 30 may communicate via a direct wired and / or wireless connection and / or one or more wired and / or wireless networks 20.

[0131] Exemplary Computational Entities 8 provides an illustrative schematic diagram depicting an exemplary computational entity 10 that may be used with embodiments of the present invention. In various embodiments, computational entity 10 is configured to enable a user to provide input to quantum computer 110 (e.g., via a user interface of computational entity 10) and receive, display, analyze, etc., output from quantum computer 110.

[0132] 8 , computing entity 10 may include an antenna 812, a transmitter 804 (e.g., wireless), a receiver 806 (e.g., wireless), and a processing element 808 that provides signals to transmitter 804 and receives signals from receiver 806, respectively. The signals provided to transmitter 804 and received from receiver 806 may each include signaling information / data in accordance with an applicable wireless system air interface standard for communicating with various entities, such as controller 30, other computing entities 10, etc. In this regard, computing entity 10 may be capable of operating with one or more air interface standards, communication protocols, modulation types, and access types. In various embodiments, computing entity 10 comprises a network interface 820 configured to enable communication between computing entity 10 and controller 30 and / or various other computing devices. For example, the computing entity 10 may be configured to receive and / or provide communications using a wired data transmission protocol, such as Fiber Distributed Data Interface (FDDI), Digital Subscriber Line (DSL), Ethernet, Asynchronous Transfer Mode (ATM), Frame Relay, Data over Cable Service Interface Specification (DOCSIS), or any other wired transmission protocol.Similarly, the computing entity 10 may be configured to support general packet radio service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA), Global System for Mobile Communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), Time Division-Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized (EVDO), High Speed ​​Packet Access (HSPA), High-Speed ​​Downlink Packet Access (HSDPA), IEEE 802.11 (Wi-Fi), Wi-Fi Direct, 802.16 (WiMAX), ultra-wideband It may be configured to communicate over a wireless external communications network using any of a variety of protocols, such as Ultra Wideband (UWB), infrared (IR) protocol, near field communication (NFC) protocol, Wibree, Bluetooth protocol, wireless universal serial bus (USB) protocol, and / or any other wireless protocol.Computing entity 10 may use such protocols and standards to communicate using 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 the like.

[0133] Through these communication standards and protocols, computing entity 10 can communicate with various other entities using concepts such as Unstructured Supplementary Service information / data (USSD), Short Message Service (SMS), Multimedia Messaging Service (MMS), Dual-Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM dialer). Computing entity 10 can also download modifications, add-ons, and updates to its firmware, software (including, e.g., executable instructions, applications, program modules), and operating system.

[0134] Computing entity 10 may also comprise user interface devices comprising one or more user input / output interfaces (e.g., a display 816 and / or speakers / speaker drivers coupled to processing element 808, as well as a touchscreen, keyboard, mouse, and / or microphone coupled to processing element 808). For example, the user output interface may be configured to provide applications, browsers, user interfaces, interfaces, dashboards, screens, web pages, pages, and / or similar terms used interchangeably herein running on and / or accessible through computing entity 10 to cause a display or audible presentation of information / data or to interact with information / data via one or more user input interfaces. The user input interface may comprise any of several devices that enable computing entity 10 to receive data, such as a keypad 818 (hard or soft), a touch display, a voice / speech or motion interface, a scanner, reader, or other input device. In embodiments including a keypad 818, the keypad 818 may include (or cause the display of) conventional numeric (0-9) keys and related keys (#, *), as well as other keys used to operate computing entity 10, or may include a full set of alphanumeric keys or a set of keys that can be activated to provide a full set of alphanumeric keys. In addition to providing input, the user input interface may be used, for example, to enable or disable certain features, such as a screen saver and / or sleep mode. Through such input, computing entity 10 may collect information / data, user interaction / input, etc.

[0135] Computational entity 10 may include volatile storage or memory 822 and / or non-volatile storage or memory 824, 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, etc. Volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, registered memory, etc. Volatile and non-volatile storage or memory may store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, byte code, compiled code, interpreted code, machine code, executable instructions, etc., to implement the functionality of computational entity 10.

[0136] conclusion Many modifications and other embodiments of the inventions described herein will come to mind to one skilled in the art to which these inventions pertain having the benefit of the teachings presented in the foregoing descriptions and the associated drawings. It is to be understood, therefore, that the inventions are not to be limited to the particular embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation. [Explanation of symbols]

[0137] 10 Computational Entities 20 Network 30 Controllers 40 Cryogenic and / or Vacuum Chambers 50 Confinement Device 60 Operation source 66 Beam Delivery System 70 Magnetic field gradient source 80 Voltage Source 115 Quantum Processor 200 Linear Confinement Region 210 Radio Frequency Rail 212 Control electrode 214 Control electrode 216 RF zero axis 220 Radiation field area 230 Magnetic Gradient Area 610 Memory Subspace 612 Memory Status 620 Gate Subspace 622 Gate subspace states 630 Operation Signal 705 Processing Elements 710 memory 715 Driver Controller Elements 720 Communication Interface 725 Analog-to-Digital Converter Elements 804 Transmitter 806 receiver 808 Processing Elements 816 Display 818 keypad 820 network interface 822 Volatile Storage or Memory 824 Non-volatile storage or memory

Claims

1. 1. A method for implementing a geometric phase gate, comprising: controlling, by a controller, operation of the confinement device so that two or more quantum objects confined by the confinement device and disposed in a magnetic field gradient region of the confinement device are subjected to a magnetic field gradient; In response to determining that a gating period has elapsed with at least one of (a) the two or more quantum objects disposed within the magnetic field gradient region, or (b) the two or more quantum objects subjected to the magnetic field gradient, controlling, with the controller, operation of the confinement device such that the two or more quantum objects are no longer subjected to the magnetic field gradient; A method comprising:

2. 10. The method of claim 1, wherein the two or more quantum objects are entangled within the magnetic field gradient region during the gating period without the use of any radiation field to mediate entanglement of the two or more quantum objects.

3. The method of claim 1 , wherein the magnetic field gradient mediates entanglement of the two or more quantum objects within the magnetic field gradient region.

4. 4. The method of claim 3, wherein the gating period is determined based at least in part on the time it takes for the magnetic field gradient to mediate the entanglement of the two or more quantum objects.

5. The method of claim 1 , further comprising causing each quantum state of the two or more quantum objects to evolve into a respective gate subspace state.

6. 6. The method of claim 5, wherein the respective quantum states evolve out of a memory subspace and into a gate subspace, and the respective gate subspace states are respective states of the gate subspaces.

7. 7. The method of claim 6, wherein the memory subspace comprises two or more memory states, each a respective clock state, and the gate subspace comprises two or more gate subspace states, each a Zeeman state.

8. 6. The method of claim 5, wherein evolving the respective quantum states into the respective gate subspace states comprises causing an operation signal, characterized by a frequency substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state, to be incident on at least one of the two or more quantum objects.

9. causing the two or more quantum objects to be exempt from the magnetic field gradient, 6. The method of claim 5, comprising evolving the respective quantum states of the two or more quantum objects from the gate subspace into respective memory states.

10. 10. The method of claim 9, wherein evolving the respective quantum states of the two or more quantum objects from the gate subspace to respective memory states comprises causing an operation signal, characterized by a frequency substantially resonant with a frequency difference between at least one memory subspace state and a corresponding gate subspace state, to be incident on at least one of the two or more quantum objects.

11. 10. The method of claim 1, further comprising: performing one or more dynamic decoupling sequences on at least one quantum object of the two or more quantum objects between a start of the gate period and a completion of the gate period.

12. 12. The method of claim 11 , wherein performing the one or more dynamic decoupling sequences on the at least one quantum object of the two or more quantum objects comprises causing a dynamic decoupling manipulation signal to be incident on the at least one quantum object.

13. the magnetic field gradient is turned on in the magnetic field gradient section at least one of: (a) while the two or more quantum objects are being transported into the magnetic field gradient section; or (b) while the two or more quantum objects are disposed within the magnetic field gradient section; 10. The method of claim 1, wherein the magnetic field gradient is turned off in the magnetic field gradient section at least one of: (a) while the two or more quantum objects are being transported out of the magnetic field gradient section; (b) while the two or more quantum objects are disposed within the magnetic field gradient section; or (c) after the two or more quantum objects are transported out of the magnetic field gradient section.

14. 10. The method of claim 1, wherein either (a) the magnetic field gradient is a static magnetic field gradient and is substantially constant over the gate period, or (b) the magnetic field gradient oscillates during the gate period at a frequency that is lower than a motional mode frequency of a motional mode of each of the two or more quantum objects.

15. 1. A system configured to implement a geometric phase gate, comprising: a confinement device defining at least one magnetic field gradient region and operable to confine two or more quantum objects; a controller configured to control operation of the containment device, the controller comprising: controlling operation of the confinement device to cause the two or more quantum objects confined by the confinement device to be subjected to a magnetic field gradient within the at least one magnetic field gradient region of the confinement device; In response to determining that a gating period has elapsed with at least one of (a) the two or more quantum objects disposed within the magnetic field gradient region or (b) the two or more quantum objects subjected to the magnetic field gradient, controlling operation of the confinement device such that the two or more quantum objects are no longer subjected to the at least one magnetic field gradient. The system is configured as follows:

16. 16. The system of claim 15, wherein the containment device comprises or is associated with at least one of: (a) at least one permanent magnet; or (b) at least one electromagnet configured such that the magnetic field gradient is present in the at least one magnetic field gradient section.

17. 16. The system of claim 15, wherein the containment device defines a plurality of magnetic field gradient sections comprising the at least one magnetic field gradient section, the two or more quantum objects comprise a plurality of pairs of quantum objects, and the controller is configured to cause each of the plurality of pairs of quantum objects to be transported substantially simultaneously into and out of a respective magnetic field gradient section of the plurality of magnetic field gradient sections.

18. 16. The system of claim 15, wherein the containment device defines at least one radiation field region spatially distinct from the at least one magnetic field gradient region, and the controller is further configured to evolve a quantum state of at least one of the two or more quantum objects into a respective gate subspace state while the at least one quantum object is disposed within the at least one radiation field region prior to causing transport of the two or more quantum objects into the at least one magnetic field gradient region.

19. 1. A method for implementing a geometric phase gate, comprising: causing two or more qubits of the quantum system to be subjected to a magnetic field gradient by a controller of the quantum system; in response to determining that a gating period has elapsed since the two or more qubits of the quantum system began to be subjected to the magnetic field gradient, causing, by the controller, the two or more qubits to no longer be subjected to the magnetic field gradient; A method comprising:

20. 20. The method of claim 19, wherein the gate period is determined based at least in part on the time it takes for the magnetic field gradient to mediate the entanglement of the two or more qubits.

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