Geometric phase gates 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 of related applications This application claims priority to U.S. Patent Application No. 18 / 449,967, filed on 15 August 2023, which in turn claims priority to U.S. Patent Application No. 63 / 374,811, filed on 7 September 2022, and U.S. Patent Application No. 63 / 514,621, filed on 20 July 2023, the entire contents of which are incorporated herein by reference.

[0002] Various embodiments relate to quantum logic gates that use magnetic field gradients. Various embodiments relate to quantum logic gates that use magnetic field gradients to realize 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 may be used to entangle two qubits. Conventionally, the implementation of a quantum logic gate involves applying a laser beam or microwave to two qubits that are gated together. However, laser beams can lead to photon scattering during the implementation of a conventional quantum logic gate and / or introduce phase noise, leading to a decrease in the fidelity of the gate. Microwaves are sensitive to motional error and require the qubits to be cooled to a motional ground state. Through dedicated effort, ingenuity, and technological innovation, many of the shortcomings of such conventional quantum logic gates have been overcome by developing solutions constructed according to embodiments of the present invention. Many examples of these embodiments are described in detail herein. [Overview of the project] [Means for solving the problem]

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

[0005] In various embodiments, implementing a quantum logic gate involves causing two or more qubits to be subjected to a (near-field) magnetic field gradient. After it is determined that the gate period has elapsed since the two or more qubits began to be subjected to the magnetic field gradient, and / or in response thereto, the two or more qubits are made to no longer be subjected to the magnetic field gradient.

[0006] For example, in one exemplary embodiment, implementing a quantum logic gate involves controlling the operation of a confinement device that confines two or more quantum objects so that two or more quantum objects are 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 located within the magnetic field gradient region, they are subjected to a (near-field) magnetic field gradient. After the two or more qubits have been located within the magnetic field gradient region for the gate period, and / or in response thereto, the two or more qubits are transported out of the magnetic field gradient region. In one exemplary embodiment, the gate period is determined on at least partly the time it takes for the magnetic field gradient to realize, mediate, and / or induce entanglement of the 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 they are 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 their respective magnetic field-affected quantum states (e.g., via one or more single-qubit gates), thereby causing the two or more qubits to receive the (near-field) magnetic field gradient present in the magnetic field gradient region. After the two or more qubits have received the (near-field) magnetic field of the magnetic field gradient region for the duration of the gate period, and / or in response thereto, the quantum states of the two or more qubits are again associated with or coupled to their respective magnetic field-independent quantum states.

[0008] According to one embodiment, a method for implementing a geometric phase gate is provided. In one exemplary embodiment, the method comprises the step of controlling the operation of a confinement device by a controller so that two or more quantum objects to be confined by the confinement device are transported to a magnetic field gradient area of ​​the confinement device. The two or more quantum objects are subjected to a (near-field) magnetic field gradient while they are located in the magnetic field gradient area. The method further comprises the step of controlling the operation of the confinement device by a controller so that the two or more quantum objects are no longer subjected to a (near-field) magnetic field gradient, in response to the determination that the gate period has elapsed in at least one of the following states: (a) the two or more quantum objects are located in the magnetic field gradient area, or (b) the two or more quantum objects are subjected to a magnetic field gradient.

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

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

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

[0012] In one exemplary embodiment, the method further comprises the step of ensuring that the quantum states of two or more quantum objects are unfolded into their respective gate subspace states before transporting the two or more quantum objects into a magnetic field gradient region.

[0013] In one exemplary embodiment, each quantum state expands outside the memory subspace and into the gate subspace, and each gate subspace state is a state within the gate subspace.

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

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

[0016] In one exemplary embodiment, the method further comprises the steps of transporting two or more quantum objects outside the magnetic field gradient region after determining that the gate period has elapsed, and unfolding the quantum states of the two or more quantum objects from the gate subspace into their respective memory states.

[0017] In one exemplary embodiment, the step of unfolding the respective quantum states of two or more quantum objects from gate subspace to their respective memory states comprises the step of injecting an operational signal into at least one of the two or more quantum objects, the operational signal being characterized by a frequency substantially resonating with the frequency difference between at least one memory subspace state and the corresponding gate subspace state.

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

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

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

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

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

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

[0024] According to another aspect, a system configured to implement a geometric phase gate is provided. In certain exemplary embodiments, the system comprises a confinement device that (at least partially) defines at least one magnetic field gradient region and is operable to confine two or more quantum objects. The system further comprises a controller configured to control the operation of the confinement device. The controller is configured to control the operation of the confinement device to transport two or more quantum objects confined by the confinement device into at least one magnetic field gradient region of the confinement device. The two or more quantum objects are subject to a (near-field) magnetic field gradient while disposed within the magnetic field gradient region. The controller is further configured to control the operation of the confinement device such that the two or more quantum objects are no longer subject to at least one (near-field) magnetic field gradient in response to determining that a gate period has elapsed in at least one of (a) a state in which two or more quantum objects are disposed within the magnetic field gradient region or (b) a state in which two or more quantum objects have been subject to the magnetic field gradient.

[0025] In one exemplary embodiment, the confinement 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 exists in at least one magnetic field gradient region.

[0026] In one exemplary embodiment, the confinement device defines a plurality of magnetic field gradient regions including at least one magnetic field gradient region, the two or more quantum objects comprise a plurality of pairs of quantum objects, and the controller is configured such that each of the plurality of pairs of quantum objects is transported substantially simultaneously into and out of respective ones of the plurality of magnetic field gradient regions.

[0027] In one exemplary embodiment, the plurality of magnetic field gradient regions form a periodic array of magnetic field gradient regions.

[0028] In one exemplary embodiment, the confinement device defines at least one radiation field region spatially distinct from at least one magnetic field gradient region, and the controller is further configured such that, while at least one of the two or more quantum objects is disposed within the at least one radiation field region, the respective quantum state of each of the at least one quantum objects evolves into respective gate subspace states before causing the transport of the two or more quantum objects into the at least one magnetic field gradient region.

[0029] In one exemplary embodiment, the two or more quantum objects entangle within the magnetic field gradient region during the gate period without using any radiation field to realize / mediate the entanglement of the two or more quantum objects.

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

[0031] 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 / realize / cause the entanglement of two or more quantum objects.

[0032] In one exemplary embodiment, the controller is further configured such that, before transporting two or more quantum objects into a magnetic field gradient region, the quantum state of each of the two or more quantum objects is unfolded into its respective gate subspace state.

[0033] In one exemplary embodiment, each quantum state expands outside the memory subspace and into the gate subspace, and each gate subspace state is a state within the gate subspace.

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

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

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

[0037] In one exemplary embodiment, the step of unfolding the respective quantum states of two or more quantum objects from gate subspace to their respective memory states comprises the step of injecting an operational signal into at least one of the two or more quantum objects, the operational signal being characterized by a frequency substantially resonating with the frequency difference between at least one memory subspace state and the corresponding gate subspace state.

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

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

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

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

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

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

[0044] In another embodiment, a controller is provided which is configured to control one or more components of a quantum system and to cause the quantum system to perform a geometric phase gate. In one exemplary embodiment, the controller comprises a processing device, a memory for storing executable instructions, and a driver controller element. When executed by the processing device, the executable instructions are configured to cause the controller to use the driver controller element to control the operation of the confinement device so that two or more quantum objects to be confined by the confinement device are transported into the magnetic field gradient area of ​​the confinement device. The two or more quantum objects are subjected to a (near-field) magnetic field gradient while they are located in the magnetic field gradient area. When executed by the processing device, the executable instructions are further configured to cause the controller to use the driver controller element to control the operation of the confinement device so that the two or more quantum objects are no longer subjected to the magnetic field gradient in response to the controller determining that a gate period has elapsed in at least one of the following states: (a) the two or more quantum objects are located in the magnetic field gradient area, or (b) the two or more quantum objects are subjected to the magnetic field gradient.

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

[0046] In one exemplary embodiment, a magnetic field gradient realizes / mediates entanglement of two or more quantum objects within a magnetic field gradient region.

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

[0048] In one exemplary embodiment, the executable instruction is further configured to cause the controller to use a driver controller element so that, when executed by the processing device, the quantum state of each of the two or more quantum objects is unfolded into its 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 expands outside the memory subspace and into the gate subspace, and each gate subspace state is a state within the gate subspace.

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

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

[0052] In one exemplary embodiment, the executable instruction is further configured such that, once executed by the processing device, after determining that the gate period has elapsed, the controller uses a driver controller element to transport two or more quantum objects out of the magnetic field gradient region and to unpack the respective quantum states of the two or more quantum objects from the gate subspace into their respective memory states.

[0053] In one exemplary embodiment, the step of unfolding the respective quantum states of two or more quantum objects from gate subspace to their respective memory states comprises the step of injecting an operational signal into at least one of the two or more quantum objects, the operational signal being characterized by a frequency substantially resonating with the frequency difference between at least one memory subspace state and the corresponding gate subspace state.

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

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

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

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

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

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

[0060] In another embodiment, a method for implementing a geometric phase gate is provided. In one exemplary embodiment, the method comprises the steps of: having a controller of the quantum system cause two or more qubits of the quantum system to be subjected to a (near-field) magnetic field gradient; and, in response to the determination that the gate period has elapsed since the two or more qubits of the quantum system began to be subjected to the magnetic field gradient, having the controller cause 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 at least in part on the time it takes for the magnetic field gradient to mediate / realize / cause entanglement of two or more qubits.

[0062] In one exemplary embodiment, two or more qubits become entangled within a magnetic field gradient region during a gate period without using any radiation field to realize / mediate entanglement between the two or more qubits.

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

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

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

[0066] Although the present invention has been described using general terminology, the attached drawings, which are not necessarily drawn to scale, are referred to here. [Brief explanation of the drawing]

[0067] [Figure 1] This is a block diagram of an exemplary quantum charge-coupled device (QCCD) based quantum system according to one exemplary embodiment. [Figure 2] This is a schematic diagram of the upper surface of an exemplary confinement region of a confinement device including a magnetic field gradient region, according to an exemplary embodiment. [Figure 3] This is a schematic diagram of the top surface of at least a portion of a confinement device according to an exemplary embodiment. [Figure 4] This is a flowchart illustrating a process, procedure, and / or operation for implementing a geometric phase gate according to an exemplary embodiment. [Figure 5] This flowchart shows the processes, procedures, and / or operations for implementing geometric phase gates according to various embodiments. [Figure 6] This is an exemplary partial quantum state diagram showing a memory subspace and a gate subspace according to an exemplary embodiment. [Figure 7] This is a schematic diagram of an exemplary controller for a quantum system according to one exemplary embodiment. [Figure 8]This is a schematic diagram of an exemplary computational entity of a quantum system that may be used according to a particular exemplary embodiment. [Modes for carrying out the invention]

[0068] Herein, the present invention is described more fully below with reference to the accompanying drawings, which illustrate some, but not all, embodiments of the invention. In practice, the invention may be embodied in many different forms and should not be construed as being limited to the embodiments described herein. Rather, these embodiments are provided to satisfy the legal requirements to which this disclosure is applicable. The terms “or” (also written as “ / ”) are used herein in both substitutive and conjunctive senses unless otherwise indicated. The terms “exemplary” and “exemplary” are used as examples without indicating a level of quality. The terms “approximately” and “about” mean, unless otherwise indicated, within the limits of appropriate processing and / or manufacture, and / or within the user’s measurement capabilities. Similar numbers refer to similar elements as a whole.

[0069] Various embodiments provide methods, quantum systems, controllers, computer program products, etc., for implementing quantum logic gates. As used herein, quantum logic gates are implemented on two or more quantum objects by gating two or more quantum objects to each other and / or by causing interactions between two or more quantum objects so that the logic function of the quantum logic gate is realized through the interactions of two or more quantum objects. In various embodiments, the quantum logic gate is a geometric phase gate involving the 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 quantum logic gates, no radiation field is used to realize, mediate, and / or cause the entanglement of two or more qubits. Rather, the magnetic field gradient is used to remove the spin-motion entanglement of the quantum object that embodies the qubit, and to realize, mediate, and / or induce entanglement between the respective quantum states of the quantum object.

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

[0071] As used herein, the near-field magnetic field gradient is the gradient of the near-field portion of the magnetic field generated by each magnetic field gradient source. For example, the near-field portion of a magnetic field is the gradient of the magnetic field at a distance r from the magnetic field gradient source where the amplitude of the magnetic field is 1 / r 2This is the portion of the magnetic field that is proportional to [a certain value]. For example, the near-field portion of a magnetic field is the portion of the magnetic field within a distance c / f from the magnetic field gradient source, where f is the frequency of any oscillation of the magnetic field and c is the speed of light. In one 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 the non-radiated magnetic field.

[0072] In various embodiments, implementing a quantum logic gate involves causing two or more qubits to be subjected to a magnetic field gradient. After it is determined that the gate period has elapsed since the two or more qubits began to be subjected to the (near-field) magnetic field gradient, and / or in response thereto, the two or more qubits are made to no longer be subjected to the (near-field) magnetic field gradient.

[0073] For example, in one exemplary embodiment, implementing a quantum logic gate involves controlling the operation of a confinement device that confines two or more quantum objects so that two or more quantum objects are 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 located within the magnetic field gradient region, they are subjected to the magnetic field gradient. After the two or more qubits have been located within the magnetic field gradient region for the gate period, and / or in response thereto, the two or more qubits are transported out of the magnetic field gradient region. In one exemplary embodiment, the gate period is determined on at least partly the time it takes for the magnetic field gradient to realize, mediate, and / or induce entanglement of the quantum states of the two or more quantum objects.

[0074] Conventional implementations of quantum logic gates require a radiation field, such as a laser beam or microwave, to realize, mediate, and / or induce qubit entanglement. However, these radiation fields can lead to various gate errors, such as photon scattering, and / or affect the transitions of the observer qubit, which can lead to crosstalk problems, phase noise, and so on. These gate errors can lead to low-fidelity logic gates and noisy computations. Moreover, quantum logic gates that use radiation fields are highly sensitive to the state of one or more motion modes of the qubit. Thus, spin-motion coupling can lead to additional gate errors, and / or require a long time to cool the qubits to near their motion ground state before implementing the quantum logic gate. Consequently, various technical problems exist regarding 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 a (near-field) magnetic field gradient to realize, mediate, and / or induce entanglement of two or more qubits. Since the (near-field) magnetic field gradient is the gradient of at least a portion of a magnetic field that is a non-radiative field, the quantum logic gates disclosed herein are unaffected by phase noise and major mechanisms that would lead to crosstalk-related errors. In addition, the quantum logic gates of various embodiments are unresponsive to the motion mode and / or temperature of the qubits. 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 the quantum system to implement improved quantum logic gates, and the like.

[0076] Here, various embodiments of exemplary quantum logic gates are described in relation to exemplary QCCD-based quantum systems.

[0077] Exemplary QCCD-based quantum systems Figure 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 Figure 1 is a quantum computer system comprising a quantum object confinement device 50 (e.g., an ion trap) that defines at least a portion of at least one magnetic field gradient region. For example, the confinement device 50 comprises or is physically associated with a magnetic field gradient source 70.

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

[0079] In various embodiments, the 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 unchanging over time (e.g., over the gate period). In various embodiments, the magnetic field gradient source 70 is configured to generate an oscillating magnetic field gradient, in which case the magnetic field gradient oscillates over time at a frequency slower and / or lower than the motion frequency of the motion modes of the quantum body embodying the qubit. For example, in one exemplary embodiment, the magnetic field gradient oscillates at a frequency of about 100 kHz, or a frequency more detuned from the motion frequencies of one or more motion modes of the quantum body embodying the qubit. For example, the magnetic field gradient may oscillate so that the spin-motion coupling of the quantum body decreases and / or disappears through the interaction of the quantum body with the magnetic field gradient during the implementation of a quantum logic gate.

[0080] In various embodiments, the confinement device 50 is configured to confine a quantum object to one or more confinement regions defined by the confinement device 50. In various embodiments, the quantum object is a neutral or charged atom, a neutral, charged, or multipolar molecule, a quantum particle, a quantum dot, or any other object that can be confined by the confinement device and has a quantum state that can be manipulated through interaction with one or more operational signals and / or electric and / or magnetic fields. In various embodiments, the quantum object embodies a qubit of a QCCD-based quantum system 100. In one exemplary embodiment, the confinement device 50 is an ion trap, and the quantum object is an ion.

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

[0082] In various embodiments, one or more operating sources 60 are configured to generate and / or provide operating signals (e.g., light beams) configured to operate and / or induce the development of controlled quantum states of one or more quantum objects confined by the confinement device 50. For example, in one exemplary embodiment in which one or more operating sources 60 comprises one or more lasers, the lasers may provide one or more light beams and / or laser beams (e.g., π pulses) to the confinement device 50 in the cryogenic and / or vacuum chamber 40 via their respective beam delivery systems 66. In various embodiments, the beam delivery system 66 comprises one or more optical elements, photonic integrated circuits (PICs), optical fibers, free-space optical elements, waveguides, and the like.

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

[0084] In various embodiments, the computational entity 10 is configured to allow a user to provide input to the quantum computer 110 (for example, through the user interface of the computational entity 10) and to receive, view, etc., outputs from the quantum computer 110. The computational entity 10 may communicate with the controller 30 of the quantum computer 110 via one or more wired or wireless networks 20 and / or via direct wired and / or wireless communication. In one exemplary embodiment, the computational entity 10 can convert, configure, format, etc., information / data, quantum computation algorithms, etc., into a computational language, executable instructions, instruction set, etc., that the controller 30 can understand and / or implement.

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

[0086] Figure 2 shows a top view of a portion of the confinement device 50. The indicated portion of the confinement device 50 includes radio frequency (RF) rails 210A, 210B, and three sets of control electrodes 212A, 212B, 212C. Each set of control electrodes 212 comprises a plurality of control electrodes 214. For example, the indicated portion of the set of control electrodes 212A includes control electrodes 214A, 214B, ..., 214N.

[0087] In various embodiments, the RF voltage source of the voltage source 80 generates and provides RF voltage signals that are applied to RF rails 210A, 210B to generate pseudopotentials that define one or more linear confinement regions 200 of the confinement device 50. The zero points of the pseudopotentials generated by the RF voltage signals applied to RF rails 210A, 210B define an RF zero axis 216 that extends substantially along the centerline of the linear confinement region 200. A quantum object confined by the confinement device 50 is confined to one or more linear confinement regions 200.

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

[0089] In various embodiments, the confinement device 50 and one or more beam delivery systems 66 define a radiation field area 220. In various embodiments, the radiation field area 220 is configured such that an operation signal can be incident on a quantum object when the quantum object is placed within the radiation field area 220. For example, the beam delivery system 66 is configured such that an operation signal generated by an operation source 60 is applied to the confinement device 50 within the radiation field area 220 so that the operation signal can be incident on a quantum object placed within the radiation field area 220.

[0090] A quantum object confined by the confinement device 50 can be transported between different locations in the confinement device 120 by applying a set of voltage signal sequences to the control electrode 212. For example, a quantum object (or multiple quantum objects) can be repeatedly transported between the radiation field area 220 and the magnetic field gradient area 230 and / or other locations defined by the confinement device 50. For example, the controller 30 is configured to control the voltage source 80 to trigger the implementation of a transport operation for a quantum object (or group of quantum objects) between various locations defined by the confinement device 50.

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

[0092] Exemplary operation of a quantum system for implementing quantum logic gates In various systems, quantum systems such as QCCD-based quantum system 100 use (near-field) magnetic field gradients to realize, mediate, and / or induce entanglement of two or more qubits corresponding to quantum logic gates. It is operable to implement quantum logic gates. Figure 4 provides flowcharts illustrating various processes, procedures, and operations that may be performed (for example, by the controller 30) to implement quantum logic gates according to various embodiments.

[0093] In various embodiments, the quantum logic gates implemented through the processes, procedures, and operations shown in Figure 4 induce entanglement of two or more qubits using entanglement realized, mediated, and / or induced by a (near-field) magnetic field gradient. In various embodiments, no radiation field is used to realize, mediate, and / or induced entanglement of two or more qubits when the quantum logic gates are implemented.

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

[0095] In response to the determination that two or more quantum objects should interact with each other via quantum logic gates, the controller 30 transports the two or more quantum objects to a common location. In one exemplary embodiment, the common location is within the magnetic field gradient region 230. In another exemplary embodiment, the common location is outside the magnetic field gradient region 230.

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

[0097] In various embodiments, two or more quantum objects receive a magnetic field gradient that is slowly turned on (by moving the quantum objects into the magnetic field gradient region 230 or by turning on a magnetic field generating circuit). Specifically, the quantum objects receive a magnetic field gradient that is turned on and / or increased at a lower time axis compared to the motion frequency of the qubits defined by trap confinement (e.g., the operation of the confinement device).

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

[0099] In various embodiments, the gate period is determined on at least partly the time it takes for the (near-field) magnetic field gradient to realize, mediate, and / or induce entanglement of two or more quantum objects. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 100 T / m, and the gate period is 10 4The duration is less than μs. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 200 T / m, and the gate period is 3 × 10⁻⁶. 3 It is less than μs. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 300 T / m, and the gate period is 10 3 It is less than μs. For example, in various embodiments, the gate period is determined at least in part on a function of the amplitude of the magnetic field strength and / or magnetic field gradient, the motion frequency of one or more motion modes of the quantum body, etc.

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

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

[0102] In various embodiments, two or more quantum objects receive a magnetic field gradient that is slowly turned off (by moving the quantum objects out of the magnetic field gradient region 230 or by turning off the magnetic field generating circuit). Specifically, the quantum objects receive a magnetic field gradient that is turned off and / or reduced at a lower time axis compared to the motion frequency of the qubits defined by trap confinement (e.g., the operation of the confinement device).

[0103] Figure 5 provides a flowchart illustrating various processes, procedures, and operations that may be implemented (e.g., by the controller 30) to ensure that quantum logic gates are implemented according to various embodiments. In various embodiments, the quantum logic gates implemented through the processes, procedures, and operations of Figure 5 induce entanglement of quantum states of two or more quantum objects using entanglement realized, mediated, and / or induced by a (near-field) magnetic field gradient. In various embodiments, no radiation field is used to realize, mediate, and / or induced entanglement of quantum states of two or more quantum objects when the quantum logic gates are implemented.

[0104] In various embodiments, the controller 30 determines that a quantum logic gate should be implemented on two or more quantum objects that are confined by the confinement device 50 (for example, based on a quantum circuit and / or algorithm being executed by the quantum processor 115). In response, the controller 30 may initiate the 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 associated with and / or corresponding gate subspace states in the gate subspace, expanded to and / or transformed to them. For example, a memory subspace is defined as a subset of the quantum states of a quantum object. Figure 6 shows a partial energy diagram illustrating some of the quantum states of a quantum object. The memory subspace 610 is defined in the ground state manifold 605 (e.g., S-manifold) of the quantum object. In the embodiment shown, the memory subspace 610 comprises two quantum states: a first memory state 612A and a second memory state 612B. In the embodiment shown, the first memory state 612A and the 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 selected and / or chosen such that a first memory state 612A can be coupled to the first gate subspace state 622A via a first operation signal 630A. For example, in one exemplary embodiment, the first operation signal 630A 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 first memory state 612A and the first gate subspace state 622A.

[0107] The second gate subspace state 622B is selected and / or chosen such that the second memory state 612B can be coupled to the second gate subspace state 622B via the second operation signal 630B. For example, the second operation 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 and second operation signals are characterized by the same frequency (for example, 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 and second operation signals are characterized by different frequencies.

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

[0109] Returning to Figure 5, in step / operation 502, the controller 30 ensures that a single qubit gate is applied to each of the two or more quantum objects on which a quantum logic gate is to be performed in order to map each of the two or more quantum objects to their respective quantum states and / or transform their respective gate subspace states 622. For example, the controller 30 may ensure that each of the two or more quantum objects on which a quantum logic gate is to be performed is transported to the radiation field area 220. In various embodiments, the two or more quantum objects may be transported to the same radiation field area 220 or to different radiation field areas. In various embodiments, the two or more quantum objects may be transported to the radiation field area 220 in series or in parallel. The controller 30 then controls the operation of one or more operating sources 60 and / or beam delivery systems 66 so that a first operating signal 630A and / or a second operating signal 630B are incident on at least a portion of the radiation field area 220 (and therefore on at least one of the two or more quantum objects). As a result of the first and / or second operation signals being incident on at least one of two or more quantum objects, the quantum states of the quantum objects are mapped and / or transformed from their respective memory states 612 (or superpositions of memory states 612) to their respective gate subspace states 622 (or superpositions of gate subspace states 622).

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

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

[0112] In one exemplary embodiment, a (near-field) magnetic field gradient exists in the magnetic field gradient region 230 before two or more quantum objects are transported into the magnetic field gradient region 230. In various embodiments, the magnetic field gradient source 70 comprises one or more electromagnets, and as two or more quantum objects are transported into the magnetic field gradient region 230 and / or when two or more quantum objects are placed within the magnetic field gradient region 230, the magnetic field gradient region is turned on and / or made to exist (for example, the current to the electromagnets is increased to a stable state current with an absolute value greater than 0).

[0113] In step / operation 508, the controller 30 ensures that one or more dynamic decoupling sequences are performed on at least one of the two or more quantum objects on which the quantum logic gate is being implemented. In various embodiments, one or more dynamic decoupling sequences are performed to prevent and / or mitigate the effects of spin decoherence on 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 inversion of the qubit. In one exemplary embodiment, one or more dynamic decoupling sequences comprises 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 performed on one or more of two or more quantum objects during a gate period. For example, in one exemplary embodiment, during a gate period t g For this, one or more dynamic decoupling sequences are performed at time 0 <t≦t g This may be performed for each quantum object, and time t=0 is when the transport of two or more quantum objects into the magnetic field gradient region 230 is complete. In various embodiments, the timing of the execution of the dynamic decoupling sequence is determined in part based on the dynamic decoupling sequence being used.

[0115] In various embodiments, the controller 30 is configured to perform a dynamic decoupling sequence on quantum objects by controlling the operation of one or more operation sources 60 so that one or more dynamic decoupling operation signals are incident on each of two or more quantum objects. In one exemplary embodiment, the dynamic decoupling operation signal is a π pulse configured to correct and / or prevent errors caused by the energy splitting of disordered qubit drift during the execution of a quantum logic gate.

[0116] In various embodiments, one or more dynamic decoupling operation signals are incident on each quantum object while the quantum object is located within the magnetic field gradient region 230. For example, in one exemplary embodiment, when the dynamic decoupling sequence is performed, the (near-field) magnetic field gradient is turned off (for example, if the magnetic field gradient source 70 comprises one or more electromagnets, the current to the electromagnets is reduced nominally to 0), the dynamic decoupling operation signals are applied to each quantum object, and the (near-field) magnetic field gradient is turned on again (for example, the current to the electromagnets is increased to a stable state current with an absolute value greater than 0). In one exemplary embodiment, when the dynamic decoupling sequence is performed on a quantum object, the quantum object is transported out of the magnetic field gradient region 230 (for example, possibly into the radiation field region 220), the dynamic decoupling operation signals are incident on the quantum object, and the quantum object is transported back into the magnetic field gradient region 230.

[0117] In various embodiments, the clock used to determine that a gate period has elapsed since two or more quantum objects began to receive a (near-field) magnetic field gradient and / or since the (initial) transport of two or more quantum objects to the magnetic field gradient region 230 was completed is paused during the execution of one or more dynamic decoupling sequences. In one exemplary embodiment, the gate period is determined and / or defined to include the time during which one or more dynamic decoupling sequences should be executed, and the clock is not paused for the execution of one or more dynamic decoupling sequences.

[0118] In step / operation 510, after determining that a gate period has elapsed after two or more quantum objects begin to experience a (near-field) magnetic field gradient and / or after the (initial) transport of two or more quantum objects into the magnetic field gradient region 230, and / or in response thereto, the controller 30 controls the operation of the voltage source 80 and / or the confinement device 50 to cause the two or more quantum objects to be transported out of the magnetic field gradient region 230. For example, after determining that two or more quantum objects are located within the magnetic field gradient region 230 during the gate period and / or in response thereto, the controller 30 may control the operation of the voltage source 80 and / or the confinement device 50 to cause the two or more quantum objects to be transported out of the magnetic field gradient region 230. In one exemplary embodiment, as a result of being transported out of the magnetic field gradient region 230, the two or more quantum objects cease to experience a (near-field) magnetic field gradient. For example, in various embodiments where 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 electromagnet is nominally reduced to zero) before, during, or after the 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 achieve, mediate, and / or cause entanglement of the two or more quantum objects. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 100 T / m, and the gate period is less than 10 4 μs. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 200 T / m, and the gate period is less than 3×10 3 μs. In one exemplary embodiment, the (near-field) magnetic field gradient has a magnetic field strength and / or amplitude greater than 300 T / m, and the gate period is 10 3It is less than μs. For example, in various embodiments, the gate period is determined on at least part of a function of the magnetic field strength and / or amplitude of the (near-field) magnetic field gradient, the motion frequency of one or more motion modes of the quantum body, etc. In one exemplary embodiment, the gate period is determined on at least part of 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, the controller 30 ensures that a single qubit gate is applied to each of the two or more quantum objects through which the quantum logic gate has been implemented, in order to reassociate and / or transform each of the quantum states of the two or more quantum objects from their respective gate subspace states 622 to their corresponding states in the memory subspace 610. For example, each quantum state of the two or more quantum objects is associated with, expanded to, and / or transformed to, their respective and / or corresponding memory states 612 in the memory subspace 610. For example, the controller 30 may ensure that each of the two or more quantum objects through which the quantum logic gate has been implemented is transported to the radiation field area 220. In various embodiments, the two or more quantum objects may be transported to the same radiation field area 220 or to different radiation field areas. In various embodiments, the two or more quantum objects may be transported to the radiation field area 220 in series or in parallel. The controller 30 then controls the operation of one or more operating sources 60 and / or beam delivery systems 66 so that the first operating signal 630A and / or the second operating signal 630B are incident on at least a portion of the radiation field area 220 (and thus at least one of the two or more quantum objects). As a result of the first operating signal and / or the second operating signal being incident on at least one of the two or more quantum objects, the quantum state of the quantum object is mapped and / or transformed from each gate subspace state 622 (or a superposition of gate subspace states 622) to each memory state 612 (or a superposition of memory states 612).

[0121] After the execution of the quantum logic gates is complete, the controller 30 may continue to control the operation of various components of the quantum processor 115 to cause the quantum processor 115 to continue and / or terminate the execution of the quantum circuit and / or algorithms containing the quantum logic gates. For example, each of two or more quantum objects may be transported according to the quantum circuit and / or algorithm, and one or more single qubit gates may be executed on it, one or more qubit gates may be executed on it, and one or more read operations may be executed on it.

[0122] As can be understood, the first and second operation signals used to associate the respective quantum states of two or more quantum objects, from memory subspace states to gate subspace states and vice versa, as well as the dynamic decoupling operation signals used to perform one or more dynamic decoupling sequences, each act independently on a single quantum object. In other words, the first and second operation signals and the dynamic decoupling operation signals do not realize, mediate, and / or cause interactions and / or entanglement between two or more quantum objects. Interactions and / or entanglement between two or more quantum objects are realized, mediated, and / or caused solely by the (near-field) magnetic field gradient.

[0123] Technical advantages Conventional implementations of quantum logic gates require a radiation field, such as a laser beam or microwave, to realize, mediate, and / or induce qubit entanglement. However, these radiation fields can lead to various gate errors, such as photon scattering, and / or affect the transitions of the observer qubit, which can lead to crosstalk problems, phase noise, and so on. These gate errors can lead to low-fidelity logic gates and noisy computations. Moreover, quantum logic gates that use radiation fields are highly sensitive to the state of one or more motion modes of the qubit. Thus, spin-motion coupling can lead to additional gate errors, and / or require a long time to cool the qubits to near their motion ground state before implementing the quantum logic gate. Consequently, various technical problems exist regarding 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 non-radiated magnetic field gradient) to realize, mediate, and / or induce entanglement of two or more qubits. Since the (near-field) magnetic field gradient oscillates (or is static) at a frequency lower than one of the motion frequencies of one or more quantum bodies embodying the qubits, the quantum logic gates disclosed herein are unaffected by phase noise and major mechanisms that would lead to crosstalk-related errors. Since no light beam is used to realize, mediate, or induce entanglement of two or more quantum bodies, the source of photon scattering errors is reduced. In addition, the quantum logic gates of various embodiments are unresponsive to the motion mode and / or temperature of the qubits. 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 the quantum system to implement improved quantum logic gates, and the like.

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

[0126] As shown in Figure 7, in various embodiments, the controller 30 may comprise various controller elements, including a processing element 705, memory 710, driver controller element 715, communication interface 720, analog-to-digital converter element 725, and so on. For example, the processing element 705 may comprise a programmable logic device (CPLD), microprocessor, coprocessing entity, application-specific instruction set processor (ASIP), integrated circuit, application-specific integrated circuit (ASIC), field-programmable gate array (FPGA), programmable logic array (PLA), hardware accelerator, other processing devices and / or circuits, etc. and / or controllers. The term "circuit" may refer to an entire hardware embodiment or a combination of hardware and computer program products. In one exemplary embodiment, the processing element 705 of the controller 30 comprises and / or communicates 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 include non-temporary memory such as volatile and / or non-volatile memory storage, such as one or more of the following: hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. In various embodiments, memory 710 may store qubit records corresponding to the qubits of the quantum computer (e.g., in a qubit record data store, qubit record database, qubit record table, etc.), calibration tables, executable queues, computer program code (e.g., one or more computer languages, a dedicated controller language, etc.). In one exemplary embodiment, the execution of at least a portion of computer program code stored in memory 710 (for example, by processing element 705) causes the controller 30 to perform one or more steps, operations, processes, procedures, etc., as described herein, to track the phases of atomic objects in an atomic system and cause adjustments to the phases of one or more manipulated 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 drivers and / or driver controllers. For example, a driver controller may be configured so that one or more corresponding drivers 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 operating source 60 to provide an input light beam, operate the voltage source 80 to provide respective electrical control signals to their respective control electrodes 214, operate any electromagnets of the magnetic field gradient source 70, and so on. In various embodiments, the driver controller element 715 may enable 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 includes means for communicating and / or receiving signals from one or more optical receiving components, such as cameras, MEMS cameras, CCD cameras, photodiodes, and photomultiplier tubes. For example, the controller 30 may include one or more analog-to-digital converter elements 725 configured to receive signals from one or more optical receiving components, calibration sensors, and the like.

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

[0131] Exemplary Computation Entity Figure 8 provides a schematic diagram for illustrative purposes representing an exemplary computational entity 10 that may be used in conjunction with embodiments of the present invention. In various embodiments, the computational entity 10 is configured to allow a user to provide input to a quantum computer 110 (for example, through the user interface of the computational entity 10) and to receive, display, analyze, and so on, output from the quantum computer 110.

[0132] As shown in Figure 8, the 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 the transmitter 804 and receives signals from the receiver 806, respectively. The signals provided to the transmitter 804 and received from the 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 the controller 30 and other computing entities 10. In this regard, the computing entity 10 may be able to operate with one or more air interface standards, communication protocols, modulation types, and access types. In various embodiments, the computing entity 10 includes a network interface 820 configured to enable communication between the computing entity 10 and the controller 30 and / or various other computing devices. For example, the computing entity 10 may be configured to receive and / or provide communications using wired data transmission protocols such as Fiber Distributed Data Interface (FDDI), Digital Subscriber Line (DSL), Ethernet, Asynchronous Transfer Mode (ATM), Frame Relay, Data Over Cable Service Interface Specification (DOCSIS), or any other wired transmission protocol.Similarly, computing entity 10 handles 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), and ultra-wideband. It may be configured to communicate over a wireless external communication network using any of the following protocols: UWB (Ultra-Wide Blocking), infrared (IR) protocol, near-field communication (NFC) protocol, Wibree, Bluetooth protocol, wireless universal serial bus (USB) protocol, and / or any other wireless protocol.Computational entity 10 may use protocols and standards such as Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), and HyperText Markup Language (HTML) to communicate.

[0133] Through these communication standards and protocols, the compute 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). The compute entity 10 can also download changes, add-ons, and updates to its firmware, software (including executable instructions, applications, and program modules), and operating system, for example.

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

[0135] Computation 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, register memory, etc. Volatile and non-volatile storage or memory can store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, bytecode, compiled code, interpreted code, machine code, executable instructions, etc., in order to implement the functions of computation entity 10.

[0136] conclusion Many modifications and other embodiments of the invention described herein will be recalled by those skilled in the art who benefit from the teachings presented in the above description and the accompanying drawings. It should therefore be understood that the invention should not be limited to any particular embodiment disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. Certain terms are used herein, but they are used in a general sense, not for limitation. [Explanation of Symbols]

[0137] 10 Computation Entities 20 Networks 30 controllers 40 Cryogenic and / or vacuum chamber 50 Confinement device 60 Operation source 66 Beam Delivery Systems 70 Magnetic field gradient source 80 Voltage source 115 Quantum Processors 200 Linear confinement region 210 Radio frequency rail 212 Control electrodes 214 Control electrodes 216 RF Zero Axis 220 Radiation field area 230 Magnetic field gradient area 610 memory subspaces 612 Memory Status 620 Gate subspace 622 Gate subspace state 630 Control signal 705 Processing elements 710 memory 715 Driver Controller Element 720 Communication Interfaces 725 Analog-to-Digital Converter Element 804 Transmitter 806 Receiver 808 processing elements 816 displays 818 Keypad 820 Network Interfaces 822 Volatile storage or memory 824 Non-volatile storage or memory

Claims

1. A method for implementing a geometric phase gate, The steps include controlling the operation of the confinement device by a controller so that two or more quantum objects confined by the confinement device and placed in the magnetic field gradient area of ​​the confinement device are subjected to the magnetic field gradient, (a) In response to the determination that the gate period has elapsed in at least one of the following states: the state in which the two or more quantum objects are located within the magnetic field gradient area, or (b) the state in which the two or more quantum objects are subjected to the magnetic field gradient, the controller controls the operation of the confinement device so that the two or more quantum objects are no longer subjected to the magnetic field gradient. Equipped with, A method wherein the magnetic field gradient causes entanglement between the two or more quantum objects, and the entanglement between the two or more quantum objects is realized solely by the magnetic field gradient, and the magnetic field gradient is the near-field portion of the magnetic field.

2. The method according to claim 1, further comprising the step of performing one or more dynamic decoupling sequences on 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.

3. The method according to claim 1, wherein (a) the magnetic field gradient is a static magnetic field gradient and is constant over the gate period, or (b) the magnetic field gradient oscillates during the gate period at a frequency lower than the motion mode frequency of each of the two or more quantum bodies' motion modes.

Images