Method and apparatus for implementing sequence of single-qubit gates

Abstract

The application discloses a method and device for implementing a single quantum bit gate sequence. The method comprises the following steps: in response to a gate operation in the single quantum bit gate sequence, controlling the starting time and running time of the gate operation to satisfy the following conditions: when the gate operation is performed, t1 < t < t2, wherein t2-t1 is an integer; when the gate operation is performed, t3 < t < t4; using a time-dependent driving wave packet to apply a periodic driving to a quantum bit, the wave packet being non-zero within time t1-t2 and zero at other times; calibrating the wave packet so that the quantum bit is transformed from a state to a state after two gate operations are continuously performed; adjusting the integer to change the running time, determining different corresponding gate fidelities, and selecting the maximum value of the fidelity as the optimal running time. The application improves the fidelity of the single quantum bit gate.

Description

Technical Field

[0001] This application relates to the field of superconducting quantum computing technology, specifically to a method and apparatus for realizing single-qubit gate sequences for high-fidelity manipulation of superconducting qubits. Background Technology

[0002] Quantum computing utilizes the properties of quantum mechanics for information processing, with the qubit as its basic unit. Quantum gates are the fundamental operations acting on qubits; a series of quantum gates can be used to construct quantum circuits to execute quantum algorithms. In superconducting quantum computing, single-qubit gates are typically implemented by applying resonant microwave or magnetic flux to the qubit, inducing Rabi oscillations.

[0003] Traditional implementation schemes typically rely on the Rotating Wave Approximation (RWA), which ignores the high-frequency oscillation term in the Hamiltonian when the driving frequency resonates with the qubit frequency and the driving strength is much smaller than the qubit frequency. This approximation holds true when the driving is weak, but when pursuing high-speed quantum gate operations, the driving strength increases, the rotating wave approximation fails, and the gate operation fidelity decreases.

[0004] For superconducting qubits like Fluxonium, which exhibit high anharmonicity, the qubit frequency is typically low, making the conditions for applying the rotating wave approximation more stringent and limiting the improvement of their gate operation speed. Furthermore, traditional methods require separate calibration of gate operations rotating around the X and Y axes, a cumbersome process. Summary of the Invention

[0005] This application provides a method, apparatus, electronic device, and storage medium for realizing a single-qubit gate sequence, so as to at least solve the above-mentioned technical problems existing in the prior art.

[0006] According to a first aspect of this application, a method for implementing a single-qubit gate sequence is provided, wherein the resonant frequency of the qubit is calibrated. Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is The method includes:

[0007] Control the start time in response to each gate operation in a single-qubit gate sequence. and running time At least one of the following conditions must be met:

[0008] When execution When the door opens, start time Running time ,in, It is an integer;

[0009] When execution When the door opens, start time Running time ;

[0010] Using time-dependent driving wave packets Applying a periodic drive to the qubit, the wave packet in time to Non-zero at time intervals, zero at other times;

[0011] For the wave packet Calibration is performed to enable continuous execution of two... Behind the door, the quantum bits from State transformation State; Adjusting integer Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

[0012] In some alternative implementations, the qubit is a Fluxonium qubit.

[0013] In some alternative implementations, the use of time-dependent driving wave packets Applying periodic drive to qubits includes:

[0014] A time-dependent magnetic flux is applied to the Josephson junction and inductor circuit of the Fluxonium qubit by an alternating current source. The Proportional to ,in The wave packet is the envelope function. and Proportional, φ represents the initial phase of the magnetic flux driving signal.

[0015] In some alternative implementations, the driving Hamiltonian is... Determined by the following formula:

[0016]

[0017] in, and For Pauli matrices, To reduce Planck's constant, Time variable.

[0018] In some alternative implementations, the wave packet Calibration includes:

[0019] By experimentally measuring two consecutive... The state change of a qubit after gate interaction;

[0020] Adjust the amplitude or shape of the wave packet until the desired effect is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

[0021] In some alternative implementations, the determination of different The corresponding door fidelity includes:

[0022] Constructed by random and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The corresponding fidelity of the value is determined, and the optimal value is selected.

[0023] In some alternative implementations, the method further includes:

[0024] A gate operation is performed when the qubit is at its sweet spot, wherein the magnetic flux is fixed. , It is a magnetic flux quantum.

[0025] According to a second aspect of this application, an apparatus for implementing a single-qubit gate sequence is provided, comprising:

[0026] Setting unit, used to calibrate the resonant frequency of quantum bits. Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is ;

[0027] The control unit is used to control the start time of each gate operation in a single-qubit gate sequence. and running time At least one of the following conditions must be met:

[0028] When execution When the door opens, start time Running time ,in, It is an integer;

[0029] When execution When the door opens, start time Running time ;

[0030] Drive unit for using time-dependent drive wave packets Applying a periodic drive to the qubit, the wave packet in time to Non-zero at time intervals, zero at other times;

[0031] A calibration unit is used for calibrating the wave packet. Calibration is performed to ensure that two consecutive executions are performed. Behind the door, the quantum bits from State transformation state;

[0032] Selecting a cell is used to adjust the integer. Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

[0033] In some alternative implementations, the qubit is a Fluxonium qubit.

[0034] In some alternative embodiments, the driving unit is further configured to:

[0035] A time-dependent magnetic flux is applied to the Josephson junction and inductor circuit of the Fluxonium qubit by an alternating current source. The Proportional to ,in The wave packet is the envelope function. and Proportional, φ represents the initial phase of the magnetic flux driving signal.

[0036] In some alternative implementations, the driving Hamiltonian is... Determined by the following formula:

[0037]

[0038] in, and For Pauli matrices, To reduce Planck's constant, Time variable.

[0039] In some alternative embodiments, the calibration unit is further configured to:

[0040] By experimentally measuring two consecutive... The state change of a qubit after gate interaction;

[0041] Adjust the amplitude or shape of the wave packet until the desired effect is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

[0042] In some alternative implementations, the selection unit is further configured to:

[0043] Constructed by random and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The corresponding fidelity of the value is determined, and the optimal value is selected.

[0044] In some alternative embodiments, the control unit is further configured to:

[0045] A gate operation is performed when the qubit is at its sweet spot, wherein the magnetic flux is fixed. , It is a magnetic flux quantum.

[0046] According to a third aspect of this application, a non-transitory computer-readable storage medium is provided that stores computer instructions for causing the computer to perform the steps of the method for implementing the single-qubit gate sequence.

[0047] According to a fourth aspect of this application, an electronic device is provided, comprising:

[0048] At least one processor;

[0049] and a memory communicatively connected to the at least one processor; wherein,

[0050] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the steps of the method for implementing the single-qubit gate sequence.

[0051] The technical solution of this application effectively alleviates the systematic error introduced by RWA failure by eliminating initial time dependence, and significantly improves the fidelity of single-qubit gates. It allows for the use of higher Rabi frequencies for gate operations without sacrificing gate speed to maintain RWA validity, which helps shorten the overall algorithm runtime and reduce decoherence effects. The embodiments of this application are not only applicable to Fluxonium qubits, but theoretically also applicable to any qubit system where RWA failure occurs due to a low operating frequency. The embodiments of this application, by digitally constraining the pulse start time and duration, are easily implemented on modern arbitrary waveform generators (AWGs) and have good engineering application prospects.

[0052] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent from the following description. Attached Figure Description

[0053] The above and other objects, features, and advantages of exemplary embodiments of this application will become readily apparent from the following detailed description taken in conjunction with the accompanying drawings. Several embodiments of this application are illustrated in the drawings by way of example and not limitation, in which:

[0054] In the accompanying drawings, the same or corresponding reference numerals indicate the same or corresponding parts.

[0055] Figure 1 A flowchart illustrating the implementation method of a single-qubit gate sequence according to an embodiment of this application is shown;

[0056] Figure 2 A schematic diagram illustrating the Fluxonium superconducting quantum bit driven by an alternating current source according to an embodiment of this application is shown.

[0057] Figure 3 A flowchart illustrating the implementation method of a single-qubit gate sequence according to an embodiment of this application is shown;

[0058] Figure 4 A schematic diagram of the composition structure of a device for implementing a single-qubit gate sequence according to an embodiment of this application is shown;

[0059] Figure 5 A schematic diagram of the composition structure of an electronic device according to an embodiment of this application is shown. Detailed Implementation

[0060] To make the objectives, features, and advantages of this application more apparent and understandable, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] The embodiments of this application precisely control the timing parameters of the gate operation to synchronize with the intrinsic period of the driving Hamiltonian, replacing the fine calibration of the driving phase, and structurally suppress the influence of high-frequency error terms, effectively mitigating the operational errors introduced by the failure of the Rotating Wave Approximation (RWA), thereby improving the fidelity and reliability of the quantum gate.

[0062] Figure 1 This paper illustrates a flowchart of a method for implementing a single-qubit gate sequence according to an embodiment of this application. Before the method is executed, the system parameters need to be calibrated, specifically, the resonant frequency of the quantum bit is calibrated. Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is Construct a time-dependent Hamiltonian H(t) for realizing a single-qubit gate. This Hamiltonian contains a linearly polarized periodic driving term that resonates with the qubit. This linearly polarized periodic driving term consists of a time-dependent wave packet Ω(t), a start time, and a time period. It is defined together with the phase φ. When executing any single-qubit gate, its start time... Constrain it to be a periodic T (T=) of the non-RWA term in the Hamiltonian. / The time constraint is also imposed on the single-qubit gate, ensuring it is also an integer multiple of the period T. Under this time constraint, experiments were conducted to determine the method that allows for precise flipping of the qubit state (e.g., from |0 to T). To |1 The optimal time-dependent wave packet Ω(t) is obtained and fixed for use in all subsequent operations. Through the above processing, the effect of each gate is deterministic and consistent regardless of when the gate sequence starts execution, fundamentally solving the problem of initial time dependence.

[0063] like Figure 1 As shown, the implementation method of a single-qubit gate sequence in this application includes the following processing steps:

[0064] Step 101: Control the start time of each gate operation in the single-qubit gate sequence. and running time The corresponding conditions are met.

[0065] In this embodiment of the application, the qubit is a superconducting qubit, specifically a Fluxonium qubit.

[0066] Control door operation start time and running time The following conditions must be met:

[0067] When execution When the door opens, start time Running time ,in It is an integer;

[0068] When execution When the door opens, start time Running time ,in It is an integer.

[0069] In the embodiments of this application, The door consists of two consecutive Door structure, The door consists of two consecutive Door structure.

[0070] Step 102, using time-dependent driving wave packets Apply periodic drive to the qubit.

[0071] The wave packet in this embodiment is the driving envelope function, which is a time-dependent real number function that determines the instantaneous amplitude or intensity of the driving signal. Its specific shape can be Gaussian, square wave, trigonometric function wave packet, etc. The wave packet in this embodiment is only used during gate operation. to The integral area is non-zero inside and zero at other times; the angle of the quantum state rotation is determined by the integral area.

[0072] To apply periodic drive to the qubit, specifically, to apply time-dependent magnetic flux through an alternating current source in the Josephson junction and inductor loop of the Fluxonium qubit. , Proportional to ,in, For envelope function, wave packet and Proportional This represents the initial phase of the flux-driven signal. For superconducting qubits (such as Fluxonium), if driven by microwave pulses, This represents the initial phase of the microwave signal. If driven by magnetic flux, The initial phase for generating magnetic flux signals from an alternating current source.

[0073] In this embodiment of the application, the driving Hamiltonian is... Determined by the following formula:

[0074]

[0075] in, and For Pauli matrices, To reduce Planck's constant, Time variable.

[0076] In traditional methods, the driving phase is in a rotating coordinate system. It directly determines which axis the quantum state revolves around on the Bloch sphere, when At that time, the effective Hamiltonian of the driving force is proportional to To achieve rotation around the X-axis (e.g.) (door), when At that time, the effective Hamiltonian of the driving force is proportional to To achieve rotation around the Y-axis (e.g.) (Gate). Therefore, precise control and calibration of the phase are required. Only by controlling the start time of the quantum gate can quantum gates with different axes be realized. This application's embodiments control the start time of the quantum gate. This indirectly sets the effective relative phase, thereby bypassing the need for... Perform independent and precise calibration.

[0077] Specifically, setting door ,set up door , to these two different Substituting into the Hamiltonian Item, and combined The conditions are equivalent to automatically and discretely changing the effective driving phase, thereby realizing rotations about the X-axis and Y-axis respectively. Therefore, no additional calibration or precise settings are required. The value only needs to be a fixed one. (e.g., 0), and then by precisely controlling the start time of the door. This allows you to obtain the required gate type. This greatly simplifies the calibration process.

[0078] Step 103: Calibrate the wave packet experimentally. This allows two consecutive executions. Behind the door, the quantum bits from State transformation state.

[0079] Specifically, through experimental measurement of two consecutive... The state change of the qubit after gate interaction; adjusting the amplitude or shape of the wave packet until the desired state is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

[0080] Hamiltonian The shape of the envelope of the driving signal (e.g., Gaussian) determines the angle of quantum state rotation through its integral area. This can be demonstrated experimentally (e.g., by performing two...). The gate is then observed to determine if completion is achieved. arrive (flipping) to calibrate The amplitude, so that it corresponds precisely. The rotation angle. After calibration, the shape of this wave packet is fixed as a standard pulse. By scanning different integers... That is, change the gate time The gate fidelity at different speeds was evaluated using randomized benchmark tests, and the optimal gate fidelity was selected. This achieves the best balance between speed and errors caused by leakage, distortion, etc.

[0081] Step 104, Adjust the integer Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

[0082] Specifically, constructing a system composed of random... and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The value corresponds to the fidelity, and the value that maximizes the fidelity is selected. The value is used as the optimal running time.

[0083] The following specific examples further illustrate the essence of the technical solutions in the embodiments of this application.

[0084] This application's embodiments are applicable to all cases where the Rabi oscillation frequency is close to the qubit frequency, and there are no limitations on practical systems. This application's embodiments solve the problem of low quantum gate operation speed for fluxonium qubits. By combining fluxonium with this application's embodiments, superconducting qubits can achieve both low leakage error rates and fast single-qubit gate operations. Therefore, even with high single-qubit gate speeds, errors caused by the failure of the rotating wave approximation can be sufficiently mitigated. This application's embodiments require only one calibration of the rotation angle to implement a single quantum gate, eliminating the need for relative phase calibration, thus simplifying the calibration process.

[0085] First, let's declare some constants used. Imaginary unit: Planck's constant: Reduce Planck's constant: Unit charge: Superconducting flux quantum: Three Pauli matrices: , , The basis vectors can be computed and written in an equivalent form: , , The frequency referred to in this article is the angular frequency: (energy of the first excited state) (Ground state energy) × / .

[0086] The Fluxonium in this embodiment is a superconducting quantum bit, composed of a superconducting Josephson junction and a superconducting inductor connected in parallel. The superconducting inductor is composed of many superconducting Josephson junctions connected in series, and its equivalent circuit element is an inductor. The equivalent circuit of Fluxonium is as follows: Figure 2As shown, the equivalent circuit of Fluxonium consists of capacitors. Josephson knot (Josephson knot is a type of knot) The system consists of inductors L connected in parallel, with one end grounded. A fixed magnetic flux is used. This fixed magnetic flux, passing through the Josephson junction and the inductor loop, is induced by a direct current source. This flux is set to... This is called the sweet spot, and this setting makes the qubit least sensitive to magnetic flux noise. The dynamic variable of the circuit is the nodal magnetic flux. .

[0087] A single-qubit gate is implemented using a time-dependent Hamiltonian. The start time of a single-qubit gate is... The running time is recorded as A time-dependent Hamiltonian typically contains a linearly polarized periodic drive, and its general form is:

[0088]

[0089] in, It is the frequency of a quantum bit. It is a time-dependent wave packet, and its specific form is not limited. It can be a Gaussian wave packet, a trigonometric function wave packet, etc. It is the driving frequency. It is the time point at which the wave packet begins. It is the driving phase. satisfy: ; hour ; .

[0090] A quantum gate is a unitary operator that is proportional to the integral of a time-dependent Hamiltonian over time.

[0091] To achieve resonance between the driving frequency and the quantum bit frequency: The quantum petrified frequency is denoted as... ;

[0092] In the rotating coordinate system, the time-dependent Hamiltonian becomes

[0093]

[0094] This refers to Hermitian conjugate. Existing schemes generally use a rotating wave approximation here, which is directly omitted. It is conjugate with its Hermitian counterpart. Its condition for validity is... The maximum value is much smaller than If this condition is met, Its Hermitian conjugate will become a high-frequency oscillation term, making the rotating wave approximation accurate.

[0095] After using the rotating wave approximation With initial time Irrelevant.

[0096] If the conditions for the rotating wave approximation do not hold, i.e. The maximum value is close to , Its conjugate with Hermione cannot be neglected. In this case... The initial time of the quantum gate This is a function. This will lead to a decrease in the fidelity of single quantum gate sequences. It can be seen that... The period of its Hermitian conjugate is .

[0097] The following describes the embodiments of this application. , , , These are four types of single quantum gates, and the methods for implementing gate sequences. The start time of the first gate in the quantum gate sequence is uniformly recorded as 0.

[0098] Figure 3 A flowchart illustrating the implementation method of a single-qubit gate sequence according to an embodiment of this application is shown, as follows: Figure 3 As shown, the implementation method of a single-qubit gate sequence in this application includes:

[0099] First, the frequency of the quantum bits needs to be calibrated. , Door start time Conditions to be met: Where n is an integer. Door running time Conditions must be met Where m is an integer. Time-dependent wave packet. It needs to be calibrated in the experiment so that two consecutive runs are possible. Behind the door, the quantum bits from State transition to State. After calibration, It can then be saved as a specific function. The door operates by running two consecutive times. The door is realized. Door start time Conditions to be met: Where n is an integer. Door running time Conditions must be met Where m is an integer. Time-dependent wave packet. Use the saved function form. The door operates by running two consecutive times. The door is realized.

[0100] Due to the quantum gate runtime It is an integer multiple of the Hamiltonian period, which makes the effect of the quantum gate independent of the start time of each quantum gate, thus alleviating... The fidelity reduction caused by its Hermite conjugation.

[0101] In this embodiment, an optimal value of m is determined to maximize the fidelity of the single quantum gate sequence. Since excessively short or long quantum gate runtimes will decrease fidelity if m is too small or too large, there will always exist a value of m that maximizes the gate fidelity; thus, the optimal single quantum gate runtime can be determined. Gate fidelity is typically determined using random values. and A sequence of gates is used for random benchmarking. Different... Different gate fidelity values ​​were tested, and the value of m that maximized the fidelity was selected.

[0102] To realize a single-qubit gate, a magnetic flux drive is applied to the Fluxonium, which is achieved using the principle of mutual inductance through an alternating current source. For example... Figure 2 As shown, a fixed magnetic flux passes through the Josephson junction and the inductor loop. Become . It is a time-dependent magnetic flux, induced by an alternating current source. The alternating current is proportional to... .in, It is an envelope function. Proportional to Due to mutual inductance, Also proportional to .

[0103] According to classical circuit theory, the system's Lagrangian for:

[0104]

[0105] The capacitance of the Josephson junction. For inductance, For Josephson junction energy, For magnetic flux quanta, For nodal flux, conjugate momentum for:

[0106]

[0107] The classical Hamiltonian of the system is obtained through Legendre transformation:

[0108]

[0109] Classical mechanical variables are transformed into quantum mechanical operators through canonical quantization. Nodal magnetic flux. Transform into a flux operator conjugate momentum Transform into momentum operator They satisfy the canonical quantum commutation formula:

[0110]

[0111] For superconducting quantum circuits, dimensionless reduction operators are generally used. The reduction operators are: momentum reduction operator. ;Reduced flux operator Transform the following physical quantities into their corresponding reduced physical quantities: fixed magnetic flux becomes reduced fixed magnetic flux. Time-dependent magnetic flux is converted into reduced time-dependent magnetic flux. .

[0112] Systematic Hammite Operator Writing:

[0113]

[0114] in, It is the system's capacitance energy. It is inductive energy. It is the Josephson junction.

[0115] Expand the quadratic terms in the system's Hamiltonian operator and omit the non-operator terms:

[0116]

[0117] The operators within the square brackets are undriven Fluxonium Hamiltonian operators. :

[0118]

[0119] The second item is flux drive.

[0120] Fluxonium qubits exhibit good anharmonicity. In practical applications, only the ground state is considered. and the first excited state The Hamiltonian operator of Fluxonium without a driver operates in... and In Hilbert space, the expansion of a qubit using basis vectors takes the following form:

[0121]

[0122] Among them, the Pauli matrix . It is the frequency of the quantum bit. It is equal to the energy difference between the first excited state and the ground state. The values ​​need to be calibrated through measurement in the experiment.

[0123] reduced flux operator In the Hilbert space of a qubit, it is proportional to .

[0124] System Hamiltonian Operator The form of a qubit in Hilbert space is:

[0125]

[0126] in, The wave packet is driven by magnetic flux, and its specific functional form is determined by adjusting the amplitude and envelope of the alternating current source. The specific values ​​are determined by measurement and calibration during the experiment.

[0127] This application's embodiments structurally suppress errors caused by the failure of the rotating wave approximation, enabling high-fidelity single-qubit gate operations even with high drive strength (fast gate speed). This is particularly beneficial for qubits like Fluxonium, which have low intrinsic frequencies and are severely limited by the rotating wave approximation in traditional methods, allowing them to achieve fast gate operations and fully leverage their advantages of high anharmonicity and low leakage errors. This application's embodiments only require one calibration of the rotation angle of the X_π / 2 gate; the Y gate is automatically obtained by changing the start time, eliminating the need for separate calibration of the drive phase, significantly reducing calibration steps and time. This application can be directly implemented in existing superconducting quantum chip measurement and control systems by updating the control waveform timing, without hardware modification, thus improving its versatility.

[0128] Figure 4 A schematic diagram of the structural composition of a single-qubit gate sequence implementation device according to an embodiment of this application is shown, as follows: Figure 4 As shown, the apparatus for implementing a single-qubit gate sequence according to an embodiment of this application includes:

[0129] Setting unit 40 is used to calibrate the resonant frequency of quantum bits. Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is ;

[0130] Control unit 41 is used to control the start time of each gate operation in a single-qubit gate sequence. and running time At least one of the following conditions must be met:

[0131] When execution When the door opens, start time Running time ,in, It is an integer;

[0132] When execution When the door opens, start time Running time ;

[0133] Drive unit 42 is used to drive time-dependent wave packets. Applying a periodic drive to the qubit, the wave packet in time to Non-zero at time intervals, zero at other times;

[0134] Calibration unit 43 is used for calibrating the wave packet Calibration is performed to enable continuous execution of two... Behind the door, the quantum bits from State transformation state;

[0135] Select unit 44 to adjust the integer. Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

[0136] In some alternative implementations, the qubit is a Fluxonium qubit.

[0137] In some alternative embodiments, the drive unit 42 is further configured to:

[0138] A time-dependent magnetic flux is applied to the Josephson junction and inductor circuit of the Fluxonium qubit by an alternating current source. The Proportional to ,in The wave packet is the envelope function. and Proportional, φ represents the initial phase of the magnetic flux driving signal.

[0139] In some alternative implementations, the driving Hamiltonian is... Determined by the following formula:

[0140]

[0141] in, and For Pauli matrices, To reduce Planck's constant, Time variable.

[0142] In some alternative embodiments, the calibration unit 43 is further configured to:

[0143] By experimentally measuring two consecutive... The state change of a qubit after gate interaction;

[0144] Adjust the amplitude or shape of the wave packet until the desired effect is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

[0145] In some alternative embodiments, the selection unit 44 is further configured to:

[0146] Constructed by random and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The corresponding fidelity of the value is determined, and the optimal value is selected.

[0147] In some alternative embodiments, the control unit 41 is further configured to:

[0148] A gate operation is performed when the qubit is at its sweet spot, wherein the magnetic flux is fixed. , It is a magnetic flux quantum.

[0149] In an exemplary embodiment, each processing unit in the single-qubit gate sequence implementation apparatus of this application embodiment can be implemented by one or more central processing units (CPUs), graphics processing units (GPUs), application-specific integrated circuits (ASICs), DSPs, programmable logic devices (PLDs), complex programmable logic devices (CPLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers (MCUs), microprocessors, or other electronic components.

[0150] Regarding the apparatus in the above embodiments, the specific manner in which each processing unit performs its operations has been described in detail in the embodiments related to the method, and will not be elaborated upon here.

[0151] According to embodiments of this application, this application also describes an electronic device and a readable storage medium.

[0152] Figure 5 A schematic block diagram of an example electronic device that can be used to implement embodiments of this application is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the application described and / or claimed herein.

[0153] like Figure 5 As shown, the electronic device 800 of this application embodiment includes a computing unit 801, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 802 or a computer program loaded from a storage unit 808 into a random access memory (RAM) 803. The RAM 803 may also store various programs and data required for the operation of the electronic device 800. The computing unit 801, ROM 802, and RAM 803 are interconnected via a bus 804. An input / output (I / O) interface 805 is also connected to the bus 804.

[0154] Multiple components in electronic device 800 are connected to I / O interface 805, including: input unit 806, such as keyboard, mouse, etc.; output unit 807, such as various types of displays, speakers, etc.; storage unit 808, such as disk, optical disk, etc.; and communication unit 809, such as network card, modem, wireless transceiver, etc. Communication unit 809 allows electronic device 800 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0155] The computing unit 801 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 801 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 801 performs the various methods and processes described above, such as the implementation method of a single-qubit gate sequence. For example, in some embodiments, the implementation method of a single-qubit gate sequence can be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as storage unit 808. In some embodiments, part or all of the computer program can be loaded and / or installed on the electronic device 800 via ROM 802 and / or communication unit 809. When the computer program is loaded into RAM 803 and executed by the computing unit 801, one or more steps of the implementation method of the single-qubit gate sequence described above can be performed. Alternatively, in other embodiments, computing unit 801 may be configured by any other suitable means (e.g., by means of firmware) to perform steps of the implementation method of a single-qubit gate sequence.

[0156] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), system-on-a-chip (SoCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transferring data and instructions to the storage system, the at least one input device, and the at least one output device.

[0157] The program code used to implement the methods of this application may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, as a standalone software package partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0158] In the context of this application, a machine-readable medium can be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, apparatus, or device. A machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. Machine-readable media can be, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0159] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0160] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0161] Computer systems can include clients and servers. Clients and servers are generally located far apart and typically interact via communication networks. Client-server relationships are created by computer programs running on the respective computers and having a client-server relationship with each other. Servers can be cloud servers, servers in distributed systems, or servers incorporating blockchain technology.

[0162] It should be understood that the various forms of processes shown above can be used to rearrange, add, or delete steps. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this application can be achieved, and this is not limited herein.

[0163] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

[0164] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for implementing a single-qubit gate sequence, characterized in that, calibrating the resonant frequency of quantum qubits Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is Construct a time-dependent Hamiltonian H(t) for realizing a single-qubit gate. This Hamiltonian contains a linearly polarized periodic driving term that resonates with the qubit. This linearly polarized periodic driving term consists of a time-dependent wave packet Ω(t), a start time, and a time period. Defined together with phase φ; when executing any single-qubit gate, its start time is... The method involves constraining the time of the single-qubit gate to be an integer multiple of the period T of the non-RWA term in the Hamiltonian; and also constraining the running time of the single-qubit gate to be an integer multiple of the period T. Control the start time in response to each gate operation in a single-qubit gate sequence. and running time At least one of the following conditions must be met: When execution When the door opens, start time Running time ,in, It is an integer; When execution When the door opens, start time Running time ; Using time-dependent driving wave packets Applying a periodic drive to the qubit, the wave packet in time to Non-zero at time intervals, zero at other times; For the wave packet Calibration is performed to enable continuous execution of two... Behind the door, the quantum bits from State transformation State; Adjusting integer Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

2. The method according to claim 1, characterized in that, The qubits are Fluxonium qubits.

3. The method according to claim 2, characterized in that, The use of time-dependent driving wave packets Applying periodic drive to qubits includes: A time-dependent magnetic flux is applied to the Josephson junction and inductor circuit of the Fluxonium qubit by an alternating current source. The Proportional to ,in The wave packet is the envelope function. and Proportional, φ represents the initial phase of the magnetic flux driving signal.

4. The method according to claim 3, characterized in that, Driving Hamiltonian Determined by the following formula: in, and For Pauli matrices, To reduce Planck's constant, Time variable.

5. The method according to claim 1, characterized in that, The wave packet Calibration includes: By experimentally measuring two consecutive... The state change of a qubit after gate interaction; Adjust the amplitude or shape of the wave packet until the desired effect is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

6. The method according to claim 1, characterized in that, The determination is different The corresponding door fidelity includes: Constructed by random and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The corresponding fidelity of the value is determined, and the optimal value is selected.

7. The method according to claim 1, characterized in that, The method further includes: A gate operation is performed when the qubit is at its sweet spot, wherein the magnetic flux is fixed. , It is a magnetic flux quantum.

8. A device for realizing a single-qubit gate sequence, characterized in that, The device includes: Setting unit, used to calibrate the resonant frequency of quantum bits. Determine its corresponding Larmor period Set drive frequency With quantum bit frequency Resonance, that is Construct a time-dependent Hamiltonian H(t) for realizing a single-qubit gate. This Hamiltonian contains a linearly polarized periodic driving term that resonates with the qubit. This linearly polarized periodic driving term consists of a time-dependent wave packet Ω(t), a start time, and a time period. Defined together with phase φ; when executing any single-qubit gate, its start time is... Constraints are imposed to make it an integer multiple of the period T of the non-RWA term in the Hamiltonian; the running time of the single-qubit gate is also constrained to be an integer multiple of the period T. The control unit is used to control the start time of each gate operation in a single-qubit gate sequence. and running time At least one of the following conditions must be met: When execution When the door opens, start time Running time ,in, It is an integer; When execution When the door opens, start time Running time ; Drive unit for using time-dependent drive wave packets Applying a periodic drive to the qubit, the wave packet in time to Non-zero at time intervals, zero at other times; A calibration unit is used for calibrating the wave packet. Calibration is performed to enable continuous execution of two... Behind the door, the quantum bits from State transformation state; Selecting a cell is used to adjust the integer. Change runtime and determine the different The corresponding door fidelity is selected to maximize the fidelity. The value is used as the optimal running time.

9. The apparatus according to claim 8, characterized in that, The qubits are Fluxonium qubits.

10. The apparatus according to claim 9, characterized in that, The drive unit is further configured to: A time-dependent magnetic flux is applied to the Josephson junction and inductor circuit of the Fluxonium qubit by an alternating current source. The Proportional to ,in The wave packet is the envelope function. and Proportional, φ represents the initial phase of the magnetic flux driving signal.

11. The apparatus according to claim 10, characterized in that, Driving Hamiltonian Determined by the following formula: in, and For Pauli matrices, To reduce Planck's constant, Time variable.

12. The apparatus according to claim 8, characterized in that, The calibration unit is also used for: By experimentally measuring two consecutive... The state change of a qubit after gate interaction; Adjust the amplitude or shape of the wave packet until the desired effect is achieved. arrive The complete transformation is recorded, and the corresponding wave packet function form is saved as calibration parameters.

13. The apparatus according to claim 8, characterized in that, The selection unit is further configured to: Constructed by random and A sequence of gates is used to execute the sequence and measure the fidelity of the quantum states, comparing different... The corresponding fidelity of the value is determined, and the optimal value is selected.

14. The apparatus according to claim 8, characterized in that, The control unit is also used for: A gate operation is performed when the qubit is at its sweet spot, wherein the magnetic flux is fixed. , It is a magnetic flux quantum.

Images