阅读说明：本技术 基于脉冲的量子门实现方法及装置、电子设备和介质 (Pulse-based quantum gate implementation method and device, electronic equipment and medium ) 是由 孟则霖 王鑫 晋力京 王青鹤 于 2021-09-17 设计创作，主要内容包括：本公开提供了一种基于脉冲的量子门实现方法、装置、电子设备、计算机可读存储介质和计算机程序产品,涉及量子计算领域,尤其涉及量子门、脉冲控制技术领域。实现方案为：确定脉冲包络参数与单脉冲时长之间的对应关系,并确定待优化参数；确定最大脉冲数量、初始化当前脉冲数量以及预设的误差容忍度。执行迭代操作：基于当前脉冲数量以及待优化参数的一组参数值,确定待实现的量子门矩阵和损失函数；调整待优化参数的一组参数值以最小化损失函数；确定最小化损失函数后与目标量子门矩阵之间的误差；响应于当前脉冲数量小于最大脉冲数量且误差大于误差容忍度,将当前脉冲数量加一。基于迭代操作后所得到的脉冲数量以及一组参数值,生成相应的脉冲。(The present disclosure provides a method and an apparatus for implementing a quantum gate based on a pulse, an electronic device, a computer-readable storage medium, and a computer program product, which relate to the field of quantum computing, and in particular to the technical field of quantum gates and pulse control. The implementation scheme is as follows: determining a corresponding relation between the pulse envelope parameters and the single pulse duration, and determining parameters to be optimized; determining a maximum pulse number, initializing a current pulse number and presetting error tolerance. Performing an iterative operation: determining a quantum gate matrix and a loss function to be realized based on the current pulse number and a group of parameter values of the parameter to be optimized; adjusting a set of parameter values of a parameter to be optimized to minimize a loss function; determining the error between the minimized loss function and the target quantum gate matrix; and in response to the current pulse number being less than the maximum pulse number and the error being greater than the error tolerance, incrementing the current pulse number by one. And generating corresponding pulses based on the number of pulses obtained after the iterative operation and a set of parameter values.)

1. A method for implementing a pulse-based quantum gate, comprising:

determining a corresponding relation between the pulse envelope parameters and the single pulse duration, and determining parameters to be optimized based on the corresponding relation;

determining the maximum pulse number, the initialized current pulse number and a preset error tolerance, wherein the initialized current pulse number is less than the maximum pulse number;

performing an iterative operation until the number of pulses reaches the maximum number of pulses or the quantum gate error to be achieved is not greater than the error tolerance:

initializing based on the current pulse number to obtain a group of parameter values of parameters to be optimized, wherein the group of parameter values corresponds to the current pulse number;

determining a quantum gate matrix to be realized through Schrodinger equation based on the current pulse number and the set of parameter values;

determining a loss function based on the quantum gate matrix to be realized and a target quantum gate matrix; and

adjusting a set of parameter values of the parameter to be optimized to minimize the loss function;

determining a quantum gate matrix to be realized obtained after minimizing a loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix;

in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one;

and generating corresponding pulses based on the current pulse number obtained after the iterative operation and a group of parameter values of the parameters to be optimized so as to realize the quantum gate.

2. The method of claim 1, wherein the parameters to be optimized comprise a first parameter and a second parameter, wherein the method further comprises:

determining one or more parameter values of the first parameter to perform the iterative operation at each parameter value of the first parameter, respectively, wherein the second parameter is a parameter to be optimized in the iterative operation.

3. The method of claim 2, wherein generating the corresponding pulse based on the current number of pulses obtained after the iterative operation and a set of parameter values of the parameter to be optimized comprises:

determining an error and a total pulse duration obtained after the iterative operation is executed at each parameter value of the first parameter;

determining a parameter value of an optimal first parameter based on the error and the total pulse duration;

determining the current pulse number obtained by executing the iterative operation at the parameter value of the optimal first parameter and a group of parameter values of the parameter to be optimized; and

and generating corresponding pulses based on the parameter value of the optimal first parameter, the current pulse number and a group of parameter values of the parameter to be optimized.

4. The method of claim 1, wherein the target quantum gate matrix of single quantum bits is determined based on the following equation:

where { θ, φ, λ } is a parameter of the target quantum gate.

5. The method of claim 1, wherein the loss function is determined based on the following equation:

wherein the content of the first and second substances,a set of parameter values representing parameters to be optimized in said iterative operation,representing the matrix of quantum gates to be implemented,representing the inverse of the target quantum gate matrix and Tr () representing the traces of the matrix.

6. The method of claim 1, wherein adjusting the set of parameter values for the parameter to be optimized to minimize the loss function comprises:

adjusting a set of parameter values of the parameter to be optimized by an optimization algorithm to minimize the loss function, wherein the optimization algorithm includes any one of: gradient descent method, Newton method, conjugate gradient method, and heuristic method.

7. The method of claim 1, wherein the pulse envelope comprises a Gaussian pulse envelope, the pulse envelope parameters comprising a pulse amplitude, a pulse center position, and a standard deviation, wherein,

determining a corresponding relation between the pulse envelope parameters and the single pulse duration, and determining the parameters to be optimized based on the corresponding relation comprises the following steps:

determining the pulse center position and the standard deviation based on the single pulse duration; and

and determining the corresponding relation between the pulse amplitude and the single pulse duration so as to determine the parameter to be optimized based on the corresponding relation.

8. The method of claim 7, wherein the pulse amplitude versus the single pulse duration is determined based on the following equation:

wherein, T_k(l)Which represents the duration of a single pulse or pulse,representing the pulse amplitude, C₁、C₂Is a hyper-parameter, wherein C₁，C₂＞0。

9. The method of any of claims 1-8, further comprising: in response to including at least two channels, pulses are alternately generated in the at least two channels based on the current number of pulses.

10. An apparatus for pulse-based quantum gate implementation, comprising:

the first determining unit is configured to determine a corresponding relation between the pulse envelope parameters and the single pulse duration, and determine parameters to be optimized based on the corresponding relation;

a second determining unit configured to determine a maximum pulse number, an initialized current pulse number, and a preset error tolerance, wherein the initialized current pulse number is smaller than the maximum pulse number;

an iteration unit configured to perform the following iteration operations until the number of pulses reaches the maximum number of pulses or a quantum gate error to be achieved is not greater than the error tolerance:

initializing based on the current pulse number to obtain a group of parameter values of parameters to be optimized, wherein the group of parameter values corresponds to the current pulse number;

determining a quantum gate matrix to be realized through Schrodinger equation based on the current pulse number and the set of parameter values;

determining a loss function based on the quantum gate matrix to be realized and a target quantum gate matrix; and

adjusting a set of parameter values of the parameter to be optimized to minimize the loss function;

determining a quantum gate matrix to be realized obtained after minimizing a loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix;

in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one;

and the pulse generation unit is configured to generate corresponding pulses based on the current pulse number obtained after the iterative operation and a group of parameter values of the parameters to be optimized so as to realize the quantum gate.

11. The apparatus of claim 10, wherein the parameters to be optimized comprise a first parameter and a second parameter, and further comprising: means for determining one or more parameter values of the first parameter to perform the iterative operation at each parameter value of the first parameter, respectively,

and the second parameter is a parameter to be optimized in the iterative operation.

12. The apparatus of claim 11, wherein the pulse generating unit comprises:

means for determining an error and a total pulse duration resulting from performing the iterative operation at each parameter value of the first parameter;

means for determining a parameter value of an optimal first parameter based on the error and a total pulse duration;

means for determining a current number of pulses resulting from performing the iterative operation at the parameter value of the optimal first parameter and a set of parameter values for a parameter to be optimized; and

means for generating a corresponding pulse based on the parameter value of the optimal first parameter, the current number of pulses, and a set of parameter values of a parameter to be optimized.

13. The apparatus of any of claims 10-12, further comprising: means for, in response to comprising at least two channels, alternately generating pulses in the at least two channels based on the current number of pulses.

14. An electronic device, comprising:

at least one processor; and

a memory communicatively coupled to the at least one processor; wherein

The memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-9.

15. A non-transitory computer readable storage medium having stored thereon computer instructions for causing the computer to perform the method of any one of claims 1-9.

16. A computer program product comprising a computer program, wherein the computer program realizes the method of any one of claims 1-9 when executed by a processor.

Technical Field

The present disclosure relates to the field of quantum computers, and in particular, to the field of quantum gates and pulse control technologies, and in particular, to a method and apparatus for implementing a quantum gate based on a pulse, an electronic device, a computer-readable storage medium, and a computer program product.

Background

In the field of quantum control, in the process of compiling quantum logic gates at a quantum software level into physical pulse signals which can be identified by quantum hardware, the signals are interfered by a plurality of non-ideal factors (such as high-energy leakage, crosstalk and the like). Therefore, the physical pulse signal needs to be designed properly to suppress or even eliminate the influence of the non-ideal factors, so as to improve the fidelity of the quantum gate.

Disclosure of Invention

The present disclosure provides a pulse-based quantum gate implementation method, apparatus, electronic device, computer-readable storage medium, and computer program product.

According to an aspect of the present disclosure, there is provided a method for implementing a pulse-based quantum gate, including: determining a corresponding relation between the pulse envelope parameters and the single pulse duration, and determining parameters to be optimized based on the corresponding relation; determining the maximum pulse number, the initialized current pulse number and a preset error tolerance, wherein the initialized current pulse number is less than the maximum pulse number; performing an iterative operation until the number of pulses reaches the maximum number of pulses or the quantum gate error to be achieved is not greater than the error tolerance: initializing based on the current pulse number to obtain a group of parameter values of parameters to be optimized, wherein the group of parameter values corresponds to the current pulse number; determining a quantum gate matrix to be realized through Schrodinger equation based on the current pulse number and the set of parameter values; determining a loss function based on the quantum gate matrix to be realized and a target quantum gate matrix; and adjusting a set of parameter values of the parameter to be optimized to minimize the loss function; determining a quantum gate matrix to be realized obtained after minimizing a loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix; in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one; and generating corresponding pulses based on the current pulse number obtained after the iterative operation and a group of parameter values of the parameters to be optimized so as to realize the quantum gate.

According to another aspect of the present disclosure, there is provided a pulse-based quantum gate implementation apparatus, including: the first determining unit is configured to determine a corresponding relation between the pulse envelope parameters and the single pulse duration, and determine parameters to be optimized based on the corresponding relation; a second determining unit configured to determine a maximum pulse number, an initialized current pulse number, and a preset error tolerance, wherein the initialized current pulse number is smaller than the maximum pulse number; an iteration unit configured to perform the following iteration operations until the number of pulses reaches the maximum number of pulses or a quantum gate error to be achieved is not greater than the error tolerance: initializing based on the current pulse number to obtain a group of parameter values of parameters to be optimized, wherein the group of parameter values corresponds to the current pulse number; determining a quantum gate matrix to be realized through Schrodinger equation based on the current pulse number and the set of parameter values; determining a loss function based on the quantum gate matrix to be realized and a target quantum gate matrix; and adjusting a set of parameter values of the parameter to be optimized to minimize the loss function; determining a quantum gate matrix to be realized obtained after minimizing a loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix; in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one; and the pulse generation unit is configured to generate corresponding pulses based on the current pulse number obtained after the iterative operation and a group of parameter values of the parameters to be optimized so as to realize the quantum gate.

According to another aspect of the present disclosure, there is provided an electronic device including: at least one processor; and a memory communicatively coupled to the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform a method according to the present disclosure.

According to another aspect of the present disclosure, there is provided a non-transitory computer readable storage medium having stored thereon computer instructions for causing a computer to perform a method according to the present disclosure.

According to another aspect of the disclosure, a computer program product is provided, comprising a computer program which, when executed by a processor, implements the method according to the disclosure.

According to one or more embodiments of the present disclosure, the pulse duration is considered in the optimization process, so that the pulse shape is effectively constrained, the hardware is more friendly, and the difficulty of pulse generation in a real quantum computer is reduced.

It should be understood that the statements in this section do not necessarily identify key or critical features of the embodiments of the present disclosure, nor do they limit the scope of the present disclosure. Other features of the present disclosure will become apparent from the following description.

Drawings

The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the embodiments and, together with the description, serve to explain the exemplary implementations of the embodiments. The illustrated embodiments are for purposes of illustration only and do not limit the scope of the claims. Throughout the drawings, identical reference numbers designate similar, but not necessarily identical, elements.

FIG. 1 shows a flow diagram of a method of implementing a pulse-based quantum gate according to an embodiment of the present disclosure;

FIG. 2 shows a schematic diagram of a pulse circuit with alternating generation of pulses according to an embodiment of the present disclosure;

FIG. 3 illustrates a flow chart for generating a corresponding pulse based on an optimized set of parameter values according to an embodiment of the disclosure;

FIG. 4 shows a flow diagram of a method of determining pulse parameters according to an embodiment of the present disclosure;

FIG. 5 shows parameter C according to an embodiment of the present disclosure₁A line graph corresponding to the distortion degree;

FIG. 6 shows parameter C according to an embodiment of the present disclosure₁A line graph corresponding to the total pulse duration;

FIG. 7 shows a schematic diagram of a pulse sequence corresponding to optimized pulse parameters according to an embodiment of the disclosure;

FIG. 8 shows a block diagram of a pulse-based quantum gate implementation, according to an embodiment of the present disclosure; and

FIG. 9 illustrates a block diagram of an exemplary electronic device that can be used to implement embodiments of the present disclosure.

Detailed Description

Exemplary embodiments of the present disclosure are described below with reference to the accompanying drawings, in which various details of the embodiments of the disclosure are included to assist understanding, and which are to be considered as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.

In the present disclosure, unless otherwise specified, the use of the terms "first", "second", etc. to describe various elements is not intended to limit the positional relationship, the timing relationship, or the importance relationship of the elements, and such terms are used only to distinguish one element from another. In some examples, a first element and a second element may refer to the same instance of the element, and in some cases, based on the context, they may also refer to different instances.

The terminology used in the description of the various described examples in this disclosure is for the purpose of describing particular examples only and is not intended to be limiting. Unless the context clearly indicates otherwise, if the number of elements is not specifically limited, the elements may be one or more. Furthermore, the term "and/or" as used in this disclosure is intended to encompass any and all possible combinations of the listed items.

Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

To date, the various types of computers in use are based on classical physics as the theoretical basis for information processing, called traditional computers or classical computers. Classical information systems store data or programs using the most physically realizable binary data bits, each represented by a 0 or 1, called a bit or bit, as the smallest unit of information. The classic computer itself has inevitable weaknesses: one is the most fundamental limitation of computing process energy consumption. The minimum energy required by the logic element or the storage unit is more than several times of kT so as to avoid the misoperation of thermal expansion and dropping; information entropy and heating energy consumption; thirdly, when the wiring density of the computer chip is high, the uncertainty of the electronic position is small and the uncertainty of the momentum is large according to the heisenberg uncertainty relation. The electrons are no longer bound and there are quantum interference effects that can even destroy the performance of the chip.

Quantum computers (quantum computers) are physical devices that perform high-speed mathematical and logical operations, store and process quantum information in compliance with quantum mechanical properties and laws. When a device processes and calculates quantum information and runs a quantum algorithm, the device is a quantum computer. Quantum computers follow a unique quantum dynamics law, particularly quantum interference, to implement a new model of information processing. For parallel processing of computational problems, quantum computers have an absolute advantage in speed over classical computers. The transformation of each superposed component by the quantum computer is equivalent to a classical calculation, all the classical calculations are completed simultaneously and superposed according to a certain probability amplitude to give an output result of the quantum computer, and the calculation is called quantum parallel calculation. Quantum parallel processing greatly improves the efficiency of quantum computers, allowing them to accomplish tasks that classic computers cannot accomplish, such as factorization of a large natural number. Quantum coherence is essentially exploited in all quantum ultrafast algorithms. Therefore, quantum parallel computation of a classical state is replaced by a quantum state, so that the computation speed and the information processing function which are incomparable with a classical computer can be achieved, and meanwhile, a large amount of computation resources are saved.

Quantum control is a bridge connecting software and hardware of quantum and is an indispensable ring in quantum computation. In quantum computing, in addition to concerns about the performance of quantum hardware (including the quality and number of qubits), there is also a need to consider how quantum hardware can be efficiently controlled, thereby enabling quantum tasks to be performed efficiently. In particular, it is necessary to compile quantum logic gates at the quantum software level into physical pulse signals that the quantum hardware can recognize.

Currently, there are several quantum hardware candidates in the industry. The superconducting circuit has been developed greatly in recent years due to the advantages of long coherence time and easy expansion of qubits. Moreover, a number of valuable quantum tasks are realized and validated in superconducting platforms. However, in practical superconducting circuits, there are many non-ideal factors (e.g., high level leakage, crosstalk, etc.) that limit the fidelity of real quantum gates. To solve this problem, researchers often suppress or even eliminate their effects by designing reasonable pulses, which in turn greatly improves the fidelity of the quantum gate. The common technical scheme is that researchers simulate and optimize by establishing a physical model, calculate a group of pulse parameters, and then perform pulse calibration in a real quantum hardware system, so that the fidelity is further improved. Limited by the coherence time of the qubit, the efficiency and effectiveness of the overall quantum control system can be greatly affected if the quantum gate time is too long. Besides the pulse time, the quantum gate pulse capable of generating high fidelity under the influence of environmental noise is also an important index for measuring the pulse technical scheme.

Accordingly, a method for implementing a pulse-based quantum gate is provided according to an embodiment of the present disclosure. Fig. 1 shows a flow diagram 100 of a method of implementing a pulse-based quantum gate according to an embodiment of the present disclosure. As shown in fig. 1, the method includes: determining a corresponding relation between the pulse envelope parameters and the single pulse duration, and determining parameters to be optimized based on the corresponding relation (step 110); determining a maximum pulse number, initializing a current pulse number, and presetting an error tolerance, wherein the initialized current pulse number is less than the maximum pulse number (step 120); an iterative operation is performed until the number of pulses reaches a maximum number of pulses or the quantum gate error to be achieved is not greater than the error tolerance (step 130): initializing a group of parameter values of parameters to be optimized based on the current pulse number, wherein the group of parameter values corresponds to the current pulse number (step 1301); determining a quantum gate matrix to be implemented by Schrodinger equation based on the current pulse number and the set of parameter values (step 1302); determining a loss function based on the quantum gate matrix to be realized and the target quantum gate matrix (step 1303); and adjusting a set of parameter values for the parameter to be optimized to minimize a loss function (step 1304); determining a quantum gate matrix to be realized obtained after minimizing the loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix (step 1305); in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one (step 1306); based on the current number of pulses obtained after the iterative operation and a set of parameter values of the parameter to be optimized, a corresponding pulse is generated to implement the quantum gate (step 140).

According to the embodiment of the disclosure, the pulse duration is considered in the optimization process, so that the pulse shape is effectively constrained, the hardware is more friendly, and the difficulty of pulse generation in a real quantum computer is reduced.

In experiments with quantum computing, some simulation and emulation is usually performed prior to the experiment. In the process, a quantum system needs to be modeled, and an evolution result of the system at any moment is obtained by solving the Schrodinger equation. In quantum optimization control, a core target is a control item for designing a system, so that a time sequence evolution operator of the system after time t is as close as possible to a matrix of a target quantum gate. Thus, embodiments of the method according to the present disclosure may be described in terms of simulation and emulation processes.

The quantum gate matrix to be implemented according to the present disclosure is a matrix of quantum gates that needs to be generated according to the optimized pulse parameters, i.e., a matrix form of true quantum gates.

In some embodiments, a three-level superconducting quantum bit is described, with the example of a single-bit quantum gate implemented by applying a pulse to the X-Y channel. It is understood that other energy level systems and other numbers of channels in the system (e.g., only X channels, X-Y-Z channels) are similar and will not be described herein.

Under the interaction expression, the Hamiltonian H (t) of the system can be expressed as formula (1):

in the formula (1), α_qRepresenting the detuning strength of the superconducting qubit; respectively a generation operator and an annihilation operator; further, |0>＝[1，0，0]^T，|1>＝[0,1，0]^T，|2＞＝[0，0,1]^T；Gaussian envelope functions corresponding to the X (Y) channel pulses, wherein M (N) respectively represents the pulse number of the X (Y) channel, and k (l) respectively represents the pulse sequence number of the X (Y) channel; whileSpecifically, it can be expressed as formula (2):

in the formula (2), the first and second groups,parameters of the gaussian pulse for the x (y) channels, respectively, exp represents scalar exponential operations. After obtaining a system HamiltonianAll information of the system is obtained, including the time evolution information of the system.

Given the Hamiltonian H (t) of a quantum system, the kinetic equation satisfied by the timing evolution operator U (t) can be described by Schrodinger equation (i.e., equation (3)):

wherein i is an imaginary unit,is the Planck constant. By solving the time-dependent differential equation, the time sequence evolution operator U (t) of the system at any time can be obtained.

In the above embodiment implementing single-bit quantum gates, the target quantum gate matrix may be determined based on equation (4):

where { θ, φ, λ } is a parameter of the target quantum gate. That is, the single-qubit-gate operation can be described by three parameters { θ, φ, λ }, i.e., when the parameters { θ, φ, λ } are determined, the corresponding single-qubit gates can be determined according to equation (4).

According to some embodiments, the loss function may be determined based on equation (9):

wherein the content of the first and second substances,a set of parameter values representing parameters to be optimized in said iterative operation,to show stand toIn the existing quantum gate matrix, the quantum gate matrix,representing the inverse of the target quantum gate matrix and Tr () representing the traces of the matrix.

As described above, when a target quantum gate matrix U is determined_GoalAfter (θ, φ, λ), the target function (i.e., the loss function) can be used to measure the difference between the real quantum gate and the target quantum gate generated by the current pulse parameters. WhereinFor the pulse parameter vector to be optimized,using pulse parametersAnd obtaining a real quantum gate matrix by calculating Schrodinger equation (3), wherein Tr is a trace representing the matrix, namely the sum of diagonal elements of the matrix. After the objective function is determined, the interface uses an optimization algorithm to minimize the objective function, resulting in the pulse parameters needed to achieve a given quantum operation.

According to some embodiments, adjusting a set of parameter values of a parameter to be optimized to minimize a loss function comprises: adjusting a set of parameter values of the parameter to be optimized by an optimization algorithm to minimize the loss function. The optimization algorithm includes, but is not limited to: gradient descent, newton's method, conjugate gradient method, heuristic method, etc.

On recent superconducting qubit platforms, the performance of the qubit is limited by its coherence time, and it is therefore desirable to have the quantum gates operate as short as possible, minimizing the effects of decoherence. However, in a general pulse parameter optimization, the pulse parameters to be optimized are: mainly parameters describing pulse shape, but not including duration T of single pulse_k(l). In general, T_k(l)As a fixed parameter, does not participate in the optimization process. I.e. for different quantum tasks, T in the above scheme_k(l)Is constant, which makes the scheme less flexible. There is thus still a great deal of room for improvement in the problem of optimizing pulse duration. In addition, in the above scheme, if the pulse duration is not set reasonably, a pulse with a small pulse amplitude but a long duration or a pulse with a large pulse amplitude but a short duration may occur, and such a pulse may affect the efficiency of the whole experiment in the experiment.

Therefore, in the method according to the present disclosure, the pulse duration is considered in the optimization process by determining the proportional relationship between the single pulse duration and the pulse amplitude, so as to effectively constrain the shape of the pulse and reduce the difficulty of pulse generation in a real quantum computer.

According to some embodiments, the pulse envelope may be a gaussian pulse envelope, as described above with reference to equation (2), and the pulse envelope parameters include pulse amplitude, pulse center position, and standard deviation. Thus, determining a correspondence between the pulse envelope parameter and the duration of a single pulse, and determining the parameter to be optimized based on the correspondence may comprise: determining a pulse center position and a standard deviation based on the single pulse duration; and determining a corresponding relation between the pulse amplitude and the single pulse duration so as to determine the parameter to be optimized based on the corresponding relation.

In some examples, to control the degree of freedom in optimizing the pulses, only the pulse amplitude in equation (2) may be selectedAs pulse parameters to be optimized and fixing the center positionAnd standard deviation ofFor example, the formula (6) and the formulaEquation (7) to determine the center positionAnd standard deviation ofRespective and single pulse duration T_k(l)The corresponding relationship of (1).

Wherein, T_k(l)For the duration of a single pulse, the coefficients in equation (6) and equation (7) are merely exemplary, and may be adjusted according to actual conditions, and are not limited herein.

According to some embodiments, the single pulse duration T may also be determined by equation (8) and equation (9)_k(l)And pulse amplitudeThe corresponding relation of (1):

C₁,C₂equation > 0 (9)

Wherein, C₁And C₂Are two adjustable hyper-parameters. Wherein, C₁Determines the steepness of the pulse shape (i.e., how fast the amplitude rises), and C₂The shortest duration of the pulse is determined. It can thus be seen that C₁Determines the relation between the duration of a single pulse and the amplitude of the pulse, and fixes the shape of the pulse to a certain extent. If a suitable C is selected₁The shape of the Gaussian pulse can be ensured to be relatively regular, so that the method is easier to realize in experiments; in the method according to the present disclosureIn (1), the single pulse duration T is considered_k(l)The total pulse duration can thus be dynamically adjusted by parameter optimization to be as short as possible.

According to some embodiments, the method according to the present disclosure may further comprise: in response to including at least two channels, pulses are alternately generated in the at least two channels based on the current number of pulses.

In general, in determining the pulse parameters for implementing the quantum gate, the number of pulses on each channel and the channel corresponding to each pulse are fixed. In the embodiment of the method according to the present disclosure, in order to improve the flexibility of the method, the number of pulses on each channel may not be fixed, and is set as a dynamically adjusted variable, and the maximum value of the number of pulses is set to N. Thus, at the start of the program, a total pulse number (e.g., starting from 1 and starting at X-channel) may be initialized, i.e., the current pulse number; if the error of the quantum gate after iterative optimization is smaller than the preset error tolerance or the current total pulse number is larger than the maximum value of the set pulse number, ending the program; if the error of the quantum gate after the iterative optimization is larger than the preset error tolerance and the current total pulse number is smaller than the maximum value of the set pulse number, adding one pulse and carrying out optimization again. Here, the pulses may be applied in an interleaved manner on the X and Y channels, as shown in fig. 2, which shows a schematic diagram of a pulse circuit with a pulse number of 6.

The fidelity of the quantum gate can be a key performance indicator of the compilation quality. The realization effect of quantum tasks is determined by the fidelity of the quantum gate, and the improvement of the fidelity of the quantum gate becomes an important target in the quantum control technology. Thus, in some embodiments, fidelity may be used to measure the error or distance between quantum gates. Of course, it should be understood that other methods or algorithms that may be used to measure the error or distance between the quantum gates are possible, including but not limited to trace distance, F-norm, etc., and are not limited thereto.

According to some embodiments, the parameters to be optimized may comprise a first parameter and a second parameter. Thus, the method 100 according to the present disclosure may further include: one or more parameter values of the first parameter are determined to perform the iterative operation separately at each parameter value of the first parameter. Note that the second parameter is a parameter to be optimized in the iterative operation.

As described above, C may be₁As a first parameter, the pulse amplitudeAs the parameter to be optimized in the iterative operation. For example, parameter C may be fixed₂And specify C₁To scan over the range of values (i.e., to optimize as an external variable). That is, C₁The optimization is performed as a hyperparameter and the optimization of the pulse parameters is completely separated, i.e. before each iteration operation, a C is fixed₁Then optimizing the pulse parameters under the conditions; c is to be₁Change the value of (C) to another value, and repeat the iteration … … until C₁And taking all preset values within a preset value range.

According to some embodiments, as shown in fig. 3, generating the corresponding pulse based on the current pulse number obtained after the iterative operation and the set of parameter values of the parameter to be optimized includes: determining an error and a total pulse duration obtained after the iterative operation is performed at each parameter value of the first parameter (step 310); determining an optimal parameter value for the first parameter based on the error and the total pulse duration (step 320); determining a current number of pulses resulting from performing the iterative operation at the parameter value of the optimal first parameter and a set of parameter values of the parameter to be optimized (step 330); and generating a corresponding pulse based on the parameter value of the optimized first parameter, the current number of pulses, and a set of parameter values of the parameter to be optimized (step 340).

In one embodiment according to the present disclosure, a three-level superconducting quantum bit is first modeled, here using the quantum system defined by the Hamiltonian in equation (1). Illustratively, the detuning strength of a superconducting qubit is set to α_q-0.33 × 2 pi GHz. Randomly generating a U3 quantum gate to doFor the target quantum gate:

u3(θ 0.9933716, Φ 5.03114766, λ 3.01783983) formula (10)

Fig. 4 shows a flow chart of a method of determining pulse parameters in the present embodiment. As shown in FIG. 4, first, a specified quantum gate, a maximum number of pulses, and a target fidelity are determined (step 401). Then, the corresponding relation between the pulse envelope parameter and the single pulse duration can be determined according to the formulas (6) to (9). Illustratively, C may be expressed according to equation (8)₂Fixed at 3.0, then at 0.01 ≧ C₁10 points are selected and scanned ≧ 0.10 equidistantly (step 402). The current number of pulses is set starting from 1 (step 403). Illustratively, the pulse parameters may be randomly initialized (step 404). A pulse circuit is performed based on the pulse parameters to obtain an evolving unitary matrix (step 405). The resulting evolving unitary matrix is compared to the target unitary matrix and the fidelity is calculated based on the loss function (step 406). Optimizing pulse amplitude after setting the loss functionAnd judging whether the loss function reaches the minimum (step 407), and if not, iteratively optimizing the pulse parameters through an optimization algorithm (step 407, No). If the loss function has reached a minimum (step 407, yes), a determination is made as to whether the fidelity has reached the target fidelity (e.g., set to 0.0003) or the number of pulses has reached the set maximum number of pulses (e.g., set to 4) (step 408), and if so, the loop is ended (step 408, yes). Judging whether all C are scanned₁Value (step 409), otherwise continue scanning for next C₁A value; if the fidelity has not reached the target fidelity and the number of pulses has not reached the set maximum number of pulses ("no" at step 408), an additional pulse is added to continue the iteration to optimize the pulse parameters. After scanning all C₁After the value, the best C is determined by measuring the fidelity and the pulse duration₁Value (step 410) to be based on the best C₁The values result in the optimal pulse parameter settings (step 411). Wherein, whether the quantum gates meet the corresponding requirements can be judged by obtaining the corresponding distortion degreeAnd (5) the requirement of fidelity. As shown in Table 1, at each C₁Is optimized to obtain the total pulse duration t_gAnd a corresponding distortion factor.

C1	tg(ns)	Degree of distortion
			0.01	62.88973186561621	1.0776225123354521e-07
0.02	46.3150608996611	9.12831953470139e-07
			0.03	39.00074648068719	1.5606953091995557e-05
0.04	34.64745447981032	8.041684951243244e-05
			0.05	31.680216425083902	8.057591426424704e-05
0.06	24.0011804574133	0.29420386053094616
			0.07	28.999975684835725	0.06759744193332984
0.08	43.99886908295048	0.0004278678372359179
			0.09	38.000175037408276	0.0009871222780023503
0.10	29.307151626231807	0.0006729465275425728

TABLE 1

Thus, an optimal parameter value for the first parameter, i.e. C, may be determined based on the obtained distortion measure and the total pulse duration₁The value of (a). By way of example, C may be₁And the distortion degree is processed, for example, by taking the logarithm, to obtain the line graph shown in fig. 5. C is to be₁And total pulse duration t_gAfter processing, the line graph shown in fig. 6 is obtained. At the total pulse duration t_gAfter the distortion factor, C can be selected₁0.05 is the optimal parameter value. Fig. 7 shows a pulse sequence for an optimal parameter value.

It will be appreciated that other quantum gates (e.g., multi-qubit quantum gates) and pulse envelopes based on other functions are similar to those described above and will not be described in detail here.

Through a plurality of experiments, compared with a common pulse generation method, the method according to the embodiment of the disclosure has the advantages that the pulse duration can be shortened by 18%, and the distortion can be reduced by 32%. According to the method disclosed by the embodiment of the disclosure, under the condition of lower fidelity, the pulse time can be greatly reduced, so that the quantum gate is more efficient on a real machine.

According to an embodiment of the present disclosure, as shown in fig. 8, there is also provided a pulse-based quantum gate implementation apparatus 800, including: a first determining unit 810 configured to determine a corresponding relationship between the pulse envelope parameter and the single pulse duration, and determine a parameter to be optimized based on the corresponding relationship; a second determining unit 820 configured to determine a maximum number of pulses, an initialized current number of pulses, and a preset error tolerance, wherein the initialized current number of pulses is less than the maximum number of pulses; an iteration unit 830 configured to perform the following iteration operations until the number of pulses reaches the maximum number of pulses or the quantum gate error to be achieved is not greater than the error tolerance: initializing based on the current pulse number to obtain a group of parameter values of parameters to be optimized, wherein the group of parameter values corresponds to the current pulse number; determining a quantum gate matrix to be realized through Schrodinger equation based on the current pulse number and the set of parameter values; determining a loss function based on the quantum gate matrix to be realized and a target quantum gate matrix; and adjusting a set of parameter values of the parameter to be optimized to minimize the loss function; determining a quantum gate matrix to be realized obtained after minimizing a loss function and calculating an error between the quantum gate matrix to be realized and the target quantum gate matrix; in response to determining that the current number of pulses is less than the maximum number of pulses and the error is greater than the error tolerance, incrementing the current number of pulses by one; the pulse generating unit 840 is configured to generate corresponding pulses based on the current pulse number obtained after the iterative operation and a set of parameter values of the parameter to be optimized, so as to implement a quantum gate.

Here, the operations of the units 810 to 840 of the pulse-based quantum gate implementation apparatus 800 are similar to the operations of the steps 110 to 140 described above, and are not described herein again.

According to an embodiment of the present disclosure, there is also provided an electronic device, a readable storage medium, and a computer program product.

Referring to fig. 9, a block diagram of a structure of an electronic device 900, which may be a server or a client of the present disclosure, which is an example of a hardware device that may be applied to aspects of the present disclosure, will now be described. Electronic device is intended to represent various forms of digital electronic computer devices, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other suitable computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be examples only, and are not meant to limit implementations of the disclosure described and/or claimed herein.

As shown in fig. 9, the apparatus 900 includes a computing unit 901, which can perform various appropriate actions and processes in accordance with a computer program stored in a Read Only Memory (ROM)902 or a computer program loaded from a storage unit 908 into a Random Access Memory (RAM) 903. In the RAM 903, various programs and data required for the operation of the device 900 can also be stored. The calculation unit 901, ROM 902, and RAM 903 are connected to each other via a bus 904. An input/output (I/O) interface 905 is also connected to bus 904.

A number of components in the device 900 are connected to the I/O interface 905, including: an input unit 906, an output unit 907, a storage unit 908, and a communication unit 909. The input unit 906 may be any type of device capable of inputting information to the device 900, and the input unit 906 may receive input numeric or character information and generate key signal inputs related to user settings and/or function controls of the electronic device, and may include, but is not limited to, a mouse, a keyboard, a touch screen, a track pad, a track ball, a joystick, a microphone, and/or a remote control. Output unit 907 may be any type of device capable of presenting information and may include, but is not limited to, a display, speakers, a video/audio output terminal, a vibrator, and/or a printer. Storage unit 908 may include, but is not limited to, a magnetic disk, an optical disk. The communication unit 909 allows the device 900 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunications networks, and may include, but is not limited to, modems, network cards, infrared communication devices, wireless communication transceivers, and/or chipsets, such as bluetooth (TM) devices, 1302.11 devices, WiFi devices, WiMax devices, cellular communication devices, and/or the like.

The computing unit 901 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of the computing unit 901 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various dedicated Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, and so forth. The computing unit 901 performs the various methods and processes described above, such as the method 100. For example, in some embodiments, the method 100 may be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 908. In some embodiments, part or all of the computer program may be loaded and/or installed onto device 900 via ROM 902 and/or communications unit 909. When loaded into RAM 903 and executed by computing unit 901, may perform one or more of the steps of method 100 described above. Alternatively, in other embodiments, the computing unit 901 may be configured to perform the method 100 by any other suitable means (e.g., by means of firmware).

Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuitry, Field Programmable Gate Arrays (FPGAs), Application Specific Integrated Circuits (ASICs), Application Specific Standard Products (ASSPs), system on a chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs that are executable and/or interpretable on a programmable system including at least one programmable processor, which may be special or general purpose, receiving data and instructions from, and transmitting data and instructions to, a storage system, at least one input device, and at least one output device.

Program code for implementing the methods of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the program codes, when executed by the processor or controller, cause the functions/operations specified in the flowchart and/or block diagram to be performed. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package partly on the machine and partly on a remote machine or entirely on the remote machine or server.

In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and a pointing device (e.g., a mouse or a trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a 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 may be received in any form, including acoustic, speech, or tactile input.

The systems and techniques described here can be implemented in a computing system that includes a back-end component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such back-end, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), Wide Area Networks (WANs), and the Internet.

The computer system may include clients and servers. A client and server are generally remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server with a combined blockchain.

It should be understood that various forms of the flows shown above may be used, with steps reordered, added, or deleted. For example, the steps described in the present disclosure may be performed in parallel, sequentially or in different orders, and are not limited herein as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved.

Although embodiments or examples of the present disclosure have been described with reference to the accompanying drawings, it is to be understood that the above-described methods, systems and apparatus are merely exemplary embodiments or examples and that the scope of the present invention is not limited by these embodiments or examples, but only by the claims as issued and their equivalents. Various elements in the embodiments or examples may be omitted or may be replaced with equivalents thereof. Further, the steps may be performed in an order different from that described in the present disclosure. Further, various elements in the embodiments or examples may be combined in various ways. It is important that as technology evolves, many of the elements described herein may be replaced with equivalent elements that appear after the present disclosure.