Method and system for modulating quantum control waveform by keeping robustness unchanged

Abstract

The invention relates to a method and a system for modulating a quantum control waveform while keeping robustness unchanged. The method comprises the following steps: generating a first pre-variational function according to an original waveform; converting the first pre-variational function into an orthogonal component group, and reserving a first vertical component vertical to the robustness function gradient so as to keep the robustness unchanged; correcting the first vertical component to obtain a first variational function so as to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform; and performing iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output. According to the method, robustness can be kept unchanged in the continuous transformation process, other evaluation indexes such as fidelity, high energy level leakage, total energy, smoothness and bandwidth are improved, the robust waveform of the quantum gate with continuous parameters is achieved, and a group of quantum gate waveforms with all rotation angles can be obtained.

Description

Technical Field

[0001] The present application relates to the field of quantum bit waveform control technology, and in particular to a method and system for modulating a quantum control waveform while maintaining unchanged robustness. Background Art

[0002] In quantum computing platforms such as superconducting quantum bits, microwave pulses are an important means of controlling quantum bits. By inputting a modulated microwave waveform into a quantum bit, different quantum gates can be realized. In the framework of quantum mechanics, a quantum gate can rotate a quantum bit in an abstract Hilbert space, but the rotation axis and rotation angle need to be determined. Usually, after the microwave pulse and quantum bit parameters are determined, the rotation axis and rotation angle are already determined. When further optimizing the microwave waveform, the goals of the current technical field are: (1) to ensure that the rotation angle is as accurately as possible equal to the rotation angle of the target quantum gate, that is, to improve the fidelity of the quantum gate; (2) to reduce the impact of noise and ensure that the expected fidelity can be achieved under certain noise influences, that is, to improve noise robustness. Current optimization algorithms and methods for generating control waveforms for specific quantum gates do not take robustness into consideration, or cannot keep robustness unchanged during waveform transformation. Therefore, robustness cannot be maintained when optimizing fidelity. Moreover, existing robustness optimization algorithms or robustness control methods can only generate a control waveform for a specific application scenario each time. This knowledge about robustness cannot be transferred between interrelated but different physical processes, and there is no way to achieve robust control of quantum gates containing continuous parameters.

[0003] Therefore, the problem faced in this field is that robustness is not considered or cannot be maintained during the transformation of the quantum bit control waveform, or the robustness cannot be transferred during the transformation, resulting in low fidelity of the optimization algorithm of the quantum gate waveform and a set of quantum gate waveforms for all rotation angles cannot be achieved, resulting in limited application.

[0004] Therefore, the prior art still needs to be improved and developed. Summary of the invention

[0005] In view of this, the present application proposes a quantum waveform control method and system that maintains robustness unchanged, with the aim of solving the problem that the prior art does not consider robustness, or cannot maintain robustness unchanged, or cannot migrate robustness during the transformation process, resulting in low fidelity of the optimization algorithm for the quantum gate waveform, and cannot achieve a set of quantum gate waveforms for all rotation angles, resulting in limited application. The quantum bit waveform control method that maintains robustness unchanged in the present application can keep the robustness of any quantum gate waveform unchanged during the continuous variation process, improve other evaluation indicators, such as fidelity, high-energy level leakage, total energy, smoothness and bandwidth, and realize the robust waveform of the quantum gate with continuous parameters, and can obtain a set of quantum gate waveforms for all rotation angles.

[0006] The technical solution of this application is as follows:

[0007] The first aspect of the present application provides a quantum waveform control method for maintaining robustness, comprising the following steps:

[0008] generating a first prevariation function according to the original waveform;

[0009] Converting the first prevariation function into an orthogonal component group, retaining a first vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged;

[0010] Correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform;

[0011] Iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are output.

[0012] Specifically, the converting the first prevariation function into an orthogonal component group and retaining a first vertical component perpendicular to the gradient of the robustness function to keep the robustness unchanged includes:

[0013] Calculating the robustness function gradient of the original waveform;

[0014] Converting the first prevariation function into a group of orthogonal components;

[0015] A component perpendicular to the gradient of the robustness function is found from the orthogonal component group, which is the first perpendicular component.

[0016] Specifically, the correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform, includes:

[0017] Correcting the length of the first vertical component to obtain the first variation function;

[0018] Adding the first variation function to the original waveform to obtain the first quantum gate waveform;

[0019] Outputting the first quantum gate waveform and recording the corresponding first rotation angle;

[0020] Specifically, the first quantum gate waveform is consistent with the robustness of the original waveform.

[0021] Specifically, performing iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output includes:

[0022] Taking the first quantum gate waveform as a reference quantum gate waveform, performing variation on the reference quantum gate waveform to obtain a target quantum gate waveform;

[0023] The target quantum gate waveform is used as a new reference quantum gate waveform, and the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform is returned to be executed, and the variation is repeated until the set restriction conditions are met, and all the quantum gate waveforms are output.

[0024] Specifically, the step of taking the first quantum gate waveform as a reference quantum gate waveform and performing variation on the reference quantum gate waveform to obtain a target quantum gate waveform includes:

[0025] Variation of the reference quantum gate waveform according to the rotation angle to generate a target pre-variation function;

[0026] Converting the target pre-variation function into an orthogonal component group, retaining the target vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged;

[0027] The target vertical component is corrected according to the rotation angle variation value to obtain a target variation function to calculate the target quantum gate waveform, and the corresponding rotation angle of the target quantum gate waveform is recorded.

[0028] Specifically, the cyclic variation until the set restriction condition is met includes determining whether the rotation angle corresponding to the latest quantum gate waveform exceeds the rotation range, and if so, ending the cycle and outputting all the quantum gate waveforms; if not, continuing with the next variation.

[0029] Specifically, before generating the first pre-variation function according to the original waveform, the method includes:

[0030] The original waveform is generated according to the control task and robustness requirement, and the rotation range and the rotation angle variation value are determined.

[0031] A second aspect of the present application is to provide a system for modulating quantum control waveforms with unchanged robustness, comprising:

[0032] A preprocessing module is used to set the rotation range and the rotation angle variation value, and filter the original waveform according to the control task and robustness requirements;

[0033] A continuous variation module, for implementing a continuous variation process, including obtaining a reference quantum gate waveform according to the original waveform on the basis of maintaining the robustness unchanged, obtaining a target quantum gate waveform according to the reference quantum gate waveform, using the obtained target quantum gate waveform as the reference quantum gate waveform for the next variation, returning to perform the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform, until the set restriction condition is met, obtaining all the quantum gate waveforms, and obtaining all the quantum gate waveforms within the rotation range;

[0034] The output module is used to record and output all the quantum gate waveforms and corresponding rotation angles.

[0035] Specifically, the continuous variation module includes a calculation variation function unit, a variation unit and a judgment unit;

[0036] The calculation variational function unit is used to generate a pre-variational function based on the current initial waveform, calculate the robustness function gradient of the current initial waveform, and implement Schmidt orthogonalization to obtain a vertical component, and correct the vertical component to obtain a variational function.

[0037] The variation unit is used to add the variation function to the current initial waveform, so as to obtain a new quantum gate waveform and the corresponding rotation angle.

[0038] The judging unit is used to judge whether the corresponding rotation angle of the new quantum gate waveform exceeds the preset rotation range. If so, the loop is terminated and the result is sent to the output module to output all the quantum gate waveforms and the corresponding rotation angles; if not, the current quantum gate waveform is set as the initial waveform and input into the calculation variation function unit to continue the variation.

[0039] The third aspect of the present application is to provide a non-transitory computer-readable storage medium, on which is stored a program of a control method for a quantum waveform that maintains unchanged robustness, and when the program is executed by a processor, the following steps are implemented:

[0040] generating a first prevariation function according to the original waveform;

[0041] Converting the first prevariation function into an orthogonal component group, retaining a first vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged;

[0042] Correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform;

[0043] Iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are output.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The present application provides a quantum waveform control method and system that maintains robustness unchanged, with the purpose of solving the problem that the prior art does not consider robustness, or cannot maintain robustness unchanged, or cannot migrate robustness during the transformation process, resulting in low fidelity of the optimization algorithm of the quantum gate waveform, and cannot achieve a set of waveforms for all rotation angles, resulting in limited application. The quantum bit waveform control method that maintains robustness unchanged in the present application can keep the robustness of any quantum gate waveform unchanged during the continuous variation process, improve other evaluation indicators, such as fidelity, high-energy level leakage, total energy, smoothness and bandwidth, and realize the robust waveform of the quantum gate with continuous parameters, and can obtain a set of quantum gate waveforms for all rotation angles. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0047] Figure 1 This is a flow chart of a method for modulating a quantum control waveform while maintaining unchanged robustness according to an embodiment of the present application.

[0048] Figure 2 It is a schematic diagram of Schmidt orthogonalization of a modulated quantum control waveform while maintaining unchanged robustness according to an embodiment of the present application.

[0049] Figure 3 A continuous iterative process cycle diagram of a method for modulating a quantum control waveform while maintaining robustness according to an embodiment of the present application.

[0050] Figure 4 It is a schematic diagram of a group of quantum gate waveforms outputted by a method for modulating quantum control waveforms to maintain unchanged robustness according to an embodiment of the present application.

[0051] Figure 5 It is a schematic diagram of a continuous variation process of a method for modulating a quantum control waveform while maintaining unchanged robustness according to an embodiment of the present application.

[0052] Figure 6 It is a schematic diagram of a system for modulating quantum control waveforms while maintaining unchanged robustness according to an embodiment of the present application. DETAILED DESCRIPTION

[0053] The following will be combined with the implementation methods of this application to clearly and completely describe the technical solutions in the implementation methods of this application. Obviously, the described implementation methods are only part of the implementation methods of this application, not all of the implementation methods. Based on the implementation methods in this application, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0054] It should be understood that the terms used in this specification of the embodiments of the present application are only for the purpose of describing specific embodiments and are not intended to limit the embodiments of the present application. As used in the specification of the embodiments of the present application and the appended claims, unless the context clearly indicates otherwise, the singular forms of "a", "an" and "the" are intended to include plural forms.

[0055] On quantum computing platforms such as superconducting qubits, microwave pulses are an important means of controlling qubits. By inputting a modulated microwave waveform into the qubit, different quantum gates can be realized. In the framework of quantum mechanics, a quantum gate can cause a qubit to rotate in an abstract Hilbert space, but the axis of rotation and the angle of rotation need to be determined. Usually, after the carrier frequency and qubit parameters are determined, the axis of rotation and the angle of rotation are already determined. In the existing technical solutions, the current optimization algorithms and algorithms for generating control waveforms for specific quantum gates cannot naturally take robustness into consideration. Existing robustness optimization algorithms or robustness control methods can only generate control waveforms for a specific application scenario at a time. This knowledge about robustness cannot be transferred between different physical processes that are interrelated but different from each other.

[0056] Therefore, in order to solve a series of problems in the prior art that the robustness is not considered or the robustness cannot be maintained unchanged during the transformation of the quantum gate waveform, or the robustness cannot be transferred during the transformation, resulting in low fidelity of the optimization algorithm of the quantum gate waveform and inability to achieve a set of waveforms for all rotation angles, the present application performs continuous variations (or multiple small perturbations) on the original quantum waveform within the rotation range while maintaining the robustness unchanged, and finally outputs a set of quantum gate waveforms that maintain the same robustness.

[0057] Since the quantum gate waveform can be determined by a list of parameters A, the robustness function R of the quantum gate is a function of the waveform, which is naturally a function R(A) of the waveform parameter A. In this application, the parameter A is used to represent the original quantum gate waveform, called the original waveform A0, θ∈[θmin ,θ max ] represents the preset rotation range in the continuous variation process, θ min is the minimum value of the rotation angle of the quantum gate waveform in the continuous variation process, θ max Indicates the maximum value of the rotation angle of the quantum gate waveform in the continuous variation process. Where θ(A0) = θ min .

[0058] Specifically, the first aspect of the present application is to provide a method for modulating a quantum control waveform while maintaining robustness, such as Figure 1 As shown, the following steps are included:

[0059] S1. Generate the first pre-variation function dA according to the original waveform A0 pre ;

[0060] S2, converting the first pre-variation function into an orthogonal component group, retaining the gradient of the robustness function The first vertical component dA ′ , to keep the robustness unchanged;

[0061] S3, correcting the first vertical component dA ′ Obtaining a first variation function dA to calculate a first quantum gate waveform A1, and recording a first rotation angle θ(A1) corresponding to the first quantum gate waveform A1;

[0062] S4. Perform iterative continuous variation based on the first quantum gate waveform A1 until all quantum gate waveforms are output.

[0063] Specifically, step S1, generating a first pre-variation function dA according to the original waveform A0 pre Previously, including:

[0064] The original waveform A0 is generated according to the control task and robustness requirements, and the rotation range θ∈[θ min ,θ max ] and the rotation angle variation Δθ.

[0065] Specifically, the control task refers to the type of quantum system described in this application, the control method of quantum bits, the quantum gates to be implemented, the rotation range of the quantum gates, the fidelity and robustness of the quantum gates required by the task, the experimental objectives, etc.

[0066] Optionally, the first prevariation function dA pre You can also freely choose according to the target to be optimized or other purposes, such as fidelity, high-energy level leakage, etc. to optimize the objective function for the waveform parameter A i The derivative of can also be a randomly generated parameter vector.

[0067] Preferably, in one embodiment, θ∈[0,2π]. In another embodiment, Rotation angle variation Preferably, in another embodiment, the rotation angle variation value Δθ can be set according to the original waveform A0 that meets the requirements. Specifically, the rotation angle variation value Δθ is set in θ∈[θ min ,θ max ], and ensure that the rotation angle of any quantum gate waveform after rotation does not exceed θ max .

[0068] Specifically, in the continuous variation process, the first quantum gate waveform A1 is obtained based on the original waveform A0, and then the next quantum gate waveform is obtained in turn based on the quantum gate waveform generated by the previous variation, until the rotation angle exceeds θ∈[θ min ,θ max ] and stops the variation, and outputs a set of quantum gate waveforms and the corresponding rotation angles. The rotation angle variation value Δθ in each variation process is the same.

[0069] Specifically, in the process of obtaining the first quantum gate waveform A1 based on the variation of the original waveform A0, the first pre-variation function is first generated according to the original waveform A0, and the expression of the first pre-variation function is:

[0070]

[0071] Among them, dA pre represents the pre-variation function in the current variation process, A now represents the initial waveform in the current variation process. In the first variation, A now is the original waveform A0, and the rotation angle is θ(A0)=θ min .

[0072] Specifically, S2, convert the first pre-variation function into an orthogonal component group, retaining the gradient of the robustness function The first vertical component of the vertical to keep the robustness unchanged includes the steps:

[0073] S21, calculating the robustness function gradient of the original waveform;

[0074] S22, converting the first prevariation function into an orthogonal component group;

[0075] S23. Find a component perpendicular to the gradient of the robustness function from the orthogonal component group, which is the first vertical component. The robustness of the first vertical component is consistent with the robustness of the original waveform.

[0076] Specifically, the robustness function gradient of the original waveform is expressed as:

[0077]

[0078] represents the robustness function gradient in the current variational process. In the first variational process in step S23, Represents the robustness function gradient of the original waveform A0.

[0079] Specifically, converting the first prevariation function into an orthogonal component group means converting the directional prevariation function into a group of orthogonal components through Schmidt orthogonalization, and selecting the vertical component perpendicular to the robustness gradient function as the component with consistent robustness.

[0080] like Figure 2 As shown, it is a schematic diagram of converting the pre-variation function into an orthogonal component group in a certain variation process in an embodiment, and the orthogonal component group includes a gradient perpendicular to the robustness function The amount and the component parallel to the gradient of the robustness function The gradient perpendicular to the robustness function The amount As the first vertical component dA ′ , that is because have That is, the robustness R in this variation direction remains unchanged. This ensures that the robustness of the vertical component in the first variation process is consistent with the robustness of the original waveform.

[0081] In order to ensure that each change to A0 during the variation process is small enough and the corresponding Δθ are equidistant, it is also necessary to correct the size of the variation so that the true variation function dA is obtained.

[0082] Specifically, S3, the correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform A1, and recording a first rotation angle θ(A1) corresponding to the first quantum gate waveform, includes:

[0083] S31, correcting the length of the first vertical component to obtain the first variation function dA1;

[0084] S32, adding the first variation function dA1 to the original waveform A0 to obtain the first quantum gate waveform A1;

[0085] S33, outputting the first quantum gate waveform A1, and recording the corresponding first rotation angle θ(A1).

[0086] Specifically, the expression of the variational function is:

[0087]

[0088] Wherein, dA represents the variational function in the current variational process, and dA1 represents the first variational function in the first variational process.

[0089] In a certain variation process, after obtaining the variation function, add the variation function to the initial waveform to obtain the quantum gate waveform of this variation:

[0090] A new =A now +dA, (4)

[0091] Among them, A new represents the quantum gate waveform obtained after variation, A now Represents the initial waveform, and dA represents the variational function in the current variational process.

[0092] In the first variation, the initial waveform is the original waveform A0, so the first quantum gate waveform A1=A0+dA1, and the corresponding rotation angle θ(A1)=θ0+Δθ. In the second variation, the initial waveform is the first quantum gate waveform A1, so the second quantum gate waveform A2=A1+dA2, and the corresponding rotation angle is θ(A2)=θ1+Δθ=θ0+2Δθ.

[0093] Specifically, S4, performing iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output, including:

[0094] S41, using the first quantum gate waveform as a reference quantum gate waveform, performing variation on the reference quantum gate waveform to obtain a target quantum gate waveform;

[0095] S42, taking the target quantum gate waveform as a new reference quantum gate waveform, and returning to execute the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform, cyclically varying until the set restriction condition is met, and outputting all the quantum gate waveforms.

[0096] Specifically, step S41, using the first quantum gate waveform as a reference quantum gate waveform, performing variation on the reference quantum gate waveform, and obtaining a target quantum gate waveform includes:

[0097] S411, varying the reference quantum gate waveform according to the rotation angle to generate a target pre-variation function;

[0098] S412, converting the target pre-variation function into an orthogonal component group, retaining the target vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged;

[0099] S413, correcting the target vertical component according to the rotation angle variation value to obtain a target variation function to calculate the target quantum gate waveform, and recording the corresponding rotation angle of the target quantum gate waveform.

[0100] In order to more clearly describe the process of continuous variation, the specific process of S4 can be described from another perspective. Specifically, S4, iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are output, including:

[0101] S41, performing variation based on the first quantum gate waveform to obtain a second quantum gate waveform;

[0102] S42, performing variation based on the second quantum gate waveform to obtain a third quantum gate waveform;

[0103] S43. Repeat the variation until all quantum gate waveforms are obtained.

[0104] Specifically, S41, performing variation based on the first quantum gate waveform to obtain a second quantum gate waveform, comprising:

[0105] S411, varying the first quantum gate waveform according to the rotation angle to generate a second pre-variation function;

[0106] S412: convert the second prevariation function into an orthogonal component group, retaining the robustness function gradient The second vertical component of the vertical to keep the robustness unchanged;

[0107] S413. Correct the second vertical component according to the rotation angle variation value to obtain a second variation function to calculate the second quantum gate waveform, and record a second rotation angle corresponding to the second quantum gate waveform.

[0108] The calculation formulas of steps S411 to S413 are consistent with the aforementioned (1) to (4). Therefore, the final second quantum gate waveform A2=A1+dA2 is obtained, and the corresponding rotation angle is θ(A2)=θ1+Δθ=θ0+2Δθ.

[0109] In the process of cyclic variation, it includes judging the cyclic conditions. Figure 3 The figure is a schematic diagram of the continuous variation process of the embodiment of the present application. The cyclic variation until all quantum gate waveforms are obtained is limited to the condition that the latest quantum gate waveform A is determined. new The corresponding rotation angle θ(A new ) exceeds the rotation range θ maxIf it exceeds, the loop ends and all the quantum gate waveforms and corresponding rotation angles are output; if it does not exceed, the next variation is continued until all the quantum gate waveforms are output.

[0110] like Figure 4 As shown in FIG. 1 , it is a schematic diagram of the original waveform and all quantum gate waveforms output after continuous variation in one embodiment, such as Figure 5 As shown, Figure 4 The corresponding schematic diagram of the continuous variation process based on the original waveform, each closed curve represents a quantum gate waveform, and has a corresponding rotation angle. All quantum gate waveforms in the figure are closed, indicating that in the continuous variation process, the robustness of any quantum gate waveform remains unchanged compared to the original waveform.

[0111] Specifically, Figure 4 Each slice of is a microwave waveform, Figure 5 Each slice of is the error evolution diagram corresponding to the waveform. The following introduces the corresponding relationship between the error evolution diagram and the waveform: Assume that the system is affected by quasi-static noise, and the noise Hamiltonian is H n To see how the noise evolves under our control of the system, we replace the noise operator H n Transformed to the interaction representation of U0, that is Where U0 is the system Hamiltonian and the control Hamiltonian H sys +H c The evolution operator generated together. When the quantum gate ends, if H nI (T) = 0, which means that the first-order effect of the noise is just eliminated. nI (t) is a time-dependent matrix, which is not easy to visualize, so we project this matrix onto the Pauli matrix and get a three-dimensional curve. Conversely, by calculating the curvature and torsion of the curve, the control waveform can be completely restored. After calculation, it is known that when there is only one noise and only one control, the curve is actually a two-dimensional curve, and the curvature of the curve is sufficient to restore the control waveform. nI The condition of (T) = 0 means that the corresponding curve can return to the origin when t = T, that is, when the curve is a closed curve, the corresponding control waveform has first-order robustness. More complex and higher-order robustness can also be discussed, which will not be elaborated here.

[0112] The second aspect of the present application is to provide a system for modulating quantum control waveforms to maintain robustness. Figure 6 , which is a schematic diagram of a system 10 for modulating quantum control waveforms to maintain robustness, including a preprocessing module 20, a continuous variation module 30 and an output module 40;

[0113] A preprocessing module 20, used to set the rotation range and the rotation angle variation value, and filter the original waveform according to the control task and robustness requirements;

[0114] The continuous variation module 30 is used to implement the continuous variation process, including obtaining a reference quantum gate waveform according to the original waveform on the basis of maintaining the robustness unchanged, obtaining a target quantum gate waveform according to the reference quantum gate waveform, using the obtained target quantum gate waveform as the reference quantum gate waveform for the next variation, returning to perform the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform, until the set restriction condition is met, and all the quantum gate waveforms are obtained, and all the quantum gate waveforms within the rotation range are obtained;

[0115] The output module 40 is used to record and output all the quantum gate waveforms and the corresponding rotation angles.

[0116] Specifically, the continuous variation module 30 includes a variation function calculation unit 31 , a variation unit 32 , and a judgment unit 33 .

[0117] The calculation variational function unit 31 is used to generate a pre-variational function based on the current initial waveform, calculate the robustness function gradient of the current initial waveform, and perform Schmidt orthogonalization to obtain a vertical component, and correct the vertical component to obtain a variational function.

[0118] The variation unit 32 is used to add the variation function to the current initial waveform or the current reference waveform, so as to obtain a new quantum gate waveform or a target quantum gate waveform and a corresponding rotation angle.

[0119] The judging unit 33 judges whether the corresponding rotation angle of the new quantum gate waveform exceeds the preset rotation range. If so, the loop ends and the result is sent to the output module 40 to output all quantum gate waveforms and their corresponding rotation angles. If not, the current quantum gate waveform is set as the initial waveform, or the current target reference quantum gate waveform is used as the reference quantum gate waveform for the next variation and input into the calculation variation function unit 31 to continue the variation.

[0120] The third aspect of the present application is to provide a non-transitory computer-readable storage medium, on which is stored a program for a method of modulating a quantum control waveform with constant robustness, and when the program is executed by a processor, the following steps are implemented:

[0121] S1, generating a first pre-variation function according to the original waveform;

[0122] S2, converting the first pre-variation function into an orthogonal component group, retaining the gradient of the robustness function The first vertical component of the vertical to keep the robustness unchanged;

[0123] S3, correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform;

[0124] S4. Perform iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output.

[0125] The present application solves a series of problems in the prior art, such as not considering robustness or failing to maintain robustness during the transformation of quantum gate waveforms, or failing to transfer robustness during the transformation, resulting in low fidelity of the optimization algorithm for the quantum gate waveform and failure to achieve a set of waveforms for all rotation angles. The present application performs continuous variations (or multiple small perturbations) on the original quantum waveform within the rotation range while maintaining the robustness, and finally outputs a set of quantum gate waveforms that maintain the same robustness.

[0126] The technical effect of the present application is that the quantum bit waveform control method that maintains unchanged robustness can keep the robustness of any quantum gate waveform unchanged compared to the original waveform during the continuous variation process, improve other evaluation indicators, such as fidelity, high-energy level leakage, total energy, smoothness, bandwidth, etc., and realize the robust waveform of the quantum gate with continuous parameters, and a set of quantum gate waveforms for all rotation angles can be obtained.

[0127] As shown in Table 1, it is an algorithm pseudo code of a method for modulating quantum control waveforms to maintain robustness in accordance with an embodiment of the present application, and the preset rotation angle is θ∈[θ min ,θ max ], firstly, the original waveform is generated according to the control task and robustness requirements by using the existing technology, specifically, to find the rotation angle θ min The quantum gate waveform A is used as the initial waveform A0 in this continuous variation process. The judgment condition is set to perform continuous variation. Each variation or iteration generates a quantum gate waveform and a corresponding rotation angle. The next pulse waveform is obtained by variation based on the current quantum gate waveform until the rotation angle of the latest quantum gate waveform is greater than or equal to θ. max , stop the loop, and output all the robust quantum gate waveforms before the current waveform and their corresponding rotation angles. The pseudo code of the algorithm in the continuous variation process of this application is shown in Table 1.

[0128] Table 1 Algorithm pseudo code

[0129]

[0130] The method process of the present application is described below through specific embodiments:

[0131] The default rotation angle is First, use the existing technology to find the rotation angle The quantum gate waveform A is used as the initial waveform A0 in this continuous variation process. In order to maintain the robustness in the continuous variation process, the rotation angle of each variation should be small enough compared with the previous variation. First, based on A0, A1 is output after the first variation. The specific steps are:

[0132] (1) Generate prevariation

[0133] (2) Find the gradient of the robustness function

[0134] (3) Schmidt orthogonalization to obtain the first vertical component

[0135] (4) Correct the length of the first vertical component to obtain the first variation function

[0136] (5) Transform the waveform parameters A1 = A0 + dA1, θ(A1) = θ(A0) + 0.33π = 0.67π;

[0137] (6) Determine whether θ(A1) < θ max , proceed to the second variation;

[0138] (7) Let A1 = A now , using the same process as steps (1) to (4), we obtain A2 = A1 + dA2, θ(A2) = θ(A1) + Δθ;

[0139] (8)Judgment Continue with the third variation;

[0140] (9) Let A2 = A now , using the same process as steps (1) to (4), we obtain A3 = A2 + dA3, θ(A3) = θ(A2) + Δθ;

[0141] (10) Continue the variation until End the loop and output all quantum gate waveforms and the corresponding rotation angles. In this continuous variation process, the number of iterations is 6286. In order to present the continuous variation process more clearly, some waveforms obtained by variation or iteration are marked, including waveform A obtained by the 1047th variation. 1047 , waveform A obtained by the 2095th variation 2095 , waveform A obtained by the 3143rd variation 3143, waveform A obtained by the 4190th variation 4190 , waveform A obtained by the 5238th variation 5238 and waveform A obtained by the 6286th variation 6286 , and the specific corresponding angles are shown in Table 2.

[0142] like Figure 4 As shown in FIG. 1 , it is a diagram of the original waveform and all quantum gate waveforms output after continuous variation in one embodiment, such as Figure 5 As shown, Figure 4 The waveform effect diagram of the corresponding original waveform and all quantum gate waveforms output after continuous variation is the original waveform A0 finally output by this embodiment and the 6286 quantum gate waveforms A1~A generated in the corresponding continuous variation process. 6286 , and the corresponding rotation angles θ(A1)~θ(A 6286 ), the quantum gate waveforms have a common intersection, indicating that they have a common robustness, and continuous variation is achieved on the basis of maintaining the robustness unchanged, and multiple quantum gate waveforms can be generated at one time, which is efficient and convenient. Preferably, the number of continuous variations and the rotation angle can be set according to actual needs.

[0143] Table 2 The number of iterations of the continuous variation of quantum waveform and the corresponding rotation angle

[0144]

[0145] In summary, the present application provides a method and system for modulating quantum control waveforms with unchanged robustness, the method comprising the following steps: generating a first pre-variation function according to the original waveform and preset rotation parameters; converting the first pre-variation function into an orthogonal component group, retaining the first vertical component perpendicular to the gradient of the robustness function to keep the robustness unchanged; correcting the first vertical component to obtain a first variation function to calculate the first quantum gate waveform, and recording the first rotation angle corresponding to the first quantum gate waveform; performing iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output. The continuous variation method based on unchanged robustness of the present application solves the problem that the prior art does not consider robustness, or cannot maintain unchanged robustness, or cannot migrate robustness during the transformation process, which makes the optimization algorithm of the quantum gate waveform low in fidelity, and cannot achieve a set of waveforms of all rotation angles, resulting in limited application. The quantum waveform control method for maintaining robustness of the present application can maintain robustness during continuous transformations, improve other evaluation indicators, such as fidelity, high-energy level leakage, total energy, smoothness and bandwidth, and realize robust waveforms of quantum gates with continuous parameters, and obtain a set of quantum gate waveforms for all rotation angles.

[0146] The above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application. The above content is only an example and explanation of the structure of the present invention. The technicians in the relevant technical field can make various modifications or supplements to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the invention or exceed the scope defined by the present invention, they shall all belong to the protection scope of the present invention.

Claims

1. A method for modulating a quantum control waveform while maintaining robustness, characterized in that: The following steps are involved: generating a first prevariation function according to the original waveform; Converting the first prevariation function into an orthogonal component group, retaining a first vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged; Correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform; Iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are output.

2. A method for modulating a quantum control waveform while maintaining robustness according to claim 1, characterized in that: The step of converting the first prevariation function into an orthogonal component group and retaining a first vertical component perpendicular to the gradient of the robustness function to keep the robustness unchanged comprises: Calculating the robustness function gradient of the original waveform; Converting the first prevariation function into a group of orthogonal components; A component perpendicular to the gradient of the robustness function is found from the orthogonal component group, which is the first perpendicular component.

3. A method for modulating a quantum control waveform while maintaining robustness according to claim 1, characterized in that: The step of correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform and recording a first rotation angle corresponding to the first quantum gate waveform comprises: Correcting the length of the first vertical component to obtain the first variation function; Adding the first variation function to the original waveform to obtain the first quantum gate waveform; Outputting the first quantum gate waveform and recording the corresponding first rotation angle; The first quantum gate waveform has the same robustness as the original waveform.

4. A method for modulating a quantum control waveform while maintaining robustness according to claim 1, characterized in that: The iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output includes: Taking the first quantum gate waveform as a reference quantum gate waveform, performing variation on the reference quantum gate waveform to obtain a target quantum gate waveform; The target quantum gate waveform is used as a new reference quantum gate waveform, and the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform is returned to be executed, and the variation is repeated until the set restriction condition is met, and all the quantum gate waveforms are output.

5. A method for modulating a quantum control waveform while maintaining robustness according to claim 4, characterized in that: The step of using the first quantum gate waveform as a reference quantum gate waveform and performing variation on the reference quantum gate waveform to obtain a target quantum gate waveform comprises: Variation of the reference quantum gate waveform according to the rotation angle to generate a target pre-variation function; Converting the target pre-variation function into an orthogonal component group, retaining the target vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged; The target vertical component is corrected according to the rotation angle variation value to obtain a target variation function to calculate the target quantum gate waveform, and the corresponding rotation angle of the target quantum gate waveform is recorded.

6. A method for modulating quantum control waveforms to maintain robustness according to claim 4, characterized in that: The cyclic variation, until the set restriction condition is met, includes judging whether the rotation angle corresponding to the latest quantum gate waveform exceeds the rotation range, if so, ending the cycle and outputting all the quantum gate waveforms; if not, continuing with the next variation.

7. A method for modulating a quantum control waveform while maintaining robustness according to claim 5, characterized in that: Before generating the first pre-variation function according to the original waveform, the method includes: The original waveform is generated according to the control task and robustness requirement, and the rotation range and the rotation angle variation value are determined.

8. A system for modulating quantum control waveforms to maintain robustness, characterized in that: include: A preprocessing module is used to set the rotation range and the rotation angle variation value, and filter the original waveform according to the control task and robustness requirements; A continuous variation module, for implementing a continuous variation process, including obtaining a reference quantum gate waveform according to the original waveform on the basis of maintaining the robustness unchanged, obtaining a target quantum gate waveform according to the reference quantum gate waveform, using the obtained target quantum gate waveform as the reference quantum gate waveform for the next variation, returning to perform the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform, until the set restriction condition is met, obtaining all the quantum gate waveforms, and obtaining all the quantum gate waveforms within the rotation range; The output module is used to record and output all the quantum gate waveforms and corresponding rotation angles.

9. A system for modulating quantum control waveforms to maintain robustness according to claim 8, characterized in that: The continuous variation module includes a variation function calculation unit, a variation unit and a judgment unit; The calculation variational function unit is used to generate a pre-variational function based on the current initial waveform, calculate the robustness function gradient of the current quantum gate waveform, and perform Schmidt orthogonalization to obtain a vertical component, and correct the vertical component to obtain a variational function; The variation unit is used to add the variation function to the current initial waveform, so as to obtain a new quantum gate waveform and the corresponding rotation angle; The judging unit is used to judge whether the rotation angle corresponding to the new quantum gate waveform exceeds the preset rotation range, and if so, terminate the loop and send the result to the output module to output all the quantum gate waveforms and the corresponding rotation angles; If it does not exceed, the current quantum gate waveform is set as the initial waveform and input into the calculation variation function unit to continue the variation.

10. A non-transitory computer-readable storage medium, characterized in that: The non-transitory computer-readable storage medium stores a program of a control method for a quantum waveform that maintains unchanged robustness, and when the program is executed by a processor, the following steps are implemented: generating a first prevariation function according to the original waveform; Converting the first prevariation function into an orthogonal component group, retaining a first vertical component perpendicular to the gradient of the robustness function, so as to keep the robustness unchanged; Correcting the first vertical component to obtain a first variation function to calculate a first quantum gate waveform, and recording a first rotation angle corresponding to the first quantum gate waveform; Iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are output.

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