A method and system for maintaining robustness of a modulated quantum control waveform

Abstract

A method and system for maintaining robustness of modulation quantum control waveform, the method comprising: generating a first pre-variational function according to an original waveform; converting the first pre-variational function into a set of orthogonal components, retaining a first perpendicular component perpendicular to a robustness function gradient to maintain robustness unchanged; correcting the first perpendicular component to obtain a first variational function to calculate a first quantum gate waveform and record a corresponding first rotation angle of the first quantum gate waveform; iteratively continuously varying based on the first quantum gate waveform until all quantum gate waveforms are output. The method of the present application can maintain robustness unchanged in the process of continuous transformation, improve other evaluation indexes such as fidelity, high energy level leakage, total energy, smoothness and bandwidth, and realize robust waveform of quantum gate with continuous parameters, and a set of quantum gate waveforms of all rotation angles can be obtained.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum bit waveform control, and particularly relates to a method and system for maintaining robust modulation quantum control waveform. BACKGROUND

[0002] On a quantum computing platform such as a superconducting quantum bit, a microwave pulse is an important means of controlling a quantum bit. Inputting a modulated microwave waveform to a quantum bit can achieve different quantum gates. 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 also determined. When further optimizing the microwave waveform, the current technical field aims to: (1) ensure that the rotation angle is as accurate as possible to the rotation angle of the target quantum gate, that is, to improve the quantum gate fidelity; (2) reduce the influence of noise and ensure that the expected fidelity can be achieved under the influence of noise, that is, to improve the noise robustness. The current optimization algorithm and the method of generating control waveform for a specific quantum gate do not take robustness into account, or the robustness cannot be maintained during waveform transformation, so the robustness cannot be maintained when optimizing the fidelity. Moreover, the existing robustness optimization algorithm or robustness control method can only generate a control waveform for a specific application scenario each time, and in different physical processes that are related to each other but different from each other, such knowledge about robustness cannot be transferred, and there is no way to achieve robust control for quantum gates containing continuous parameters.

[0003] Therefore, the problem in the field is that the 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 quantum gate waveform optimization algorithm, and a set of quantum gate waveforms for all rotation angles cannot be achieved, which limits the application.

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

[0005] Therefore, the application provides a quantum waveform control method and system for maintaining robustness, aiming at solving the problem that the prior art does not consider robustness, or cannot maintain robustness, or the robustness cannot be migrated in the transformation process, so that the optimization algorithm of the quantum gate waveform has low fidelity, and a set of quantum gate waveforms cannot be obtained for all rotation angles, resulting in limited application. The quantum bit waveform control method for maintaining robustness can maintain the robustness of any quantum gate waveform unchanged in the continuous variational process, improve other evaluation indexes such as fidelity, high energy level leakage, total energy, smoothness and bandwidth, and realize the robust waveform of the quantum gate with continuous parameters, so that a set of quantum gate waveforms for all rotation angles can be obtained.

[0006] The technical scheme of the application is as follows:

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

[0008] generating a first pre-variational function from an original waveform;

[0009] converting the first pre-variational function into a set of orthogonal components, retaining a first vertical component perpendicular to the gradient of a robustness function to maintain the robustness unchanged;

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

[0011] iteratively performing continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output.

[0012] Specifically, the converting the first pre-variational function into a set of orthogonal components, retaining a first vertical component perpendicular to the gradient of a robustness function to maintain the robustness unchanged comprises:

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

[0014] converting the first pre-variational function into a set of orthogonal components;

[0015] finding a component perpendicular to the gradient of the robustness function from the set of orthogonal components, which is the first vertical component.

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

[0017] correcting the length of the first vertical component to obtain the first variational function;

[0018] add the first variational function to the original waveform to obtain the first quantum gate waveform;

[0019] output the first quantum gate waveform and record the corresponding first rotation angle;

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

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

[0022] take the first quantum gate waveform as a reference quantum gate waveform, and perform variation on the reference quantum gate waveform to obtain a target quantum gate waveform;

[0023] take the target quantum gate waveform as a new reference quantum gate waveform, and return to perform variation on the reference quantum gate waveform to obtain the target quantum gate waveform, and perform cyclic variation until a set limit condition is met, and output all quantum gate waveforms.

[0024] Specifically, 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] perform variation on the reference quantum gate waveform according to the rotation angle to generate a target pre-variational function;

[0026] convert the target pre-variational function into a set of orthogonal components, retain a target vertical component perpendicular to the robustness function gradient to keep the robustness unchanged;

[0027] correct the target vertical component according to the rotation angle variation value to obtain a target variational function, to calculate the target quantum gate waveform, and record the corresponding rotation angle of the target quantum gate waveform.

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

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

[0030] generate the original waveform according to the control task and the robustness requirement, and determine the rotation range and the rotation angle variation value.

[0031] The second aspect of the present application provides a system for maintaining robust modulation quantum control waveform, comprising:

[0032] a preprocessing module configured to set a rotation range and a rotation angle variation value, and to screen an original waveform according to a control task and a robustness requirement;

[0033] a continuous variation module configured to implement a continuous variation process, including obtaining a reference quantum gate waveform from the original waveform while maintaining the robustness unchanged, obtaining a target quantum gate waveform from the reference quantum gate waveform, taking the target quantum gate waveform as the reference quantum gate waveform for next variation, returning to perform variation on the reference quantum gate waveform to obtain the target quantum gate waveform until a set limitation condition is met, obtaining all the quantum gate waveforms in the rotation range, and obtaining all the quantum gate waveforms in the rotation range;

[0034] an output module configured to record and output all the quantum gate waveforms and corresponding rotation angles.

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

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

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

[0038] The judgment unit is configured to judge whether the corresponding rotation angle of the new quantum gate waveform exceeds a preset rotation range, and if so, to end the loop and send the result to the output module to output all the quantum gate waveforms and corresponding rotation angles; if not, to take the current quantum gate waveform as the initial waveform and input it to the variation function calculation unit to continue the variation.

[0039] A third aspect of the present application provides a non-transitory computer readable storage medium having a program of a quantum waveform control method for maintaining robustness stored thereon, the program being executed by a processor to implement the following steps:

[0040] generating a first pre-variation function from an original waveform;

[0041] converting the first pre-variation function into a set of orthogonal components, retaining a first vertical component perpendicular to a robustness function gradient to maintain the robustness unchanged;

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

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

[0044] The present application has the following beneficial effects relative to the prior art:

[0045] The present application provides a quantum waveform control method and system that maintains robustness unchanged, aiming to solve the problem in the prior art that robustness is not considered, or cannot be maintained unchanged, or cannot be migrated during transformation, resulting in low fidelity of the optimization algorithm of the quantum gate waveform, and a set of waveforms for all rotation angles cannot be achieved, thus limiting application. The quantum bit waveform control method that maintains robustness unchanged in the present application can maintain the robustness of any quantum gate waveform unchanged during continuous variation, improve other evaluation indexes such as fidelity, high energy level leakage, total energy, smoothness and bandwidth, and achieve robust waveforms of quantum gates with continuous parameters, and a set of quantum gate waveforms for all rotation angles can be obtained. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0047] Figure 1 is a flowchart of a method for maintaining robustness unchanged in the modulation quantum control waveform of an embodiment of the present application.

[0048] Figure 2 is a schematic diagram of Schmidt orthogonalization of a method for maintaining robustness unchanged in the modulation quantum control waveform of an embodiment of the present application.

[0049] Figure 3 is a continuous iteration process loop diagram of a method for maintaining robustness unchanged in the modulation quantum control waveform of an embodiment of the present application.

[0050] Figure 4 is a result schematic diagram of a set of quantum gate waveforms output by a method for maintaining robustness unchanged in the modulation quantum control waveform of an embodiment of the present application.

[0051] Figure 5 is a schematic diagram of a continuous variation process of a method for maintaining robustness unchanged in the modulation quantum control waveform of an embodiment of the present application.

[0052] Figure 6 is a schematic diagram of a system for maintaining robust modulation quantum control waveforms according to embodiments of the present application. DETAILED DESCRIPTION

[0053] The technical solutions in the embodiments of the present application will be clearly and completely described in combination with the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work are within the scope of protection of the present application.

[0054] It should be understood that the terms used in the specification of the embodiments of the present application herein 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 and the appended claims of the present application, unless otherwise clear from the context, the singular forms "a", "an" and "the" are intended to include the plural forms as well.

[0055] On a quantum computing platform such as a superconducting quantum bit, a microwave pulse is an important means of controlling the quantum bit. By inputting a modulated microwave waveform to the quantum bit, different quantum gates can be realized. In the framework of quantum mechanics, a quantum gate can rotate the quantum bit in the abstract Hilbert space, but the rotation axis and rotation angle need to be determined. Usually, after the carrier frequency and quantum bit parameters are determined, the rotation axis and rotation angle are also determined. In the prior art, the current optimization algorithm and the algorithm for generating control waveforms for specific quantum gates cannot naturally take robustness into account. The existing robustness optimization algorithm or robustness control method can only produce a control waveform for a specific application scenario each time, and this knowledge about robustness cannot be transferred between different physical processes that are related to each other but different from each other.

[0056] Therefore, in order to solve the problems in the prior art that robustness is not considered or cannot be maintained during the transformation of quantum gate waveforms, or robustness cannot be transferred during the transformation, resulting in low fidelity of the optimization algorithm for quantum gate waveforms and the inability to achieve a set of waveforms for all rotation angles, etc., the present application performs continuous variation (or multiple small perturbations) within the rotation range of the original quantum waveform on the basis of maintaining the same robustness, 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 column of parameters A, the robustness function R of the quantum gate is a function of the waveform, and naturally a function R(A) of the waveform parameters A. In the present application, it is assumed that the parameter A represents the original quantum gate waveform, which is referred to as the original waveform A0, θ∈[θmin ,θ max ] represents the preset rotation range in the continuous variation process, θ min It is the minimum rotation angle of the quantum gate waveform in the continuous variational process, θ. max This represents the maximum value of the rotation angle of the quantum gate waveform during the continuous variational process. Where θ(A0) = θ min .

[0058] Specifically, the first aspect of this application lies in providing a method for maintaining a modulated quantum control waveform with invariant robustness, such as... Figure 1 As shown, it includes the following steps:

[0059] S1. Generate the first prevariant function dA based on the original waveform A0. pre ;

[0060] S2. Convert the first prevariation function into a set of orthogonal components, retaining the gradient of the robust function. The first vertical component dA ′ To maintain robustness;

[0061] S3, Correct the first vertical component dA ′ Obtain the first variational function dA to calculate the first quantum gate waveform A1, and record the corresponding first rotation angle θ(A1) of 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: Generate the first prevariation function dA based on 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] is determined. 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 the qubits, the quantum gate to be implemented, the rotation range of the quantum gate, the required quantum gate fidelity and robustness, and the experimental objectives.

[0066] Optionally, the first prevariant function dA pre It can also be freely selected based on the optimization objective or other purposes, such as fidelity, high-energy-level leakage, etc., as the objective function for optimizing waveform parameter A. i The derivative can also be a randomly generated parameter vector.

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

[0068] Specifically, in the continuous variation process, first, the first quantum gate waveform A1 is varied based on the original waveform A0, and then the next quantum gate waveform is obtained according to the quantum gate waveform generated by the last variation, until the rotation angle exceeds the range of θ∈[θ min ,θ max ] in the latest variation, and the variation is stopped, and a set of quantum gate waveforms and corresponding rotation angles are output. 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 original waveform A0, first, the first pre-variation function is generated according to the original waveform A0, and the expression of the first pre-variation function is:

[0070]

[0071] Wherein, 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, the first pre-variation function is converted into a set of orthogonal components, and a first vertical component perpendicular to the robustness function gradient is retained to keep the robustness unchanged, including the steps of:

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

[0074] S22, converting the first pre-variation function into a set of orthogonal components;

[0075] S23, finding a component from the set of orthogonal components that is perpendicular to the robustness function gradient, which is the first vertical component, and 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] denotes the robustness function gradient in the current variational process, in the first variational process in step S23, denotes the robustness function gradient of the original waveform A0.

[0079] Specifically, converting the first pre-variational function into an orthogonal component group means that the pre-variational function with directionality is converted into an orthogonal component group by Schmidt orthogonalization, and the vertical component perpendicular to the robustness gradient function is selected as the component that is robustly consistent.

[0080] As Figure 2 shown is a schematic diagram of conversion of a pre-variational function into an orthogonal component group in an embodiment in a variational process, the orthogonal component group including a component perpendicular to the robustness function gradient and a component parallel to the robustness function gradient The component perpendicular to the robustness function gradient is taken as the first vertical component dA ′ , that is because that is, the robustness R in this variational direction remains unchanged. In this way, it can be ensured that the robustness of the vertical component is consistent with the robustness of the original waveform in the first variational process.

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

[0082] Specifically, S3, the first vertical component is corrected to obtain the first variational function, to calculate the first quantum gate waveform A1, and record the corresponding first rotation angle θ(A1) of the first quantum gate waveform, including:

[0083] S31, the length of the first vertical component is corrected to obtain the first variational function dA1;

[0084] S32, the first variational function dA1 is added to the original waveform A0 to obtain the first quantum gate waveform A1;

[0085] S33, the first quantum gate waveform A1 is output, and the corresponding first rotation angle θ(A1) is recorded.

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

[0087]

[0088] wherein dA represents a variational function in a current variational process. dA1 represents a first variational function in a first variational process.

[0089] In a certain variational process, after obtaining the variational function, the variational function is added to the initial waveform, and the quantum gate waveform of this time of variation is obtained:

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

[0091] wherein A represents a quantum gate waveform obtained after variation, A represents an initial waveform, and dA represents a variational function in a current variational process. new now

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

[0093] Specifically, S4, based on the first quantum gate waveform, iteratively and continuously varies until all quantum gate waveforms are output, including:

[0094] S41, taking the first quantum gate waveform as a reference quantum gate waveform, varying 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 perform the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform, and cyclically varying until a set limit condition is met, and outputting all quantum gate waveforms.

[0096] Specifically, step S41, taking the first quantum gate waveform as a reference quantum gate waveform, varying the reference quantum gate waveform to obtain a target quantum gate waveform, includes:

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

[0098] S412, converting the target pre-variational function into a set of orthogonal components, retaining a target perpendicular component perpendicular to the gradient of the robustness function to keep the robustness unchanged; ​​

[0099] S413、According to the rotation angle variation value, correct the target vertical component to obtain a target variation function, calculate the target quantum gate waveform, and record the corresponding rotation angle of the target quantum gate waveform.

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

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

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

[0103] S43, loop variation until all quantum gate waveforms are obtained.

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

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

[0106] S412, convert the second pre-variation function into a set of orthogonal components, retain the robust function gradient vertical second vertical component to keep the robustness unchanged;

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

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

[0109] In the loop variation process, a loop condition is included. For example, Figure 3 As shown in the figure, it is a schematic diagram of the continuous variation process of the embodiment of the present application. The loop variation until all quantum gate waveforms are obtained is limited by judging whether the latest quantum gate waveform A new corresponding rotation angle θ(A new ) exceeds the rotation range θ maxIf the number exceeds, the loop ends and outputs all the quantum gate waveforms and corresponding rotation angles; if the number does not exceed, the next iteration of the variation is continued until all the quantum gate waveforms are output.

[0110] As shown in Figure 4 , it is a schematic diagram of the original waveform and all the quantum gate waveforms output after continuous variation in an embodiment, as shown in Figure 5 , and Figure 4 , the 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 the quantum gate waveforms in the figure are closed, indicating that the robustness of any quantum gate waveform remains unchanged compared to the original waveform in the continuous variation process.

[0111] Specifically, Figure 4 each slice of the original waveform is a microwave waveform, Figure 5 each slice of the original waveform is an error evolution graph corresponding to the waveform. The following introduces the correspondence between the error evolution graph and the waveform: assuming that the system is affected by quasi-static noise, the noise Hamiltonian is H n . In order to observe how the noise evolves under our control of the system, we transform the noise operator H n into the interaction representation of U0, that is, where U0is the evolution operator generated by the system Hamiltonian and the control Hamiltonian H sys +H c . When the quantum gate ends, if H nI (T) = 0, it means that the first-order effect of the noise is just eliminated. Since H nI (t) is a time-dependent matrix, it is not convenient to visualize, so we project this matrix onto the Pauli matrix to obtain a three-dimensional curve. Conversely, the control waveform can be completely recovered by calculating the curvature and torsion of the curve. After calculation, it is found that when the noise has only one term and the control has only one term, the curve is actually a two-dimensional curve, and the curvature of the curve is sufficient to recover the control waveform. The aforementioned condition of H nI (T) = 0 corresponds to the curve returning to the origin at t = T, that is, the curve is a closed curve, and the corresponding control waveform has first-order robustness. More complex and higher-order robustness can also be discussed, which is not described here.

[0112] The second aspect of the present application provides a system for maintaining the robustness of the modulation quantum control waveform unchanged, as shown in Figure 6 , it is a schematic diagram of a system 10 for maintaining the robustness of the modulation quantum control waveform unchanged according to the present application, comprising a preprocessing module 20, a continuous variation module 30 and an output module 40;

[0113] The preprocessing module 20 is configured to set a rotation range and a rotation angle variation value, and to screen original waveforms according to a control task and a robustness requirement;

[0114] The continuous variation module 30 is configured to implement a continuous variation process, including obtaining a reference quantum gate waveform from the original waveforms while maintaining the robustness unchanged, obtaining a target quantum gate waveform from the reference quantum gate waveform, taking the 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 a set limit condition is met, obtaining all the quantum gate waveforms in the rotation range, and obtaining all the quantum gate waveforms in the rotation range;

[0115] The output module 40 is configured to record and output all the quantum gate waveforms and 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 variation function calculation unit 31 is configured to generate a pre-variation function based on a current initial waveform, to calculate a robustness function gradient of the current initial waveform, and to implement Schmidt orthogonalization to obtain a perpendicular component and correct the perpendicular component to obtain a variation function.

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

[0119] The judgment unit 33 is configured to judge whether the corresponding rotation angle of the new quantum gate waveform exceeds a preset rotation range. If yes, the loop is ended, and the results are sent to the output module 40 to output all the quantum gate waveforms and respective corresponding rotation angles. If not, the current quantum gate waveform is set as an initial waveform, or the current target reference quantum gate waveform is taken as a reference quantum gate waveform for the next variation and is input to the variation function calculation unit 31 for continuous variation.

[0120] A third aspect of the present application provides a non-transitory computer readable storage medium, which stores a program of a method for maintaining robustness unchanged quantum control waveform modulation, and the program is executed by a processor to implement the following steps:

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

[0122] S2, converting the first pre-variation function into a set of orthogonal components, and retaining a robustness function gradient The first vertical component is used to maintain robustness.

[0123] S3. Correct the first vertical component to obtain the first variational function, calculate the first quantum gate waveform, and record the corresponding first rotation angle of 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] This application addresses a series of problems in existing solutions, such as the lack of robustness consideration or inability to maintain robustness during the transformation of quantum gate waveforms, or the inability to transfer robustness during the transformation process, resulting in low fidelity of quantum gate waveform optimization algorithms and the inability to achieve a set of waveforms with all rotation angles. This application achieves a set of quantum gate waveforms with the same robustness by performing continuous variation (or multiple small perturbations) on the original quantum waveform within the rotation range while maintaining robustness.

[0126] The technical advantage of this application lies in the fact that the robustness-maintaining quantum bit waveform control method can keep the robustness of any quantum gate waveform unchanged compared to the original waveform during continuous variational processes, improve other evaluation indicators such as fidelity, high-level leakage, total energy, smoothness, and bandwidth, and achieve robust waveforms of quantum gates with continuous parameters, thus obtaining a set of quantum gate waveforms for all rotation angles.

[0127] Table 1 shows the pseudocode of an algorithm for a method of maintaining robustness of a modulated quantum control waveform according to an embodiment of this application, where the preset rotation angle is θ∈[θ]. min ,θ max First, using existing technology, the original waveform is generated based on the control task and robustness requirements. Specifically, the waveform with a rotation angle of θ is found. min The quantum gate waveform A is used as the initial waveform A0 in this continuous variational process. A judgment condition is set to execute the continuous variation. Each variation or iteration generates a quantum gate waveform and its 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 The loop stops, and all robust quantum gate waveforms preceding the current waveform and their corresponding rotation angles are output. The pseudocode of the algorithm in the continuous variational process of this application is shown in Table 1.

[0128] Table 1 Algorithm Pseudocode

[0129]

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

[0131] The preset rotation angle is First, find the quantum gate waveform A with a rotation angle of as the initial waveform A0 in this continuous variation process. In order to keep the robustness unchanged in the continuous variation process, the rotation angle of each variation compared to the last variation should be small enough. First, based on A0, the first variation output A1 is obtained, and the specific steps are as follows:

[0132] (1) Generate pre-variation

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

[0134] (3) Obtain the first vertical component by Schmidt orthogonalization

[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 θ(A1)<θ max , continue the second variation;

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

[0139] (8) Determine continue the third variation;

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

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

[0142] like Figure 4 The image shows the original waveform and the complete quantum gate waveforms output after continuous variation in one embodiment. Figure 5 As shown, with Figure 4 The diagram shows the waveform effects of the original waveform and all quantum gate waveforms output after continuous variation. It represents the final output waveform A0 in this embodiment, along with the 6286 quantum gate waveforms A1 to A2 generated during the continuous variation process. 6286 And the corresponding rotation angles θ(A1)~θ(A 6286 The quantum gate waveforms share a common intersection point, indicating shared robustness. This enables continuous variational analysis while maintaining robustness, and allows for the generation of multiple quantum gate waveforms simultaneously, offering high efficiency and convenience. Preferably, the number of continuous variational iterations and the rotation angle can be set according to actual needs.

[0143] Table 2. Number of iterations and corresponding rotation angles for continuous variation of quantum waveforms.

[0144]

[0145] In summary, this application provides a method and system for maintaining robustness-invariant modulated quantum control waveforms. The method includes the following steps: generating a first prevariant function based on the original waveform and preset rotation parameters; converting the first prevariant function into a set of orthogonal components, retaining a first vertical component perpendicular to the gradient of the robustness function to maintain robustness; correcting the first vertical component to obtain a first variational function to calculate a first quantum gate waveform, and recording the corresponding first rotation angle of the first quantum gate waveform; performing iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are output. The robustness-invariant continuous variational method of this application solves the problems of existing technologies that do not consider robustness, cannot maintain robustness, or cannot transfer robustness during transformation, resulting in low fidelity of quantum gate waveform optimization algorithms and the inability to achieve a set of waveforms with all rotation angles, thus limiting applications. The robustness-preserving quantum waveform control method of this application can maintain robustness during continuous transformation, improve other evaluation indicators such as fidelity, high-level leakage, total energy, smoothness and bandwidth, and realize robust waveforms of quantum gates with continuous parameters, which can obtain a set of quantum gate waveforms for all rotation angles.

[0146] The above merely provides the preferred but not limiting embodiments of the present application, and 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 merely provides the examples and descriptions of the present application structure, and any modification or supplement or adoption of similar ways to replace the described specific embodiments by the person skilled in the art shall belong to the protection scope of the present application, without departing from the structure of the present application or beyond the defined range of the present application.

Claims

1. A method of maintaining robustness invariant modulation quantum control waveforms, characterized by, 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, retaining a first vertical component perpendicular to a robustness function gradient to keep the robustness unchanged; correcting the first vertical component to obtain a first variational function, to calculate a first quantum gate waveform, and recording a corresponding first rotation angle of the first quantum gate waveform; iteratively performing continuous variation based on the first quantum gate waveform until all quantum gate waveforms are outputted; the iteratively performing continuous variation based on the first quantum gate waveform until all quantum gate waveforms are outputted comprises: 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; taking the target quantum gate waveform as a new reference quantum gate waveform, and returning to perform the variation on the reference quantum gate waveform to obtain the target quantum gate waveform, and performing cyclic variation until a set limit condition is met, and outputting all quantum gate waveforms; the 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 comprises: performing variation on the reference quantum gate waveform according to a rotation angle to generate a target pre-variational function; converting the target pre-variational function into an orthogonal component group, retaining a target vertical component perpendicular to the robustness function gradient to keep the robustness unchanged; correcting the target vertical component according to a rotation angle variation value to obtain a target variational function, to calculate the target quantum gate waveform, and recording a corresponding rotation angle of the target quantum gate waveform.

2. The method of claim 1, wherein the modulation quantum control waveform is maintained with constant robustness. the converting the first pre-variational function into an orthogonal component group, retaining a first vertical component perpendicular to a robustness function gradient to keep the robustness unchanged comprises: calculating the robustness function gradient of the original waveform; converting the first pre-variational function into an orthogonal component group; finding a component perpendicular to the robustness function gradient from the orthogonal component group, which is the first vertical component.

3. The method of claim 1, wherein the correcting the first vertical component to obtain a first variational function, to calculate a first quantum gate waveform, and recording a corresponding first rotation angle of the first quantum gate waveform comprises: correcting a length of the first vertical component to obtain the first variational function; adding the first variational function to the original waveform to obtain the first quantum gate waveform; outputting the first quantum gate waveform, and recording a corresponding first rotation angle; wherein the first quantum gate waveform is consistent with the robustness of the original waveform.

4. The method of claim 1, wherein, the cyclic variation until a set limit condition is met comprises judging whether a rotation angle corresponding to a latest quantum gate waveform exceeds a rotation range, if yes, ending the cycle and outputting all quantum gate waveforms; if no, continuing the next variation.

5. The method of claim 1, wherein before the generating a first pre-variational function according to an original waveform, the method comprises: generating the original waveform according to a control task and a robustness requirement, and determining a rotation range and a rotation angle variation value.

6. A system for maintaining robustness of a modulated quantum control waveform, comprising: ​ The pre-processing module is configured to set a rotation range and a rotation angle variation value, and to screen an original waveform according to a control task and a robustness requirement; The continuous variation module is configured to implement a continuous variation process, including obtaining a reference quantum gate waveform according to the original waveform while maintaining the robustness unchanged, obtaining a target quantum gate waveform according to the reference quantum gate waveform, taking the target quantum gate waveform as the reference quantum gate waveform for next time variation, returning to perform the step of varying the reference quantum gate waveform to obtain the target quantum gate waveform until a set limit condition is met, obtaining all the quantum gate waveforms in the rotation range, and obtaining all the quantum gate waveforms in the rotation range; The output module is configured to record and output all the quantum gate waveforms and corresponding rotation angles. The continuous variation module includes a variation function calculation unit, a variation unit, and a judgment unit. The variation function calculation unit is configured to generate a pre-variation function based on a current initial waveform, to calculate a robustness function gradient of a current quantum gate waveform, and to implement Schmidt orthogonalization to obtain a perpendicular component and correct the perpendicular component to obtain a variation function. The variation unit is configured to add the variation function to the current initial waveform to obtain a new quantum gate waveform and a corresponding rotation angle. The judgment unit is configured to determine whether the corresponding rotation angle of the new quantum gate waveform exceeds a preset rotation range, and if so, to end the loop and send the result to the output module to output all the quantum gate waveforms and corresponding rotation angles; if not, to set the current quantum gate waveform as the initial waveform and input it to the variation function calculation unit to continue the variation.

7. A non-transitory computer-readable storage medium, comprising: The non-transitory computer-readable storage medium stores a program of a quantum waveform control method for maintaining robustness unchanged, and the program is executed by a processor to implement the following steps: A first pre-variation function is generated according to an original waveform; The first pre-variation function is converted into a set of orthogonal components, a first perpendicular component perpendicular to a robustness function gradient is retained to maintain the robustness unchanged; The first perpendicular component is corrected to obtain a first variation function, to calculate a first quantum gate waveform, and to record a corresponding first rotation angle of the first quantum gate waveform; Iterative continuous variation is performed based on the first quantum gate waveform until all quantum gate waveforms are outputted; The iterative continuous variation based on the first quantum gate waveform until all quantum gate waveforms are outputted includes: The first quantum gate waveform is taken as a reference quantum gate waveform, the reference quantum gate waveform is varied to obtain a target quantum gate waveform; The target quantum gate waveform is taken 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 performed again, and the variation is repeated until a set limit condition is met, and all the quantum gate waveforms are outputted; The first quantum gate waveform is taken as a reference quantum gate waveform, the reference quantum gate waveform is varied to obtain a target quantum gate waveform includes: According to the rotation angle, the reference quantum gate waveform is varied to generate a target pre-variational function; The target pre-variational function is converted into a set of orthogonal components, and a target perpendicular component perpendicular to the gradient of the robustness function is reserved to keep the robustness unchanged; According to the rotation angle variational value, the target perpendicular component is corrected to obtain a target variational function, so as to calculate the target quantum gate waveform, and the corresponding rotation angle of the target quantum gate waveform is recorded.

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