A composite pulse calibration method and system based on phase reconstruction

Abstract

This invention discloses a composite pulse calibration method and system based on phase reconstruction, relating to the field of quantum computing technology. The method includes: determining the target parameters and experimental control parameters of the composite pulse according to the experimental task; reconstructing the phase relationship between the sub-pulses of the composite pulse based on the target parameters and a phase reconstruction strategy; applying the reconstructed composite pulse as a calibration composite pulse to the target quantum system; fitting the experimental control parameter values ​​to the measured final-state response of the target quantum system to obtain the optimal estimate of the experimental control parameters; and in the operation mode, combining the optimal estimate of the experimental control parameters with the original phase configuration before reconstruction to regenerate a standard composite pulse for quantum computation. This invention obtains the optimal calibration parameters by reconstructing the phase sequence of the composite pulse and, combined with the original phase configuration, enables the composite pulse to return to a highly robust state for quantum computation; thus achieving decoupling optimization of calibration sensitivity and operational robustness.

Description

Technical Field

[0001] This invention relates to the field of quantum computing technology, and more specifically to a composite pulse calibration method and system based on phase reconstruction. Background Technology

[0002] Quantum computing utilizes quantum mechanical properties such as quantum superposition and quantum entanglement for information processing, demonstrating potential to surpass classical computing in fields such as cryptography, materials simulation, and combinatorial optimization. In the physical implementation of quantum computing, quantum gate operations are typically achieved by driving qubits with precisely controlled classical pulse signals (such as microwave pulses or laser pulses). However, in real-world experimental environments, systematic errors inevitably exist, such as pulse amplitude errors, pulse duration deviations, frequency detuning, and environmental noise. These errors lead to a decrease in the fidelity of quantum gate operations, severely impacting the reliability of quantum computing.

[0003] Composite pulse technology is one of the important means to address the above-mentioned problems. A composite pulse consists of multiple sub-pulse sequences with specific timing relationships and phase configurations. By carefully designing the phase relationships between the sub-pulses, the errors introduced by each sub-pulse cancel each other out at the sequence level, thereby achieving high-order compensation for specific types of systematic errors. Typical composite pulse schemes include the BB1, CORPSE, SCROFULOUS, and Knill series, which exhibit excellent performance in compensating for pulse area errors, detuning errors, or a combination of both. The robustness of composite pulses (i.e., their ability to resist interference from parameter deviations) directly depends on the precise configuration of the phase relationships between the sub-pulses.

[0004] To ensure that composite pulses perform the expected quantum manipulations in practical quantum systems, their experimental control parameters (such as pulse intensity, pulse area, pulse duration, and pulse frequency) need to be calibrated. Existing composite pulse calibration methods typically employ the following strategy: apply a composite pulse under a standard phase configuration, extract parameter deviation information by measuring the final state response of the quantum system, and then correct the pulse parameters.

[0005] However, the existing calibration methods described above suffer from a fundamental contradiction: the high robustness of composite pulses is precisely the obstacle to their calibration accuracy. The initial design intent of composite pulses is to make the pulse sequence "insensitive" to parameter deviations, meaning it can maintain the stability of the output result even with a certain range of parameter deviations. While this low sensitivity to deviations is beneficial for error suppression in the computation stage, it results in an extremely weak response of the measurement signal to parameter deviations during the calibration stage, severely limiting the accuracy of parameter deviation extraction. Specifically:

[0006] Insufficient calibration sensitivity: Due to the robust structure of the composite pulse suppressing the modulation effect of parameter deviation on the final state of the quantum system, the gradient of the measurement signal with parameter change is extremely small, resulting in a very low signal-to-noise ratio for fitting the parameter deviation from the measurement data, making it difficult to improve calibration accuracy; Inefficient calibration: To obtain sufficient parameter deviation information, a large number of repeated measurements or extremely fine parameter scanning strategies are often required, which significantly increases the time and experimental resources required for calibration. The contradiction between calibration and computation: If a simple pulse (such as a single pulse) that is sensitive to parameter deviation is selected in order to improve calibration sensitivity, the error compensation advantage of composite pulses cannot be utilized; if composite pulses are used for calibration, their inherent low sensitivity limits the calibration accuracy to meet the requirements of high-fidelity quantum computation; if a simple pulse with high sensitivity is used for calibration and a composite pulse with low sensitivity is used for computation, systematic calibration deviations may be introduced by the different implementation methods of simple and composite pulses. For example, non-ideal factors such as microwave signal sources, microwave amplifiers, and thermal effects of acousto-optic and electro-optic devices can cause systematic deviations in the optimal parameters of simple and composite pulses.

[0007] Therefore, how to overcome the limitation of robustness on calibration sensitivity in the process of composite pulse calibration, and effectively balance the high sensitivity in the calibration stage with the high robustness in the calculation stage, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0008] In view of the above problems, this invention is proposed to provide a composite pulse calibration method and system based on phase reconstruction to overcome or at least partially solve the above problems. By reconstructing the phase relationship between sub-pulses within the composite pulse, the sensitivity of the calibration signal to the deviation of the target parameter is enhanced, and after calibration, the system switches to the operation mode, so that the composite pulse returns to a highly robust state for quantum operation; thus, the decoupling optimization of calibration sensitivity and operation robustness is achieved.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: In a first aspect, embodiments of the present invention provide a composite pulse calibration method based on phase reconstruction, comprising the following steps: S1. Based on the requirements of the current quantum circuit or experimental task, determine the target parameters and experimental control parameters to be achieved by the composite pulse; wherein, the experimental control parameters are used to achieve the target parameters; S2. Keeping the number of sub-pulses and the waveform shape of each sub-pulse of the composite pulse unchanged, the phase relationship between the sub-pulses of the composite pulse is reconstructed based on the target parameters and the phase reconstruction strategy. S3. The phase-reconstructed composite pulse is used as a calibration composite pulse and applied to the target quantum system in its initial quantum state; S4. Measure the final state response of the target quantum system based on different experimental control parameter values; fit the experimental control parameter values ​​based on the final state response, and obtain the best estimated values ​​of the experimental control parameters; S5. In the operation mode, the best estimated value of the experimental control parameters is combined with the original phase configuration before reconstruction to regenerate a standard composite pulse for quantum operation.

[0010] Furthermore, in step S1, the target parameter is the quantum manipulation parameter to be achieved by the composite pulse, including the equivalent rotation area of ​​the composite pulse; the experimental control parameter is the composite pulse parameter whose value needs to be determined through fitting calibration, including pulse intensity, pulse area, pulse duration, pulse frequency and detuning.

[0011] Furthermore, in step S2, the phase reconstruction strategy specifically includes: Phase mismatch calculation method: Substitute parameter values ​​different from the target parameters into the calculation position of the target parameters in the phase calculation formula of the composite pulse to calculate the phase relationship of each sub-pulse; Phase assimilation method: Set the phase of all sub-pulses of the composite pulse to the same preset value, so that the error caused by parameter deviation of each sub-pulse is transformed from coherent cancellation to coherent accumulation, and the phase relationship between each pulse is obtained. Numerical search method: Taking the sensitivity of the specified reconstruction pulse to the deviation of the target parameter as the objective and satisfying the unbiased constraint as the condition, the optimal reconstruction phase is searched through numerical optimization.

[0012] Furthermore, the unbiased constraint in the numerical search method is: when the current experimental control parameter is exactly equal to the theoretical optimal value, the pulse output corresponding to the reconstructed phase sequence is consistent with the pulse output corresponding to the original phase sequence.

[0013] Furthermore, among the phase reconstruction strategies, the phase assimilation method has the highest sensitivity, the phase mismatch calculation method has a medium sensitivity, and the sensitivity of the numerical search method is determined based on the sensitivity target.

[0014] Furthermore, the phase reconstruction strategy is selected as follows: The phase reconstruction strategy is dynamically switched based on the estimation of the deviation of the current experimental control parameters from the theoretical optimal value; the theoretical optimal value refers to the target parameter that the original combined pulse sequence should theoretically achieve when the experimental control parameters are configured to be applied to the original combined pulse sequence.

[0015] When the deviation exceeds the preset range, the phase mismatch calculation method or the numerical search method with low sensitivity as the target is selected; when the deviation is within the preset range, the target sensitivity of the numerical search method is gradually increased or the phase assimilation method is used to obtain the highest sensitivity.

[0016] Furthermore, step S4 specifically includes: Different experimental control parameter values ​​are input into the calibration composite pulse and applied to the quantum system. For each value, the expected value of the observable quantity of the final state of the target quantum system is measured. The observable quantity includes the final state population. Construct a theoretical expression for the observable quantity, wherein the theoretical expression is a functional relationship between the expected value of the observable quantity and the experimental control parameters; Based on the measured expected value and the theoretical expression, the best estimated value of the experimental control parameter is obtained by using the least squares fitting or maximum likelihood estimation algorithm.

[0017] In a second aspect, embodiments of the present invention provide a composite pulse calibration system based on phase reconstruction, employing the method described in any one of the first aspects, comprising: Target parameter input module: used to determine the target parameters and experimental control parameters to be achieved by the composite pulse according to the requirements of the current quantum circuit or experimental task; wherein, the experimental control parameters are used to achieve the target parameters; Phase reconstruction module: used to maintain the number of sub-pulses and the waveform shape of each sub-pulse of the composite pulse unchanged, and to reconstruct the phase relationship between the sub-pulses of the composite pulse based on the target parameters and the phase reconstruction strategy; Reconstructed composite pulse generation module: used to apply the phase-reconstructed composite pulse as a calibration composite pulse to the target quantum system in its initial quantum state; Quantum state measurement module: used to measure the final state response of the target quantum system based on different experimental control parameter values; to fit the experimental control parameter values ​​based on the final state response and obtain the best estimate of the experimental control parameters; Standard composite pulse generation module: used in operation mode to regenerate standard composite pulses for quantum operations by combining the best estimated values ​​of the experimental control parameters with the original phase configuration before reconstruction.

[0018] Thirdly, embodiments of the present invention provide a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the composite pulse calibration method based on phase reconstruction as described in any of the first aspects.

[0019] Fourthly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the composite pulse calibration method based on phase reconstruction as described in any of the first aspects.

[0020] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a composite pulse calibration method and system based on phase reconstruction, which has the following beneficial effects: First, by reconstructing the phase relationship between sub-pulses within a composite pulse in calibration mode, this invention breaks the original robust structure of the composite pulse, transforming the pulse sequence, which was originally insensitive to parameter deviations, into a calibration sequence that is highly sensitive to deviations. This significantly enhances the response gradient of the calibration signal to the target parameter deviation, thereby effectively solving the problem of insufficient parameter deviation extraction accuracy caused by the robustness of the composite pulse suppressing calibration sensitivity in the prior art.

[0021] Second, this invention keeps the number of sub-pulses and the waveform shape of each sub-pulse unchanged during the calibration process, and only reconstructs the phase relationship between the internal sub-pulses. It does not need to change the overall architecture of the pulse sequence, thus ensuring the compatibility of the calibration scheme with the existing composite pulse system and avoiding the systematic parameter deviations introduced by the non-ideal response of quantum manipulation devices when different numbers of pulses are used in calibration and actual operation.

[0022] Third, after calibration, this invention regenerates the standard composite pulse signal by combining the optimal calibration parameters with the original phase configuration before reconstruction, and switches to the operation mode, so that the composite pulse restores its inherent error compensation capability and high robustness state during design, ensuring high fidelity and noise resistance in actual quantum operations, and achieving effective decoupling and unification between the pursuit of maximum sensitivity in the calibration stage and the pursuit of maximum robustness in the operation stage. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0024] Figure 1 This is a flowchart of the composite pulse calibration method based on phase reconstruction provided in an embodiment of the present invention; Figure 2 This is a comparison of response curves of the quantum system's final state population as a function of the relative deviation of the pulse area under different phase reconstructions for the BB1 ​​composite pulse, provided in an embodiment of the present invention. Figure 3 This is a comparison chart showing the relationship between the final state population and the pulse area error ratio after reconstruction using the phase assimilation method and the numerical search method for a SCROFULOUS composite pulse, as provided in this embodiment of the invention. Figure 4This is a comparison chart showing the relationship between the final state population and the pulse duration error ratio and pulse frequency error ratio for the Knill composite pulse provided in this embodiment of the invention. Figure 5 This is a block diagram of a composite pulse calibration system based on phase reconstruction provided in an embodiment of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] Example 1 This invention discloses a composite pulse calibration method based on phase reconstruction, referring to... Figure 1 As shown, it includes the following steps: S1. Based on the requirements of the current quantum circuit or experimental task, determine the target parameters and experimental control parameters to be achieved by the composite pulse; among which, the experimental control parameters are used to achieve the target parameters; S2. Keeping the number of sub-pulses of the composite pulse and the waveform shape of each sub-pulse unchanged, reconstruct the phase relationship between the sub-pulses of the composite pulse based on the target parameters and the phase reconstruction strategy; S3. The phase-reconstructed composite pulse is used as a calibration composite pulse and applied to the target quantum system in its initial quantum state; S4. Measure the final state response of the target quantum system based on different experimental control parameter values; fit the experimental control parameter values ​​based on the final state response, and obtain the best estimated values ​​of the experimental control parameters; S5. In the operation mode, the best estimated value of the experimental control parameters is combined with the original phase configuration before reconstruction to regenerate the standard composite pulse for quantum operation.

[0027] This embodiment uses the pulse area calibration of BB1 recombination pulses in an ion trap quantum computing platform as a specific example for illustration. Those skilled in the art should understand that this invention is not limited to ion trap quantum computing platforms, but is also applicable to various quantum computing platforms such as superconducting qubits, neutral atoms, and semiconductor quantum dots.

[0028] The implementation steps of this embodiment are described in detail below: Step S1: Based on the requirements of the current quantum circuit or experimental task, determine the target parameters to be achieved by the composite pulse and the experimental control parameters that need to be calibrated to achieve the target parameters. The target parameters are the quantum manipulation parameters to be achieved by the composite pulse, including the equivalent rotation area of ​​the composite pulse; the experimental control parameters are the composite pulse parameters whose values ​​need to be determined through fitting calibration, including pulse intensity, pulse area, pulse duration, pulse frequency, and detuning.

[0029] In this embodiment, the target quantum system is a trapped ion qubit, whose quantum state is determined by |0|. state and |1 The state spans a two-dimensional Hilbert space description. Current quantum circuits require performing a single-qubit gate with a rotation area of ​​θ around the X-axis of a Bloch sphere on this qubit. To suppress the area error of the microwave pulse, a BB1 composite pulse is used instead of a simple single pulse to implement this rotation operation.

[0030] The BB1 ​​composite pulse consists of four sub-pulses. Ideally, the pulse areas of each sub-pulse are π, 2π, π, and θ, respectively, where θ is the target parameter to be achieved, which in this embodiment is the equivalent rotational area of ​​the composite pulse. To achieve these four sub-pulses, experimentally, this can be achieved by adjusting the pulse intensity (characterized by the Rabi frequency Ω) or the pulse duration T. In this embodiment, with a fixed pulse intensity, the pulse duration T is used as the experimental control parameter. Therefore, this calibration task can be described as finding a suitable pulse duration T for the current Rabi frequency Ω of the experimental system such that the fourth pulse area of ​​the BB1 ​​composite pulse is ΩT = θ, and the durations of the first three pulses are scaled proportionally according to the relationship between their pulse areas and θ. Within a single calibration task, the Rabi frequency of a typical experimental system can be considered a constant value; however, due to factors such as microwave source power fluctuations, transmission link losses, and quantum bit coupling efficiency drift, the specific value of the Rabi frequency is unknown, therefore the pulse duration needs to be determined by calibration. In this embodiment, let θ = π. This pulse will initialize |0. The quantum bit of the state is flipped to |1 state.

[0031] In summary, the target parameter selected in S1 of this embodiment is the equivalent area of ​​the composite pulse θ=π, and the selected experimental control parameter is the pulse duration T. It is worth noting that the method of this embodiment is also applicable to calibration using the Rabi frequency Ω as the experimental control parameter, provided that the pulse duration T is fixed.

[0032] Step S2: In calibration mode, keep the number of sub-pulses of the composite pulse and the waveform shape of each sub-pulse unchanged, and reconstruct the phase relationship between the sub-pulses of the composite pulse based on the target parameters and the phase reconstruction strategy.

[0033] In this embodiment, after entering the calibration mode, the number of the four sub-pulses of the BB1 ​​composite pulse remains unchanged, and the waveform shape and relative pulse area ratio (π:2π:π:θ) of each sub-pulse are consistent with the standard BB1 composite pulse. Only the phase relationship between the four sub-pulses is reconstructed.

[0034] Regarding phase reconstruction strategies, these include phase mismatch calculation, phase assimilation, and numerical search. Phase assimilation has the highest sensitivity, phase mismatch calculation has moderate sensitivity, and the sensitivity of numerical search is determined based on the sensitivity target.

[0035] In practical applications, the choice of reconstruction strategy is based on the user's or automated calibration system's estimate of the deviation of the parameter to be calibrated from the theoretical optimal value. This estimate is based on prior knowledge of the quantum computer's historical operation.

[0036] If the quantum computer performs parameter calibration periodically, and the parameter deviation between two calibrations is on average within 10%, then the phase assimilation method with the highest sensitivity can be directly selected, or a reconstruction sequence with similar sensitivity can be searched through numerical optimization, so as to achieve the preset target by calibrating the uncertainty of the target parameter based on the minimum amount of data.

[0037] If a quantum computer has been uncalibrated for a long time or has undergone significant hardware upgrades, the lack of prior knowledge regarding experimental control parameters may lead to calibration failure if the estimated deviation of the parameter to be calibrated from its theoretical optimum is close to or exceeds 20%. This is because the final-state response of the phase assimilation method oscillates periodically with the experimental parameter during a large-scale scan. This can cause significant bias in the fitting program, such as misclassifying parameters with a deviation of up to 40% (ΩT / π = 1.4 or 0.6) as optimal. Therefore, in such cases, the phase mismatch calculation method should be used first, or numerical optimization should be used to find a phase sequence with similar sensitivity and an observable deviation of less than 50% around a 20% parameter deviation rate for preliminary coarse calibration. After preliminary calibration, numerical optimization should be used progressively to construct a reconstructed sequence with increasing sensitivity until the highest-sensitivity phase assimilation method is finally used to complete the calibration.

[0038] This embodiment selects the phase mismatch calculation method as the phase reconstruction strategy. Specifically, in the original phase configuration of the BB1 ​​composite pulse, there is a definite functional relationship between the first sub-pulse phase φ1, the second sub-pulse phase φ2, the third sub-pulse phase φ3, the fourth sub-pulse phase φ4 and the target parameter θ: φ1=arccos(-θ / (4π)), φ2=3φ1, φ3=φ1, φ4=0. In calibration mode, when the target parameter θ determined in step S1 is substituted into the phase calculation formula, its sign is inverted, that is, it is... θ is used to perform calculations, resulting in a set of reconstructed phase sequences: φ1'=arccos(θ / (4π)), φ2'=3φ1', φ3'=φ1', φ4'=0.

[0039] Taking θ=π as an example, the phases of each sub-pulse under the original BB1 phase configuration are φ1=104.48°, φ2=313.44°, φ3=104.48°, and φ4=0°. After using the phase mismatch calculation method, the reconstructed phase sequence is: The reconstructed phase of the first sub-pulse: φ1' = 75.52°. The reconstructed second sub-pulse phase: φ2'=226.57° The reconstructed third sub-pulse phase: φ3'=75.52°, The reconstructed fourth sub-pulse phase: φ4'=0°.

[0040] Calculations verify that the reconstructed phase sequence satisfies the unbiased constraint condition: when the actual pulse area is exactly equal to the ideal value, i.e., for the current experimental system Ω, the duration of the fourth pulse is selected as π / Ω, and the durations of the other three pulses are scaled proportionally to the duration of the fourth pulse according to the BB1 ​​calculation formula, the pulse output corresponding to the reconstructed phase sequence is completely consistent with the pulse output corresponding to the original phase sequence, and both can achieve the rotation of the qubit with an equivalent area of ​​π without introducing additional deviations.

[0041] Although the reconstructed BB1 composite pulse sequence maintains the same number of sub-pulses and waveform shape as the original sequence, its internal phase relationship has been altered, and the original higher-order error compensation structure has been broken, significantly increasing the sequence's sensitivity to pulse area deviation. (Refer to...) Figure 2 As shown, this illustrates the application of a BB1 composite pulse with an equivalent area of ​​π to |0|. The original BB1 composite pulse sequence, the sequence reconstructed by the phase mismatch method, and the sequence reconstructed by the phase assimilation method are applied to |0|. After the state, we get |1 A comparison of the relationship between state population and pulse duration error ratio. When the reconstructed BB1 sequence obtained by the phase mismatch method is applied to the initial state |0... Afterwards, |1 was measured. The population P1 of the state, such as Figure 2 The orange dotted lines in the image are significantly different from the original BB1 combined pulse applied to |0. The pulse duration T is sensitive, such as Figure 2 The blue solid line in the diagram illustrates this. Specifically, the deviation of the final-state population P1 obtained by the phase mismatch method from its ideal value of 1.0 is 5 orders of magnitude larger than the original BB1 sequence when the pulse duration deviates from the ideal value by 5%, and 4 orders of magnitude larger than the original BB1 sequence when the pulse duration deviates from the ideal value by 10%. Phase reconstruction significantly improves the sensitivity of the final-state population to pulse duration errors.

[0042] It should be noted that the phase reconstruction strategy is not limited to the phase mismatch calculation method. In other embodiments, the phase assimilation method or the numerical search method can also be used.

[0043] The core idea of ​​the phase assimilation method is to unify the phase of all sub-pulses of the composite pulse to the same preset value, so that the error caused by parameter deviation of each sub-pulse changes from the coherent cancellation state in the standard composite pulse to the coherent accumulation state, thereby maximizing the response of the calibration signal to parameter deviation.

[0044] The robustness of the original composite pulse stems from the phase configuration between the sub-pulses, which allows the errors introduced by each sub-pulse to cancel each other out at the sequence level. The phase assimilation method eliminates the phase differences between the sub-pulses by unifying the phase of all sub-pulses to the same value (e.g., setting them all to zero). This causes the responses of the sub-pulses to parameter deviations to no longer cancel each other out, but to be superimposed in the same direction, thereby maximizing the sensitivity of the calibration signal to deviations.

[0045] In this embodiment, the BB1 ​​composite pulse contains four sub-pulses. When using the phase assimilation method, the phases of all four sub-pulses are set to a preset value φ0=0°, that is, the reconstructed phase sequence is: φ1'=0°, φ2'=0°, φ3'=0°, φ4'=0°.

[0046] At this point, the phases of the four sub-pulses are completely consistent, and the response directions of each sub-pulse to the pulse area deviation are the same. The error effect changes from the original coherent cancellation to coherent accumulation.

[0047] Calculations verify that the reconstructed phase sequence satisfies the unbiased constraint condition: when the actual pulse area is exactly equal to the ideal value, i.e., for the Rabi frequency Ω of the current experimental system, the duration of the fourth pulse is selected as π / Ω, and the durations of the other three pulses are scaled proportionally according to the BB1 ​​calculation formula, the pulse output corresponding to the reconstructed phase sequence is completely consistent with the pulse output corresponding to the original phase sequence, and both can achieve the rotation of the qubit with an equivalent area of ​​π without introducing additional deviations.

[0048] Reference Figure 2 As shown, Figure 2 The green dotted lines in the diagram illustrate the effectiveness of the phase assimilation method. Specifically, for a 5% pulse area error, the sensitivity of the phase assimilation method is 1 million times higher than that of the original BB1 composite pulse, and about one order of magnitude higher than that of the phase mismatch method; for a 10% pulse area error, the sensitivity of the phase assimilation method is 50,000 times higher than that of the original BB1 composite pulse, and 5 times higher than that of the phase mismatch method.

[0049] The phase preset value in this embodiment is not limited to 0°, and other fixed values ​​(such as 90°, 180°, etc.) can also be selected. Different preset values ​​will not affect the sensitivity of the reconstructed sequence. Therefore, the phase preset value can be arbitrarily selected, or it can be used as an optimizable degree of freedom in the overall quantum circuit design to meet the phase requirements of other operations in the circuit.

[0050] Phase assimilation is suitable for scenarios with extremely high calibration sensitivity requirements, and is therefore more suitable for fine calibration stages with small deviations.

[0051] Regarding the numerical search method, this embodiment takes the SCROFULOUS composite pulse as an example to introduce in detail the phase reconstruction method of the numerical search method.

[0052] The SCROFULOUS composite pulse coherently cancels pulse area errors through three sub-pulses. For a target rotation with an equivalent rotation area of ​​θ, in this embodiment, the pulse areas of the three sub-pulses are (t, π, t), and the phases are (φ1, φ2, φ1). The areas t of the first and third pulses are determined by solving the root of the equation sin(t) / t=2cos(θ / 2) / π in the interval (0, π). The phases of the first and third pulses are determined by the formula φ1=acrcos(-πcos(t) / (2t sin(θ / 2))), and the phase of the second pulse is determined by the formula φ2=φ1-arccos(-π / (2t)).

[0053] In this embodiment, let θ = π be selected; this pulse can initialize at |0 The quantum bit of the state is flipped to |1 The required three sub-pulse areas are π, and their phases are 60°, 300°, and 60°, respectively, according to the formula above.

[0054] Reference Figure 3 As shown, for a SCROFULOUS composite pulse with a target equivalent area of ​​π, the original SCROFULOUS composite pulse sequence, the sequence reconstructed by phase assimilation, and the sequence reconstructed by numerical search for a specific sensitivity are applied to |0... After the state, we get |1 A comparison chart of the relationship between state population and pulse area error ratio; Figure 3The blue solid line in the diagram illustrates the sensitivity of the composite pulse to pulse area errors. Figure 3 The orange dotted lines in the diagram illustrate the sensitivity of the SCROFULOUS composite pulse reconstructed using the phase assimilation method to pulse area errors. Because the phase assimilation method causes the errors of the sub-pulses to coherently superimpose, it defines the upper limit of the sensitivity achievable by numerical search methods.

[0055] The core idea of ​​the numerical search method is to use the sensitivity of the reconstructed pulse to the deviation of the target parameter as the optimization objective and the unbiased constraint as the constraint condition, and to search for a reconstructed phase sequence with a specific sensitivity through a numerical optimization algorithm.

[0056] Both phase mismatch calculation and phase assimilation methods determine the reconstructed phase based on analytical rules. While simple to implement, the sensitivity of the resulting reconstructed phase sequence is specific. Numerical search methods, by searching within a phase space that satisfies unbiased constraints, can find a reconstructed phase sequence with a specified calibration sensitivity, thus providing greater flexibility for calibration tasks in different scenarios.

[0057] In this embodiment, the numerical search method includes the following sub-steps: 1) Define the optimization objective function.

[0058] The sensitivity of the reconstructed phase sequence to the deviation of the target parameter is used as the optimization objective.

[0059] Sensitivity is defined as the deviation ΔO of the observable quantity caused by the deviation Δx of the experimental control parameter. Specifically, when the experimental control parameter x deviates from its theoretical optimum x0 to a deviation Δx (i.e., x = x0 + Δx), the expected value of the actual observable quantity is...<O(x)> Its expected value at the theoretical optimal value x0<O(x0)> The deviation between them is ΔO=|<O(x)> -<O(x0)> For the same Δx, the larger ΔO is, the higher the sensitivity.

[0060] In this embodiment, the final state of the quantum bit is selected as |1 The population P1 of the state is taken as an observable; the duration T of each sub-pulse is fixed, and the Rabi frequency Ω of the pulse is taken as the experimental control parameter to be calibrated; the objective of numerical optimization is that when the Rabi frequency Ω deviates from the theoretical optimum π / T by 10% (i.e., ΩT / π=1.1), the deviation of the population P1 from its optimum value of 1.0 is 0.1, i.e., P1=0.9. This optimization objective is as follows: Figure 3 As shown by the black dots in the image.

[0061] It should be noted that the sensitivity target in the numerical optimization method is not limited to a single parameter point; multiple parameter points can also be set as targets. For example, at a parameter deviation of Δx1, the observable deviation from the ideal value ΔO1 can be specified; at a parameter deviation of Δx2, the observable deviation from the ideal value ΔO2 can be specified; and at a parameter deviation of Δxn, the observable deviation from the ideal value ΔOn can be specified. The numerical optimizer can search for a phase reconstruction sequence that best meets or closely approximates this sensitivity target.

[0062] 2) Define constraints.

[0063] The constraint in this embodiment is an unbiased constraint: when the experimental control parameter x is at the theoretical optimal value x0, the reconstructed sequence should achieve the same target rotation operation as the original sequence. In this embodiment, this means that the reconstructed sequence should ensure that P1 = 1.0 at Ω = π / T.

[0064] 3) Select an optimization algorithm.

[0065] In this embodiment, for the target parameter θ=π, by analytically analyzing the phase relationship of the three sub-pulses, it can be found that when the phase parameterization of the three sub-pulses is (φ, -φ, φ), the sensitivity can be continuously adjusted between the original SCROFULOUS composite pulse (lowest sensitivity) and the phase-assimilated reconstructed composite pulse (highest sensitivity) during the numerical search process by traversing φ. Furthermore, analytical analysis also shows that the unbiased constraint condition can be naturally satisfied for the above phase parameterization method. Therefore, this embodiment uses the Brent root-finding method to numerically solve for the phase value φ that satisfies the sensitivity defined in step 1, obtaining the phase sequence (28.363°, -28.363°, 28.363°).

[0066] It should be noted that this embodiment simplifies the numerical optimization problem by analyzing the parameter structure. More generally, the numerical optimization method can also skip this analytical analysis step and directly search for sub-pulse phase value combinations (φ1, φ2, φ3) that satisfy the above sensitivity target and unbiased constraint conditions. Available numerical algorithms include, but are not limited to, grid search. This grid search method uniformly divides the selectable value range (-180° to 180°) of each sub-pulse phase into M grid points. The value of M is a preset value determined by the search accuracy and computational resources, such as 360, i.e., performing grid search with a step size of 1°. During the search process, for each combination of sub-pulse phases, the phase reconstruction module first checks whether the composite pulse reconstructed based on the combination meets the unbiased constraint conditions. If it does not, the combination is filtered out. For candidate reconstructed pulses that meet the unbiased constraint conditions, the deviation ΔO of the observable quantity caused by the deviation Δx of the preset control parameter is calculated. Finally, from all candidate reconstructed pulses that meet the unbiased constraint conditions, the sub-pulse phase value combination with the sensitivity closest to the preset sensitivity target is returned.

[0067] 4) Perform the search and output the results.

[0068] In this embodiment, the optimization algorithm selected in 3) is executed, and the resulting phase sequence output is (φ1=28.363°, φ2=-28.363°, φ3=28.363°).

[0069] The sensitivity of the SCROFULOUS composite pulse reconstructed based on this phase sequence to pulse area error is as follows: Figure 3 As shown, specifically as follows Figure 3 As shown by the short green line, its sensitivity lies between that of the phase assimilation method and the original composite pulse. By outputting this phase relationship and performing steps S3-S5 on it, the calibration of the SCROFULOUS pulse can be completed.

[0070] It should be noted that the above numerical search method is not limited to SCROFULOUS composite pulses, but is also applicable to parameter calibration of various composite pulse sequences such as BB1, SK1, and Knill composite pulses.

[0071] Step S3: The phase-reconstructed composite pulse is used as a calibration composite pulse and applied to the target quantum system in its initial quantum state.

[0072] In this embodiment, ionic qubits are first fabricated to |0| using laser pumping. The initial quantum state is then used as the initial quantum state. Then, the phase-reconstructed BB1 composite pulse sequence obtained in step S2—the area ratio of the four sub-pulses is π:2π:π:θ, and the phases are 75.52°, 226.57°, 75.52°, and 0°, respectively—is sequentially applied to the qubit.

[0073] During the pulse application process, the microwave signal is generated by an arbitrary waveform generator, up-converted to the resonant frequency of the quantum bit by a mixer, and then applied to the quantum bit through a microwave antenna.

[0074] After the application is complete, the qubit changes from its initial state |0 to |0. Evolves into a certain final state |ψ =α|0 +β|1 , where α and β are complex amplitudes, the specific values ​​of which depend on the deviation between the experimental control parameters and the ideal values, as well as the sensitivity of the reconstructed phase sequence.

[0075] It should be noted that the initial quantum state is not limited to |0. The state can be selected according to the needs of the calibration task. |1 State, superposition state (e.g., |+ (state) or any other quantum state.

[0076] Step S4: For different experimental control parameter values, measure the final state response of the target quantum system; fit the experimental control parameter deviation based on the final state response and update the best estimate of the experimental control parameters.

[0077] In this embodiment, step S4 specifically includes the following sub-steps: Step S4.1: Input the different values ​​of the experimental control parameters to be calibrated into the calibration composite pulse in step S3, and measure the expected value of the observable quantity of the target quantum system for each value.

[0078] This embodiment uses ion fluorescence readout to perform projection measurement on the qubit to determine its state at |0|. State or |1 State. This embodiment explores each different pulse duration value T of the fourth pulse; the durations of the first three pulses are proportionally scaled based on T according to the relationship determined by the BB1 ​​formula; for each group of pulse duration values, the initial state preparation-pulse application-final state measurement is repeated N times. In this embodiment, the number of repetitions is set to N=500, and |0 is statistically analyzed. state and |1 The populations of the final state are calculated by counting the occurrences of each state, where P0 + P1 = 1 and P1 represents |1 / 2|. The population of the state, P0 represents |0 The population of the state. Step S4.2: Construct the theoretical expression for P1 with respect to pulse duration T.

[0079] Since the reconstructed phase sequence is determined and the waveform shape and area of ​​each sub-pulse are known, this embodiment can derive the functional relationship between P1 and the control parameter T of the experiment to be calibrated using the unitary evolution equation of quantum mechanics: P1=f(T;Ω,φ1',φ2',φ3',φ4') Where Ω is the constant but unknown Rabi frequency in the experimental system, and φ1' to φ4' are the current reconstructed phase sequences. For this embodiment, this functional relationship refers to... Figure 2 As shown, Figure 2 The orange dotted line in the figure shows the functional relationship between P1 and pulse duration T obtained based on the aforementioned phase mismatch method under constant Ω; Figure 2 The green dotted line in the diagram illustrates the functional relationship between P1 and pulse duration T, obtained based on the aforementioned phase assimilation method.

[0080] Step S4.3, parameter deviation fitting.

[0081] In this embodiment, the experimental measurement value of P1 obtained in step S4.1 is substituted into the theoretical expression in step S4.2, and the estimated value of the current optimal pulse area duration T is obtained by least squares fitting or maximum likelihood estimation algorithm, which is used as the optimal estimated value of the current experimental control parameter.

[0082] Because the reconstructed phase sequence is significantly more sensitive to area deviation, P1 has a larger gradient with T. Therefore, even if the deviation of T is very small (e.g., 1%), it can be extracted from the measurement data with a high signal-to-noise ratio.

[0083] Step S5: In the operation mode, the best estimated value of the experimental control parameters is combined with the original phase configuration before reconstruction to regenerate the standard composite pulse for quantum operation.

[0084] In this embodiment, after the calibration process is completed, the quantum system switches from calibration mode to operational mode. The specific operation is as follows: First, the optimal pulse duration T obtained from step S5 calibration is used as the duration of the fourth pulse of BB1.

[0085] Then, based on the determined ratio of the sub-pulse areas in the BB1 ​​composite pulse (π:2π:π:θ) and the optimal duration T of the fourth pulse obtained from the above calibration, the durations of the first three pulses are calculated and set. In this embodiment, since θ=π, the durations of the four sub-pulses are T, 2T, T, and T, respectively.

[0086] Finally, using the duration of the aforementioned sub-pulses and the known phase relationships of the standard BB1 composite pulse sequence (φ1=arccos(-π / (4π))=104.48°, φ2=3φ1=313.43°, φ3=φ1=104.48°, φ4=0°), a composite pulse sequence is generated to perform the single-qubit gate operation required in the quantum circuit. Since the pulse area has been precisely corrected through calibration and the phase configuration has been restored to its original design value, the BB1 ​​composite pulse regains its inherent high-order error compensation capability, effectively suppressing potential pulse area fluctuations in subsequent operations and ensuring the fidelity of the gate operation.

[0087] Finally, the embodiments use the Knill composite pulse as an example to explain in detail that the present invention can not only amplify the sensitivity of the final state observable to the pulse area error, but also amplify the sensitivity to the pulse frequency and detuning, that is, it is effective for calibration situations where the pulse frequency or detuning is used as the experimental control parameter.

[0088] The Knill composite pulse consists of five sub-pulses, each with an area of ​​π, and phases of 60°, 30°, 120°, 30°, and 60° respectively. The overall effect is a π-area rotation of the qubit. In this embodiment, the qubit is initialized to |0. State. After applying the composite pulse to be calibrated to the initial state of the qubit, the observable for the final state selection in this embodiment is |1. Population P1. (Refer to...) Figure 4 As shown, for the Knill composite pulse, the original composite pulse sequence, the sequence reconstructed by phase assimilation, and the sequence reconstructed by numerical search are applied to |0... After the state, we get |1 A comparison of the relationship between the state population and the proportion of pulse duration errors and the proportion of pulse frequency errors. The left half of the graph shows the relationship with the proportion of pulse duration errors, which is reduced to a dimensionless number ΩT / π based on the target pulse area π; the right half of the graph shows the relationship with the proportion of pulse frequency errors, which is reduced to a dimensionless number δ / Ω based on the pulse Rabi frequency Ω.

[0089] like Figure 2 As shown by the blue solid line, the Knill composite pulse has a suppressive effect on pulse area error caused by pulse pully frequency Ω or pulse duration T and pulse frequency error caused by pulse detuning δ. For pulse area error of about 10% and pulse frequency error of about 30%, the final state P1 is close to the ideal value of 1.0.

[0090] Since the area and phase of sub-pulses are fixed values ​​in standard Knill composite pulses and do not involve computation, the phase mismatch calculation method in this embodiment is not applicable to Knill composite pulses. The phase assimilation method and numerical search method in this invention can both be applied to Knill pulses.

[0091] Based on the phase assimilation method, this embodiment sets the phase of each sub-pulse to 0°, and the pulse area is consistent with the original Knill composite pulse, i.e., all are set to π. For example... Figure 4 As shown by the orange dotted line, the composite pulse reconstructed based on the phase assimilation method significantly enhances both pulse area error and pulse frequency error compared to the original Knill composite pulse.

[0092] Based on the numerical search method, in this embodiment, when performing pulse area calibration, the optimization objective of the numerical optimization method is set as follows: when ΩT / π = 1.1, that is, when the relative pulse area error is 10%, P1 decreases from 1.0 in the ideal case to 0.9. This optimization objective is as follows: Figure 4 The left half of the diagram is marked with black dots. The constraint condition for numerical optimization is an unbiased constraint, that is, the reconstructed sequence must satisfy that when the experimental control parameters are configured to the ideal value ΩT / π=1.0, the observable P1 does not deviate from its ideal value of 1.0. In order to simplify the parameter search space of the numerical optimization problem and improve the efficiency of numerical optimization, this embodiment makes the following additional constraints on the phases φ1, φ2, φ3, φ4, and φ5 of the five sub-pulses: Symmetry constraints require φ1=φ5 and φ2=φ4, thus simplifying the problem to an optimization problem with 3 variables; Without loss of generality, the optimization requires φ1=0, meaning the phases of the five sub-pulses are set to 0, φ2, φ3, φ2, and 0, simplifying the problem to an optimization of two variables, φ2 and φ3. If a non-zero φ1 value is required in a specific scenario, the five phases can be uniformly shifted by the required φ1 value, i.e., the composite pulse can be reconstructed in the form of φ1, φ1+φ2, φ1+φ3, φ1+φ2, and φ1.

[0093] It should be noted that the simplification of the numerical optimization problem described above is a technique used in this embodiment to improve optimization efficiency, and is not a limitation on the numerical search method in this invention. Optimizing each of the five sub-phases as an independent variable is also feasible; as long as the reconstructed sequence obtained from the numerical search satisfies the aforementioned unbiased constraints and target sensitivity, it can be used for the calibration of composite pulses.

[0094] For each combination of φ2 and φ3 and the area of ​​each sub-pulse (reduced to the dimensionless number ΩT / π), the reconstructed pulse sequence acts on |0 The value of P1 obtained after the state can be obtained through unitary evolution in quantum mechanics, denoted as the function P1(ΩT / π; φ2, φ3). Furthermore, the objective and unbiased constraints of this optimization problem can be formally expressed as: P1(1.0;φ2,φ3)=1.0 (unbiased constraint); P1(1.1;φ2,φ3)=0.9 (sensitivity target).

[0095] This embodiment employs the Trust Domain Reflectometry (TRF) method to minimize the sum of squared residuals of the two equations described above. The optimizer performs optimization starting from 300 sets of randomly generated initial parameters, ultimately obtaining a phase combination (0, 149.02°, 228.95°, 149.02°, 0) that satisfies the conditions. The sensitivity of the sequence reconstructed based on this phase combination to pulse area error is as follows: Figure 4 The left half of the image is shown by the short green line.

[0096] In this implementation, the sensitivity target for pulse frequency errors is set as follows: when δ / Ω = 0.3, P1 = 0.9. Figure 4 The right half of the diagram is indicated by black dots. For a target with specified pulse frequency error sensitivity, this embodiment employs the same numerical method as described above for a target with pulse area sensitivity, obtaining a phase combination (0, 289.03°, 266.95°, 289.03°, 0) that satisfies both the target sensitivity and unbiased constraints. The effect is as follows... Figure 4 The short green line in the right half of the diagram indicates this.

[0097] Example 2 This invention discloses a composite pulse calibration system based on phase reconstruction, referring to... Figure 5 As shown, the method described in Example 1 includes: Target parameter input module: used to determine the target parameters and experimental control parameters to be achieved by the composite pulse according to the requirements of the current quantum circuit or experimental task; among which, the experimental control parameters are used to achieve the target parameters; Phase reconstruction module: used to maintain the number of sub-pulses and the waveform shape of each sub-pulse of the composite pulse unchanged, and to reconstruct the phase relationship between the sub-pulses of the composite pulse based on the target parameters and the phase reconstruction strategy; Reconstructed composite pulse generation module: used to apply the phase-reconstructed composite pulse as a calibration composite pulse to the target quantum system in its initial quantum state; Quantum state measurement module: used to measure the final state response of the target quantum system based on different experimental control parameter values; to fit the experimental control parameter values ​​based on the final state response and obtain the best estimate of the experimental control parameters; Standard composite pulse generation module: used in operation mode to regenerate standard composite pulses for quantum operations by combining the best estimate of experimental control parameters with the original phase configuration before reconstruction.

[0098] In the actual operation of ion trap quantum computers, the area of ​​the microwave pulse applied to the qubits often deviates from the theoretical value due to gain drift of the microwave control circuit amplifier and jitter in qubit coupling efficiency. This pulse area error directly reduces the fidelity of single-qubit gates. Although the BB1 ​​composite pulse has extremely strong resistance to area error (robustness), this robustness makes it difficult to deduce the error magnitude from the measurement results during the calibration phase (i.e., "low sensitivity"). The system in this embodiment aims to solve this contradiction and achieve high-precision online automatic calibration.

[0099] This embodiment utilizes a calibration system to calibrate the X-gate operation applied to the ion qubit Q1. The specific process is as follows: The system initializes parameters using a target parameter input module. First, it reads the current quantum circuit requirements and determines that a quantum gate with a rotation angle of θ=π needs to be executed. For the nominal output power of the microwave source, the system selects the pulse duration T as the optimization parameter. The calibration task is defined as finding the optimal pulse duration T to achieve the target θ=π quantum gate. Then, the system performs high-sensitivity reconstruction using a phase reconstruction module and a reconstructed composite pulse generation module. To "see" the error, the system enters calibration mode. The phase reconstruction module uses a "phase mismatch calculation method," inverting the target parameter (θ=-π) and substituting it into the BB1 ​​phase formula to calculate a new phase sequence. At this point, the originally error-insensitive BB1 ​​pulse is reconstructed into a highly error-sensitive "probe" pulse. The reconstructed composite pulse generation module sends this pulse waveform to an arbitrary waveform generator, which applies it to the ground state |0 via a microwave antenna. The system then uses the quantum state measurement module to extract errors for different pulse durations T. This module reads the response of the ion fluorescence and statistically determines the quantum bit transition to |1. The probability of the state, i.e., the population P1. Because the reconstructed pulse has high sensitivity, even a small area deviation will cause a significant change in the P1 value. The module performs least-squares fitting between the measured P value and the theoretical curve to accurately calculate the optimal pulse duration T under the current experimental conditions.

[0100] Finally, high-performance computation is restored using the standard composite pulse generation module. After calibration, the system switches to computation mode. The standard composite pulse generation module uses the precise parameters just obtained, combined with the original, robust phase configuration of BB1, to generate a standard BB1 pulse sequence for subsequent quantum algorithm execution.

[0101] In this embodiment, the ion trap quantum processor can automatically overcome pulse errors caused by environmental drift without changing the microwave pulse power and waveform envelope. It utilizes the high sensitivity of the reconstructed phase to achieve fast and accurate parameter calibration, while retaining the noise immunity of the original BB1 pulse during computation, significantly improving the long-term stability and gate operation fidelity of quantum computing.

[0102] Example 3 The present invention further provides a computer device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; when the processor executes a program, it implements the composite pulse calibration method based on phase reconstruction described in Embodiment 1. For the sake of simplicity, further details are omitted here.

[0103] It should be understood that in this embodiment, the processor can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc.

[0104] Memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of memory may also include non-volatile random access memory. For example, memory may also store information about the device type.

[0105] In the implementation process, each step of the above method can be completed by the integrated logic circuits in the processor hardware or by software instructions.

[0106] Example 4 The present invention also provides a computer-readable storage medium storing computer program instructions, which, when executed by a processor, cause the processor to perform a composite pulse calibration method based on phase reconstruction as described in any of the embodiments in Example 1.

[0107] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0108] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A composite pulse calibration method based on phase reconstruction, characterized in that, Includes the following steps: S1. Based on the requirements of the current quantum circuit or experimental task, determine the target parameters and experimental control parameters to be achieved by the composite pulse; wherein, the experimental control parameters are used to achieve the target parameters; S2. Keeping the number of sub-pulses and the waveform shape of each sub-pulse of the composite pulse unchanged, the phase relationship between the sub-pulses of the composite pulse is reconstructed based on the target parameters and the phase reconstruction strategy. S3. The phase-reconstructed composite pulse is used as a calibration composite pulse and applied to the target quantum system in its initial quantum state; S4. Measure the final state response of the target quantum system based on different experimental control parameter values; fit the experimental control parameter values ​​based on the final state response, and obtain the best estimated values ​​of the experimental control parameters; S5. In the operation mode, the best estimated value of the experimental control parameters is combined with the original phase configuration before reconstruction to regenerate a standard composite pulse for quantum operation.

2. The method as described in claim 1, characterized in that, In step S1, the target parameter is the quantum manipulation parameter to be achieved by the composite pulse, including the equivalent rotation area of ​​the composite pulse; the experimental control parameter is the composite pulse parameter that needs to be determined by fitting calibration, including pulse intensity, pulse area, pulse duration, pulse frequency and detuning.

3. The method as described in claim 1, characterized in that, In step S2, the phase reconstruction strategy specifically includes: Phase mismatch calculation method: Substitute parameter values ​​different from the target parameters into the calculation position of the target parameters in the phase calculation formula of the composite pulse, and calculate the phase relationship of each sub-pulse; Phase assimilation method: Set the phase of all sub-pulses of the composite pulse to the same preset value, so that the error caused by parameter deviation of each sub-pulse is transformed from coherent cancellation to coherent accumulation, and the phase relationship between each pulse is obtained. Numerical search method: Taking the sensitivity of the specified reconstruction pulse to the deviation of the target parameter as the objective and satisfying the unbiased constraint as the condition, the optimal reconstruction phase is searched through numerical optimization.

4. The method as described in claim 3, characterized in that, The unbiased constraint in the numerical search method is: when the current experimental control parameter is exactly equal to the theoretical optimal value, the pulse output corresponding to the reconstructed phase sequence is consistent with the pulse output corresponding to the original phase sequence.

5. The method as described in claim 3, characterized in that, Among the phase reconstruction strategies, the phase assimilation method has the highest sensitivity, the phase mismatch calculation method has a medium sensitivity, and the sensitivity of the numerical search method is determined based on the sensitivity target.

6. The method as described in claim 3, characterized in that, The phase reconstruction strategy is selected as follows: The phase reconstruction strategy is dynamically switched based on the estimation of the deviation of the current experimental control parameters from the theoretical optimal value; the theoretical optimal value refers to the target parameter that the original combined pulse sequence should theoretically achieve when the experimental control parameters are configured to be applied to the original combined pulse sequence. When the deviation exceeds the preset range, the phase mismatch calculation method or the numerical search method with low sensitivity as the target is selected; when the deviation is within the preset range, the target sensitivity of the numerical search method is gradually increased or the phase assimilation method is used to obtain the highest sensitivity.

7. The method as described in claim 1, characterized in that, Step S4 specifically includes: Different experimental control parameter values ​​are input into the calibration composite pulse and applied to the quantum system. For each value, the expected value of the observable quantity of the final state of the target quantum system is measured. The observable quantity includes the final state population. Construct a theoretical expression for the observable quantity, wherein the theoretical expression is a functional relationship between the expected value of the observable quantity and the experimental control parameters; Based on the measured expected value and the theoretical expression, the best estimated value of the experimental control parameter is obtained by using the least squares fitting or maximum likelihood estimation algorithm.

8. A composite pulse calibration system based on phase reconstruction, characterized in that, The method described in any one of claims 1-7 includes: Target parameter input module: used to determine the target parameters and experimental control parameters to be achieved by the composite pulse according to the requirements of the current quantum circuit or experimental task; wherein, the experimental control parameters are used to achieve the target parameters; Phase reconstruction module: used to maintain the number of sub-pulses and the waveform shape of each sub-pulse of the composite pulse unchanged, and to reconstruct the phase relationship between the sub-pulses of the composite pulse based on the target parameters and the phase reconstruction strategy; Reconstructed composite pulse generation module: used to apply the phase-reconstructed composite pulse as a calibration composite pulse to the target quantum system in its initial quantum state; Quantum state measurement module: used to measure the final state response of the target quantum system based on different experimental control parameter values; to fit the experimental control parameter values ​​based on the final state response and obtain the best estimate of the experimental control parameters; Standard composite pulse generation module: used in operation mode to regenerate standard composite pulses for quantum operations by combining the best estimated values ​​of the experimental control parameters with the original phase configuration before reconstruction.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the composite pulse calibration method based on phase reconstruction as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the composite pulse calibration method based on phase reconstruction as described in any one of claims 1 to 7.

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