Methods, systems, devices and storage media for measuring external field parameters of superconducting quantum systems

Abstract

This application provides a method, system, device, and storage medium for measuring the external field parameters of a superconducting quantum system, relating to the technical field of quantum information computing. The method for measuring the external field parameters of a superconducting quantum system includes: performing quantum evolution at multiple preset evolution times on multiple first preset external field parameters based on a target Hamiltonian and an initial state to determine first quantum state data; determining a target probability set based on the first quantum state data; performing quantum evolution at multiple preset evolution times on second preset external field parameters based on the target Hamiltonian and the initial state to determine second quantum state data; performing joint time-domain Bayesian estimation based on the target probability set, the second quantum state data, and a Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameters; and determining the target external field parameters based on the target posterior probability distribution and the second preset external field parameters. This application can achieve stable and high-precision measurement of unknown external field parameters.

Description

Technical Field

[0001] This application relates to the technical field of quantum information computing, and more specifically, to a method, system, device, and storage medium for measuring the external field parameters of a superconducting quantum system. Background Technology

[0002] Superconducting quantum systems, with their highly programmable manipulation capabilities, long quantum coherence times, and potential for large-scale integration, have become one of the core physical platforms for realizing quantum computing and quantum simulation. Beyond running specific quantum algorithms, using superconducting quantum processors to simulate other complex quantum systems (such as strongly correlated electronic materials and quantum chemical molecules) and estimating key physical parameters (such as coupling constants, disorder strength, and external field amplitudes) has become an important research direction in this field. In such applications, the accuracy of parameter estimation is crucial to the quantum simulation results.

[0003] Based on quantum metrology theory, by utilizing resources such as quantum entanglement, the accuracy of parameter estimation can break through the standard quantum limit of classical measurement and reach the Heisenberg limit. However, the following main problems still exist: (1) The fragility of quantum resources and the difficulty of engineering implementation: The preparation, manipulation and maintenance of multi-particle entangled probes required to achieve the highest theoretical accuracy are extremely sensitive to decoherence and various noises. Under the current technical conditions, the preparation and maintenance of large-scale entangled states with high fidelity still face severe challenges and the practicality is limited.

[0004] (2) The disconnect between theoretically optimal measurement and practical devices: Although quantum Fisher information (used to quantize the sensitivity or distinguishability of quantum states to the parameters to be estimated) provides a theoretical lower bound (i.e., the quantum Cramér-Rao bound) for the estimation variance, the optimal measurement basis required to reach this lower bound usually depends on the true value of the parameter itself and has a complex structure. In actual superconducting quantum experiments, the measurement devices (such as population measurements based on specific qubit energy levels) are usually fixed and difficult to dynamically reconstruct according to the parameters in real time, making it difficult to approach the theoretical limit in practice.

[0005] (3) Insufficient stability of estimation under real-world noise conditions: Under the constraints of finite quantum coherence time, unavoidable control errors, and measurement noise, traditional parameter estimation methods (such as curve fitting based on a single evolution time) obtain limited information, which can easily lead to multiple local peaks (multimodality) in the posterior probability distribution of parameters. This makes the estimation results unstable and have low reliability, making it difficult to achieve robust and high-precision estimation with a limited number of sampling times.

[0006] The content in the background section is merely technology known to the public and does not necessarily represent existing technology in this field. Summary of the Invention

[0007] This application provides a method, system, device, and storage medium for measuring the external field parameters of a superconducting quantum system, aiming to solve at least one of the technical problems mentioned in the background art.

[0008] The method for measuring the external field parameters of a superconducting quantum system includes: performing initialization processing through a superconducting quantum processor to enter a reference state; constructing the target Hamiltonian and initial state of a target simulation model based on the reference state using the superconducting quantum processor; performing quantum evolution at multiple preset evolution times for multiple first preset external field parameters based on the target Hamiltonian and initial state to determine the first quantum state data; determining a target probability set based on the first quantum state data, the target probability set including the probability data of the target measurement result for each first preset external field parameter at each preset evolution time; performing quantum evolution at multiple preset evolution times for a second preset external field parameter based on the target Hamiltonian and initial state to determine the second quantum state data; performing joint time-domain Bayesian estimation based on the target probability set, the second quantum state data, and a Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameter; and determining the target external field parameter based on the target posterior probability distribution and the second preset external field parameter.

[0009] According to some embodiments of this application, based on the target Hamiltonian and the initial state, performing quantum evolution at multiple preset evolution times on multiple first preset external field parameters to determine the first quantum state data includes: performing quantum evolution at each preset evolution time on each first preset external field parameter based on the initial state and the target Hamiltonian; and for each preset evolution time, performing a preset number of measurements on all qubits under a fixed computational basis to determine the first quantum state data.

[0010] According to some embodiments of this application, determining the target probability set based on the first quantum state data includes: determining the number of times the target measurement result occurs at each preset evolution time for each first preset external field parameter based on the first quantum state data; determining the probability data corresponding to the first preset external field parameter and each preset evolution time based on the number of occurrences; and traversing the probability data of all first preset external field parameters to determine the target probability set based on the probability data of all first preset external field parameters.

[0011] According to some embodiments of this application, performing joint temporal Bayesian estimation based on a target probability set, second quantum state data, and a Bayesian estimation framework to determine the external field parameters includes: determining an initial prior probability distribution in the Bayesian estimation framework; determining a target time, which is a subset of multiple preset evolution times, including at least a first target time and a second target time; determining a first posterior probability distribution of the second preset external field parameters at the first target time based on the second quantum state data, the target probability set, and the initial prior probability distribution at the first target time; using the first posterior probability distribution as the prior probability distribution at the second target time to determine a second posterior probability distribution of the second preset external field parameters at the second target time; and iterating through all target times to iterate the posterior probability distribution of the second preset external field parameters multiple times until the target posterior probability distribution is determined.

[0012] According to another aspect of this application, this application provides a superconducting quantum system external field parameter measurement system, including an initialization processing module, a data processing module, and an external field parameter measurement module. The initialization processing module performs initialization processing through a superconducting quantum processor to enter a reference state. Based on the reference state, the data processing module constructs the target Hamiltonian and initial state of a target simulation model using the superconducting quantum processor. Based on the target Hamiltonian and initial state, it performs quantum evolution at multiple preset evolution times for multiple first preset external field parameters to determine first quantum state data. Based on the first quantum state data, it determines a target probability set, which includes the probability data of the target measurement result for each first preset external field parameter at each preset evolution time. Based on the target Hamiltonian and initial state, it performs quantum evolution at multiple preset evolution times for second preset external field parameters to determine second quantum state data. The external field parameter measurement module determines the target posterior probability distribution corresponding to the second preset external field parameter based on the target probability set, the second quantum state data, and a Bayesian estimation framework. It also determines the target external field parameter based on the target posterior probability distribution and the second preset external field parameter.

[0013] According to some embodiments of this application, the data processing module performs quantum evolution at each preset evolution time for each first preset external field parameter based on the initial state and the target Hamiltonian; for each preset evolution time, the data processing module performs a preset number of measurements on all qubits under a fixed computational basis to determine the first quantum state data.

[0014] According to some embodiments of this application, the data processing module determines the number of times the target measurement result occurs at each preset evolution time for each first preset external field parameter based on the first quantum state data; the data processing module determines the probability data corresponding to the first preset external field parameter and each preset evolution time based on the number of occurrences; the data processing module iterates through the probability data of all first preset external field parameters to determine the target probability set based on the probability data of all first preset external field parameters.

[0015] According to some embodiments of this application, the external field parameter measurement module determines the initial prior probability distribution in the Bayesian estimation framework; the external field parameter measurement module determines the target time, which is a subset of multiple preset evolution times, and the target time includes at least a first target time and a second target time; the external field parameter measurement module determines the first posterior probability distribution of the second preset external field parameters at the first target time based on the second quantum state data, the target probability set, and the initial prior probability distribution at the first target time; the external field parameter measurement module uses the first posterior probability distribution as the prior probability distribution at the second target time to determine the second posterior probability distribution of the second preset external field parameters at the second target time; the external field parameter measurement module traverses all target times to iterate the posterior probability distribution of the second preset external field parameters multiple times until the target posterior probability distribution is determined.

[0016] According to another aspect of this application, an electronic device is also provided. The electronic device includes: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement the method for measuring the external field parameters of a superconducting quantum system as described above.

[0017] According to another aspect of this application, a non-volatile computer-readable storage medium is also provided. This storage medium stores a computer program that, when executed by a processor, enables the implementation of the method for measuring the external field parameters of a superconducting quantum system as described above.

[0018] Beneficial effects This application provides a method for measuring the external field parameters of a superconducting quantum system, implementing a time-domain joint Bayesian estimation method with "open-loop acquisition at the front end and joint inference at the back end." This application can acquire dynamic data at multiple preset evolution times under a fixed measurement basis and perform time-domain joint Bayesian estimation through a classical computing system, thus solving the problems of high dependence on real-time feedback control and convergence instability caused by multi-peak posterior distribution. This application can achieve stable and high-precision measurement of unknown external field parameters. Attached Figure Description

[0019] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 A flowchart illustrating the method for measuring external field parameters of a superconducting quantum system according to an embodiment of this application is shown. Figure 2a This illustration shows a schematic diagram of the potential field of the Stark-Wannier model according to an embodiment of this application; Figure 2b A schematic diagram illustrating the evolution of probability data over time according to an embodiment of this application; Figure 3 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application; Figure 4 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application; Figure 5 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application; Figure 6 A schematic diagram illustrating the posterior probability distribution at a single target time according to an embodiment of this application; Figure 7 A schematic diagram illustrating the posterior probability distribution at two target times according to an embodiment of this application; Figure 8 A schematic diagram illustrating the posterior probability distribution at three target times according to an embodiment of this application is shown. Figure 9 This is a schematic diagram of the structure of the superconducting quantum system external field parameter measurement system according to an embodiment of this application.

[0021] Explanation of reference numerals in the attached figures: Superconducting quantum system external field parameter measurement system 1; initialization processing module 10; data processing module 20; external field parameter measurement module 30. Detailed Implementation

[0022] The technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings of the embodiments. Obviously, the described embodiments are only some, not all, of the embodiments of this application. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0023] In the development of related technologies, in order to address the multiple challenges faced by superconducting quantum systems in parameter estimation, such as high-dimensional parameter spaces, complex noise environments, and limited quantum resources, the following aspects are currently being explored and researched in existing technologies: In terms of theoretical mechanisms, a systematic framework for quantum enhancement metrology has been developed, mainly including core pathways such as entanglement enhancement, criticality enhancement, and non-equilibrium dynamic enhancement. The theoretical potential of these enhancement mechanisms is uniformly characterized by the quantum Cramér-Rao lower bound theory, which sets a universal lower bound for the variance of unbiased estimators through quantum Fisher information, providing a unified standard for evaluating the limiting performance of various quantum measurement schemes.

[0024] In terms of experimental methods, statistical inference and adaptive estimation strategies have been widely applied and developed. Bayesian inference methods, by introducing the prior distribution of parameters and continuously updating the posterior distribution based on experimental observation data, can provide the best estimate of the parameters and quantify the uncertainty. Maximum likelihood estimation reaches the quantum Cramér-Rao bound under the asymptotic limit. In addition, adaptive estimation strategies can improve data acquisition efficiency and reduce the required sample size while maintaining estimation accuracy by dynamically adjusting subsequent experimental parameters (e.g., evolution time) through real-time measurement results.

[0025] Furthermore, data-driven methods based on machine learning offer a new technical approach for handling high-dimensional parameters and complex system noise. These methods utilize machine learning to learn the complex mapping relationships between parameters and observations from experimental data, or to directly optimize measurement strategies. However, such methods still face challenges such as insufficient model interpretability, high dependence on training data, and limited cross-platform generalization ability.

[0026] The adaptive phase estimation method is a quantum parameter estimation method based on dynamic feedback optimization. It achieves adaptive adjustment of the measurement strategy through real-time updates of measurement results, thereby obtaining estimation accuracy approaching the Heisenberg limit under limited measurement resources. This method can improve parameter estimation efficiency by dynamically optimizing the measurement basis or control parameters in a closed-loop process of "measurement-update-decision-feedback," ensuring the system is in an optimal information acquisition state at each measurement step.

[0027] In terms of theoretical framework, adaptive phase estimation is generally based on the Bayesian inference principle: first, an initial prior probability distribution is established for the parameters to be measured; after each measurement, the posterior distribution is corrected by Bayesian update rules based on the statistical response relationship between the observation results and the quantum measurement operator; the algorithm then calculates the optimal control parameters for the next measurement based on the characteristics of the posterior distribution to maximize the expected information gain.

[0028] As the number of measurements increases, the posterior distribution gradually converges to the true parameter values. When the system uses quantum entangled states as probes and combines them with an adaptive feedback strategy, its estimated standard deviation can approach the quantum scaling property of 1 / N (where N is the measurement resource, which is the total number of particles used in a measurement), thus achieving parameter estimation accuracy that exceeds the standard quantum limit.

[0029] However, the inventors of this application have discovered that, although the adaptive phase estimation method can theoretically achieve quantum-enhanced measurement accuracy, at least the following technical problems still exist in experiments with superconducting quantum systems: (1) It relies too heavily on the real-time feedback and control performance of the hardware system, resulting in high complexity and cost.

[0030] The adaptive phase estimation algorithm is essentially a closed-loop feedback system, and its "measurement-update-decision-feedback" cycle places stringent requirements on the hardware of the superconducting quantum system.

[0031] First, after each measurement, complex Bayesian posterior distribution updates and optimization calculations need to be completed in a very short time, and the optimized new parameters need to be immediately converted into high-fidelity quantum operation signals. This requires that the computational delay and feedback delay of the control system be sufficiently short.

[0032] Secondly, the operation of superconducting qubits has inherent errors, and the measurement has readout errors and delays. These tiny errors accumulate with the number of iterations during the rapid real-time feedback process and may be amplified by the feedback loop, causing the system to deviate from the optimal measurement path and severely degrading the actual estimation accuracy.

[0033] Furthermore, as the scale of the system under test increases, the dimension of the computation and optimization problem of the posterior distribution increases dramatically, the real-time computation burden grows exponentially, and the complexity of feedback control in multi-bit systems also increases simultaneously, making the engineering implementation of this scheme in multi-bit, multi-parameter scenarios face enormous challenges.

[0034] (2) The convergence and stability of the algorithm are difficult to guarantee, and it is easily troubled by the posterior multimodal problem.

[0035] In superconducting quantum systems, the measurement probability often exhibits periodicity with parameter variation, and the limited data volume in the early stages of experiments leads to multiple peaks (multimodal structure) in the posterior probability distribution of the parameters. This means that multiple different parameter values ​​may generate the current observation data with a high probability. Adaptive algorithms may be misled by these local extrema, and their subsequent optimization feedback may incorrectly converge to a minor peak, causing the estimate to deviate completely from the true value.

[0036] Meanwhile, under the constraint of a limited total number of measurements, if the initial feedback decisions are inappropriate, the algorithm may not have enough opportunities to escape local extrema, resulting in poor stability and repeatability of the estimation results. The same experiment may yield drastically different estimates under different random noise, which seriously affects the practicality and reliability of the scheme.

[0037] According to one aspect of this application, a method for measuring the external field parameters of a superconducting quantum system is provided for measuring the target external field parameters. The method for measuring the external field parameters of a superconducting quantum system can be performed by a superconducting quantum system external field parameter measurement system (hereinafter referred to as the measurement system) with computational capabilities.

[0038] For example, the measurement system may include a superconducting quantum system and a classical computing system. The superconducting quantum system may include a superconducting quantum processor.

[0039] For example, the external field parameter refers to the strength or amplitude parameter of the physical field applied outside the superconducting quantum system that affects its dynamic behavior. In applications, it usually refers to the strength of the real-world physical field (such as a magnetic field or electric field) to be measured.

[0040] As an example, the external field parameters may include a linear gradient in the potential field.

[0041] It is understood that, in addition to superconducting quantum processors, this application can also be applied to programmable quantum simulation platforms such as ion traps, cold atoms, and solid-state spin, as long as the corresponding system modeling, initial state preparation, and evolution control are realized according to the physical characteristics of the platform. This application does not impose any restrictions on this.

[0042] Figure 1 This is a flowchart illustrating a method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application.

[0043] According to the example embodiment, in step S100, the measurement system performs an initialization process via a superconducting quantum processor to enter a reference state.

[0044] For example, the measurement system can respond to user commands and perform initialization processing through a superconducting quantum processor in a cryogenic dilution cooling environment. This includes configuring the frequency of the qubits and calibrating the parameters of the superconducting quantum processor, so that the external field parameter measurement system of the superconducting quantum system can enter a reference state. This allows the measurement system to be in a reference state with high consistency and low noise.

[0045] For example, the initialization process includes, but is not limited to, closed-loop automated optimization of key quantum control parameters such as calibrating the transmission parameters of the readout link, coarsely calibrating the qubit frequency, determining the excitation pulse amplitude, calibrating the reference point of the fundamental quantum state in the IQ plane (the IQ plane: a two-dimensional signal coordinate system plane used to characterize, calibrate, and read out the state of qubits), and frequency. With this configuration, this application allows all qubits to be placed at a preset idle frequency point and suppresses crosstalk between qubits by keeping the coupler channels of the superconducting quantum processor switched off.

[0046] Optionally, during the initialization process, the measurement system can also respond to user commands and perform environmental stability control to suppress the interference of thermal fluctuations and external noise on the initialization consistency.

[0047] For example, environmental stability control includes, but is not limited to, controlling the current ambient temperature within a preset range (e.g., controlling the base temperature of the dilution chiller below 20mK), applying multi-layer electromagnetic shielding, and optimizing filter configuration, etc., and this application does not limit these aspects.

[0048] This application, through initialization processing, establishes a highly reliable quantum state manipulation and measurement benchmark via an integrated calibration protocol and automated optimization program. This provides highly repeatable and low-error starting conditions for subsequent external field parameter measurements and dynamic experiments. Furthermore, through initialization processing and environmental stabilization control, this application maintains high consistency and low noise levels during subsequent external field parameter measurements and dynamic experiments, reducing systematic errors caused by long-term drift of the measurement system or initial configuration deviations.

[0049] According to the example embodiment, in step S200, based on the reference state, the measurement system constructs the target Hamiltonian and initial state of the target simulation model through a superconducting quantum processor.

[0050] For example, the target simulation model can be a mathematical model of the physical system to be simulated. The measurement system can use a superconducting quantum processor to manipulate the parameters related to the Hamiltonian, thereby preparing the target Hamiltonian of the target simulation model. Furthermore, the measurement system can apply high-fidelity parameters to the target qubit using the superconducting quantum processor. Pulses are used to prepare the initial state of the target simulation model. .

[0051] For example, the parameter adjustment methods include, but are not limited to, adjusting the operating frequency of each quantum bit and adjusting the frequency of the coupler between neighboring quantum bits, etc., and this application does not limit them.

[0052] As an example, the target simulation model can be a one-dimensional chain lattice system. Taking linear in-potential gradient estimation in a one-dimensional chain lattice system as an example, this one-dimensional chain lattice system consists of L lattice points. Considering only nearest-neighbor interactions, the target Hamiltonian can be defined as:

[0053] in, For the j-th lattice point, For the decrease operator at the j-th lattice point, Let be the nearest neighbor interaction strength between the j-th grid point and the (j+1)-th grid point. Let be the potential strength at the j-th lattice point.

[0054] Figure 2a This diagram illustrates the potential field of the Stark-Wannier model according to an embodiment of this application. Figure 2b This diagram illustrates the evolution of probability data over time according to an embodiment of this application.

[0055] For example, such as Figure 2a As shown, the target simulation model is a one-dimensional qubit array containing 9 qubits (Q1-Q9), and the size of the target simulation model is denoted as L=9. . Figure 2a In the diagram, the horizontal axis represents the spatial location of the qubit, and the vertical axis (height) represents the applied linear Stark potential. This results in a potential strength of [value missing]. satisfy , The linear gradient in the potential field represents the unknown external field parameter to be measured. The physical system's Hamiltonian will change with... An increase in the ratio, undergoing a transition from the extended phase to the Stark-Wannier localized phase, can contain a wealth of physical phenomena.

[0056] Optionally, in addition to linear in-potential gradient estimation in a one-dimensional chain lattice, the external field parameters to be measured can also be the interaction strength, disorder potential amplitude, amplitude of applied magnetic field or electric field, etc. High-precision estimation of other physical parameters can be achieved simply by adjusting the form of Hamiltonian and the parameter scanning range. This application does not impose any restrictions on this.

[0057] In this embodiment, the measurement system can employ a one-dimensional chain-like superconducting quantum processor with a built-in coupler, and the target Hamiltonian can be prepared in an analogous quantum simulation manner.

[0058] For example, the measurement system can achieve the potential strength by precisely setting the operating frequency of each qubit. Regulation, such as: First, determine a reference frequency. ( (Using the reference frequency), then through frequency biasing, the operating frequency of the j-th qubit is made to satisfy... (in (where j is the operating frequency of the j-th qubit), where , For the first The potential strength of each qubit This represents the linear gradient in the potential field. With this setting, the linear gradient in the potential field... It can be encoded into the frequency space of qubits.

[0059] For example, the measurement system can fix the nearest-neighbor exchange interaction strength by adjusting the frequency of the coupler between nearest-neighbor qubits. With this setup, the measurement system measures the potential intensity... Exchange interaction strength with nearest neighbor The target Hamiltonian can be prepared by regulating the parameters.

[0060] In this embodiment, the measurement system can also prepare the initial state in a single excitation space using a superconducting quantum processor. That is, a superconducting quantum processor can excite only the qubit located in the middle position. It controls the remaining qubits to be in a certain state. This initial state can be obtained by applying a high-fidelity [condition] to the target qubit. The pulse is obtained.

[0061] Alternatively, in addition to the above initial state Furthermore, any non-equilibrium quantum state that can be easily prepared on a superconducting quantum processor can serve as the initial state. For example, the initial state excited at the end of the chain. The initial state, or the initial state of multiple qubits being excited (in which case a model needs to be built and data processed in the corresponding multi-excitation subspace). The choice of the initial state will affect the specific dynamic path, but as long as its evolution is sensitive to the target parameters, it can be applied to this application, and this application does not impose any restrictions on it.

[0062] According to the example embodiment, the measurement system constructs a Bayesian estimation framework based on Bayes' theorem:

[0063] in, The first preset external field parameters, Let be the linear gradient of the potential field corresponding to the i-th parameter in the target domain. The value is known. For the gradient in the linear potential field The next The in-situ potential strength of each qubit; For the first One qubit was measured to be in an excited state, i.e., the measurement result was... The number of times; It is a posterior probability distribution, which integrates prior knowledge and experimental observations to characterize the probability distribution of a given event. The final output of the selected value; It is the likelihood function, which quantifies the likelihood at... When a specific value is taken, the entire dataset is observed. The conditional probability; To represent the prior probability distribution of the external field parameters to be measured, we need to characterize the prior probability distribution of the parameters before acquiring the measurement data. Initial understanding of the value; This is the normalization factor.

[0064] It is understandable that an accurate likelihood function is crucial for achieving high-precision external field parameter estimation. However, in superconducting quantum systems, because the evolution of quantum states often exhibits periodicity or symmetry with parameter changes, at a single evolution time point... Above, different This can lead to identical or extremely similar observation probability distributions, resulting in a "many-to-one" mapping from observation data to the parameter space. Under finite sample conditions, the likelihood function constructed based on data from a single time point... and its corresponding posterior probability distribution It often exhibits multiple local maxima (i.e., multimodal structure), meaning that there are multiple candidate parameter values ​​that are highly compatible with the current data. This multimodal structure directly leads to unstable field parameter measurement results, poor repeatability, and even erroneous convergence that deviates significantly from the true values.

[0065] According to the example embodiment, in step S300, the measurement system performs quantum evolution at multiple preset evolution times on multiple first preset external field parameters based on the target Hamiltonian and the initial state, so as to determine the first quantum state data.

[0066] For example, the measurement system can be used at a series of preset evolution times. Above, each first preset external field parameter is collected. The first quantum state data of the next quantum evolution. The first quantum state data includes the quantum state data of all qubits under this quantum evolution.

[0067] As an example, multiple preset evolution times It can be Time points with uniform intervals. First preset external field parameters. The target domain can be denoted as Furthermore, the preset resolution for discrete sampling in quantum evolution can be... That is, in this embodiment, 30 first preset external field parameters are set. The choice of this domain can fully cover the extended phase and the critical region, and can also involve local phases.

[0068] The measurement system uses a superconducting quantum processor to perform discrete sampling at a preset resolution based on the defined domain, and performs time-dependent evolution for each sample. This is achieved by traversing all the first preset external field parameters within the defined domain. This yields the first quantum state data, which includes all quantum state data.

[0069] Optionally, this application may employ heuristic rules based on dynamic characteristics to determine the evolution time point array. In other embodiments, a preset evolution time may also be generated using uniform time intervals, random sampling, or offline optimization methods based on information gain indices; this application does not impose any limitations on this.

[0070] Figure 3 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application.

[0071] Optionally, such as Figure 3 As shown, step S300 may also include steps S310-S320.

[0072] In step S310, the measurement system performs quantum evolution at each preset evolution time for each first preset external field parameter based on the initial state and the target Hamiltonian.

[0073] For example, the measurement system uses a superconducting quantum processor to start from the initial state. Initially, under the condition of achieving the target Hamiltonian, each first preset external field parameter is subjected to a time period of [duration missing]. Free quantum evolution.

[0074] In step S320, for each preset evolution time, the measurement system performs a preset number of measurements on all qubits under a fixed computational basis to determine the first quantum state data.

[0075] For example, the measurement system uses a superconducting quantum processor under a fixed computational basis (i.e., the computational basis is...). Projection measurements are performed on all qubits. Each projection measurement yields a single excited quantum state. This represents the detection of an excitation at the j-th qubit. For each preset evolution time... The measurement system performs M projection measurements, and the measurement results include the quantum state data of all qubits, thus allowing the determination of the first quantum state data.

[0076] Optionally, the value of M can be much greater than 2. L As an example, M can be 45000.

[0077] According to the example embodiment, in step S400, the measurement system determines the target probability set based on the first quantum state data. The target probability set includes the probability data of the target measurement result at each preset evolution time for each first preset external field parameter.

[0078] For example, the measurement system uses a superconducting quantum processor to record probabilistic data and construct the target probability set. The superconducting quantum processor can statistically obtain the target measurement result at each preset evolution time based on the first quantum state data (e.g., the measurement result satisfies the quantum state condition). The occurrence count of ) is used to construct probability data at the preset evolution time based on the occurrence count.

[0079] Figure 4 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application.

[0080] Optionally, such as Figure 4 As shown, step S400 may also include steps S410-S430.

[0081] In step S410, the measurement system determines the number of times the target measurement result appears at each preset external field parameter based on the first quantum state data.

[0082] In step S420, the measurement system determines the probability data corresponding to the first preset external field parameter and each preset evolution time based on the number of occurrences.

[0083] In step S430, the measurement system traverses the probability data of all first preset external field parameters to determine the target probability set based on the probability data of all first preset external field parameters.

[0084] For example, the measurement system determines the target measurement result based on the first quantum state data. Number of times The total number of measurement data is recorded as follows: The measurement system can then calculate the preset evolution time. The empirical probability of each measurement result satisfy:

[0085] Big In the limit, empirical probability This can be considered as true probability data. .like Figure 2bAs shown, the horizontal axis represents the preset evolution time, and the vertical axis represents the number of the qubit.

[0086] Figure 2b Demonstrated in the form of a two-dimensional quantum walk Under these conditions, all qubits at all predetermined evolution times probability data The current measurement system is in a local phase and exhibits significant Bloch oscillations.

[0087] Finally, the measurement system can be based on the probability data of all the first preset external field parameters. Construct the target probability set .

[0088] It is understandable here that, due to readout errors during quantum evolution, multiple qubits may be in different states. In the case of a state where the particle number is conserved, it is necessary to remove these data through a post-selection process. This would reduce the total number of data available for constructing the target probability set. satisfy: .

[0089] According to the example embodiment, in step S500, the measurement system performs quantum evolution at multiple preset evolution times on the second preset external field parameters based on the target Hamiltonian and the initial state, so as to determine the second quantum state data.

[0090] For example, the second preset field parameters For unknown parameters, the second preset external field parameters This is the linear gradient in the potential field that needs to be estimated.

[0091] For example, the second preset field parameters This is a subset of the target domain. Second preset external field parameters. This is selected based on user requirements within the target domain.

[0092] For example, based on the same measurement principle as the first quantum state data, the measurement system can be used at a series of preset evolution times. Above, collect the second preset external field parameters. The second quantum state data of the next quantum evolution. The second quantum state data includes the quantum state data of all qubits under this quantum evolution.

[0093] It can be understood here that the quantum evolution and the measurement process of the second quantum state data are the same as those of the first quantum state data. Both involve performing free quantum evolution at a preset evolution time and measuring all qubits a preset number of times under a fixed computational basis. This will not be elaborated further here.

[0094] Alternatively, unlike the measurement of first quantum state data, the dynamic evolution of the measurement system is determined by the unknown parameters to be measured. This ensures that the measurement data fully carries the characteristic information of the parameter. Since Bayesian estimation does not require a high number of samples, the number of measurement repetitions M in the measurement of the second quantum state data does not need to be much greater than 2. L .

[0095] Optionally, since the theoretical modeling and analysis of this application are both limited to a single excitation subspace, the measurement system will perform a post-selection operation on the original measurement data to eliminate measurement results that do not conform to the single excitation constraint.

[0096] This setting ensures that the filtered valid count data is strictly confined to the target Hilbert subspace, thus guaranteeing the physical consistency of the subsequent likelihood function construction and effectively avoiding model mismatch problems caused by non-ideal transitions or experimental noise.

[0097] According to the example embodiment, in step S600, the measurement system performs joint time-domain Bayesian estimation based on the target probability set, the second quantum state data, and the Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameters.

[0098] For example, the measurement system uses a classical computing system to integrate measurement information from multiple time points into the same Bayesian estimation framework based on the target probability set, the second quantum state data, and the Bayesian estimation framework. This is achieved through a combination of sequential updates and iterative loops, thereby enabling high-precision estimation of unknown second preset external field parameters.

[0099] Optionally, this application uses the explicit form of Bayesian estimation for joint estimation in the time domain. However, without changing the principle of "jointly utilizing likelihood information across time points", this application can also use numerical inference methods such as numerical maximum a posteriori estimation, importance sampling, and Markov chain Monte Carlo to determine the external field parameters. This application does not impose any restrictions on this.

[0100] Figure 5 This is another schematic flowchart illustrating the method for measuring the external field parameters of a superconducting quantum system according to an embodiment of this application.

[0101] Optionally, such as Figure 5 As shown, step S600 may also include steps S610-S650.

[0102] In step S610, the measurement system determines the initial prior probability distribution in the Bayesian estimation framework.

[0103] For example, the measurement system can be in the parameter space (i.e., the target domain). Initialize a prior probability distribution Because the measurement system has limitations on the external field parameters to be measured. Since there is no prior knowledge, the measurement system can use a uniform distribution as an uninformative prior:

[0104] As an example, , Then the initial prior distribution .

[0105] Alternatively, in addition to a uniform distribution (without prior information), if there is some prior knowledge about the external field parameters to be measured (e.g., preliminary estimates from other low-precision measurements), a Gaussian distribution or other forms of parameterized distribution can be used as the prior distribution, which may accelerate the convergence of the posterior distribution. This application does not impose any restrictions on this.

[0106] In step S620, the measurement system determines the target time. Target time It is a subset of multiple preset evolution times.

[0107] Target time At least including the first target moment Second target time It can also include the third target moment. Fourth target time This application does not impose any restrictions on this.

[0108] For example, the measurement system at a preset evolution time Select at least one target time The target time Used for Bayesian iterative updates. With this configuration, this application uses preset and selected target times. This approach eliminates the need for real-time feedback and enables open-loop data acquisition, fundamentally reducing the dependence of field parameter measurements on real-time hardware control performance.

[0109] What is understandable here is that, for the target time... The selection of [aspect name] must fully consider the time-varying characteristics of the non-equilibrium dynamics of the quantum system. In the initial stage of evolution (target time...) (The system is relatively small), and its state has not been fully developed. Its dynamic response to parameters is weak, resulting in highly similar quantum state probability distributions corresponding to different values. If data is introduced at this stage, the constructed likelihood function will have a flat shape and weak discriminative ability, contributing limitedly to the update of the posterior distribution, making it difficult to effectively distinguish and suppress multimodal structures that may appear in subsequent evolution.

[0110] Optionally, the measurement system determines the target time based on the principles of avoiding initial ambiguity intervals and temporal diversity. .

[0111] For example, based on the principle of avoiding the initial ambiguity interval, the measurement system can proactively skip the "sluggish response zone" in the early stages of evolution. This avoidance threshold can be determined through pre-calibration or numerical simulation, thus avoiding periods with low information density. Based on the principle of temporal diversity, to ensure that the joint likelihood function can effectively dismantle the multi-peak structure, the selected target time... By maintaining appropriate dispersion in the time domain, characteristic responses at different stages of dynamic evolution (such as diffusion, interference, oscillation, etc.) can be captured, and their complementary discriminative capabilities in the parameter space can be utilized.

[0112] With this setup, this application can effectively improve the information efficiency of data collection, laying the foundation for the rapid construction of a discriminative and unambiguous posterior probability distribution through subsequent joint temporal Bayesian estimation.

[0113] In step S630, the measurement system determines the target time based on the first target time. Second quantum state data and target probability set and initial prior probability distribution Determine the first target time The second preset field parameters The first posterior probability distribution.

[0114] For example, the measurement system is based on the first target time. Second quantum state data, target probability set and initial prior probability distribution Determine the first target time likelihood function The measurement system is based on the first target time. likelihood function Determine the second preset external field parameters The first posterior probability distribution.

[0115] For example, at the first target time In the second quantum state data below, each quantum state The number of times it appears is Based on the target probability set probability data in The first preset external field parameters can be obtained and the first target moment Quantum states are obtained from The probability data. Therefore, by combining the current sampling results with the probability data, the probability data at the first target time can be calculated. likelihood function .

[0116] First target moment likelihood function It can satisfy:

[0117] Afterwards, the measurement system will determine the first target time. likelihood function Substituting these parameters into the Bayesian estimation framework described above, the current second preset external field parameters can be calculated. The posterior probability. Traverse all [variables] within the target domain. to obtain all The corresponding posterior probabilities, to form the first posterior probability distribution. .

[0118] In step S640, the measurement system applies the first posterior probability distribution. As the second target moment The prior probability distribution is used to determine the time of the second target. The second preset field parameters The second posterior probability distribution.

[0119] For example, the measurement system will use the first posterior probability distribution As the second target moment The prior probability distribution is used to perform a new round of iterative updates within the Bayesian estimation framework.

[0120] The measurement system is based on the second target time. Second quantum state data, target probability set and the first posterior probability distribution Determine the second target time The likelihood function. The measurement system is based on the second target time. The likelihood function determines the second preset external field parameters. Second posterior probability distribution .

[0121] Similarly, the second posterior probability distribution The calculation process and the first posterior probability distribution The same applies, so I will not repeat it here.

[0122] In step S650, the measurement system traverses all target times to iterate the second preset external field parameters multiple times. The posterior probability distribution is determined until the target posterior probability distribution is determined.

[0123] For example, the measurement system uses the posterior probability distribution obtained in the previous iteration as the prior probability distribution for the next iteration. Through multiple iterations at different target times, the final posterior probability distribution of the target can be obtained. .

[0124] According to the example embodiment, in step S700, the measurement system determines the target field parameters based on the target posterior probability distribution and the second preset field parameters.

[0125] For example, if the maximum value of the target posterior probability distribution is consistent with the second preset field parameter, it indicates that the current parameter estimation has high accuracy. In this case, the measurement system determines the second preset field parameter as the target field parameter, thereby enabling the measurement of the field parameter.

[0126] If the maximum value of the target posterior probability distribution is inconsistent with the second preset external field parameter, it indicates that the current parameter estimation accuracy is poor. In this case, the measurement system selects another second preset external field parameter in the target domain and determines the second quantum state data and performs joint time-domain Bayesian estimation again until the measurement system determines the target external field parameter.

[0127] The dynamical response of a quantum system to its parameters varies at different evolutionary moments. One such system, at the first target moment... A candidate parameter value compatible with the data (i.e., a spurious peak) is very likely to be present at the second target time. This application exhibits a very low probability. Through the fusion iteration mechanism within the aforementioned Bayesian estimation framework, sequential updates and probability multiplication across time points amplify and confirm the probability near the true parameter value using complementary information from multiple time points, while effectively suppressing and eliminating probabilities at spurious peaks. This application can transform an initial, flat, uniform distribution into a concentrated and sharp unimodal distribution.

[0128] Figure 6 A schematic diagram illustrating the posterior probability distribution at a single target time according to an embodiment of this application; Figure 7 A schematic diagram illustrating the posterior probability distribution at two target times according to an embodiment of this application; Figure 8 This diagram illustrates the posterior probability distribution at three target times according to an embodiment of this application.

[0129] in, Figure 6 a- Figure 6 The horizontal axis of c represents the linear gradient in the potential field, and the vertical axis represents the posterior probability of each linear gradient in the potential field at the single-target time. Figure 6 d- Figure 6 The horizontal axis of f represents the actual linear in-potential gradient, and the vertical axis represents the predicted linear in-potential gradient at the single-target time. Figure 7 a- Figure 7 The horizontal axis of c represents the linear gradient in the potential field, and the vertical axis represents the posterior probability of each linear gradient in the potential field under the combination of the two target time points. Figure 7 d- Figure 7 The horizontal axis of f represents the actual linear in-potential gradient, and the vertical axis represents the predicted linear in-potential gradient under the combination of the two target time points. Figure 8 The horizontal axis represents the linear in-potential gradient, and the vertical axis represents the posterior probability of each linear in-potential gradient at the three target time points. Figure 8 The horizontal axis of b represents the actual linear in-potential gradient, and the vertical axis represents the predicted linear in-potential gradient at the three target times.

[0130] For example, such as Figure 6 As shown in a-6c, let... Select a single target time and record it. , and .like Figure 6 As shown in a-6c, the posterior probability distributions all exhibit significant multi-peak or broad-peak structures, with the position of the main peak shifting significantly with time, making it impossible to determine the true parameter positions and resulting in insufficient accuracy in estimating the external parameters. Figure 6 d-6f shows The mean and variance distribution of the parameter estimates within the parameter value range. Figure 6 d-6f indicates that the posterior probability distribution at a single target time has significant uncertainty, making reliable measurement difficult.

[0131] For example, such as Figure 7 As shown in a-7c, two target time combinations are selected, and denoted as... , , .like Figure 7 As shown in a-7c, compared to the single-target time step, the multi-peak structure of the combined posterior probability distribution of two target time steps can be suppressed to some extent, and the distribution pattern tends to be more concentrated. However, obvious competing peaks can still be observed in each combination, the height difference between the main peak and the secondary peak is limited, and the identification of the true parameter position still has multiple solutions, which cannot yet meet the requirements of high-precision estimation. Figure 7 d-7f shows the mean and variance of the parameter estimates under different combinations of target time points. The distribution of [the data]. For example... Figure 7 As shown in d-7f, the estimation results still fluctuate significantly, verifying that the joint estimation at two time points is still insufficient to support reliable parameter identification.

[0132] For example, such as Figure 8 As shown in figure a, three target time combinations are selected, and denoted as... .like Figure 8As shown in Figure a, the joint posterior probability distribution of the three target time points exhibits a single sharp peak shape, all spurious peaks are completely suppressed, and the position of the main peak is stable and clear. That is, the cross-time-point joint strategy provided in this application can significantly enhance parameter resolution and achieve reliable, high-precision field parameter measurements. Figure 8 As shown in b, under the combined effect of the three target times, the estimated value tends to be stationary and consistent throughout the entire parameter interval, and the variance is significantly reduced. Therefore, this application has excellent determinism and robustness.

[0133] according to Figures 6-8 The comparison shows that single-target time-time sampling, due to insufficient dynamic information, leads to a significant multi-peak and broad-peak structure, making it impossible to accurately locate the true parameters. While sampling at two target times can suppress some spurious peaks, strong competing peaks and a wide uncertainty range still exist, making it difficult to meet the measurement accuracy requirements. Only when three typical target times with complementary dynamics are combined for Bayesian estimation and iterative updates can the posterior probability distribution completely converge from a multi-peak structure to a single peak, achieving a significantly improved parameter discrimination capability and high-precision measurement effect.

[0134] The cross-time-point joint Bayesian estimation method proposed in this application can improve the accuracy and reliability of external field parameter measurement in superconducting quantum systems under the constraints of fixed measurement basis and finite sampling resources without introducing real-time feedback control.

[0135] Through the above embodiments, this application provides a method for measuring the external field parameters of a superconducting quantum system, realizing a time-domain joint Bayesian estimation method of "open-loop acquisition at the front end and joint inference at the back end". This application can acquire dynamic data at multiple preset evolution times under a fixed measurement basis and perform time-domain joint Bayesian estimation through a classical computing system, thus solving the problems of high dependence on real-time feedback control and convergence instability caused by multi-peak posterior distribution. This application can achieve stable and high-precision measurement of unknown external field parameters.

[0136] This application abandons the complex and demanding real-time feedback loop, and adopts a strategy of pre-defining a set of target times and performing parallel or sequential open-loop measurements. This open-loop acquisition mode can reduce the dependence on the real-time performance of hardware and avoid the accumulation of feedback errors.

[0137] This application utilizes Bayes' theorem to multiply the likelihood functions of measurement data obtained at different evolutionary times to construct a joint posterior distribution. By leveraging the information complementarity of quantum dynamics in the time dimension, it effectively suppresses the multimodal structure caused by information ambiguity in the posterior probability distribution at a single objective time, ensuring that the joint posterior probability distribution retains only a single globally optimal peak near the true parameters under the common constraint of data from multiple objective times. Unlike estimation methods that simply weight and average independent estimation results at different time points, this application achieves rigorous cross-time point joint inference at the probability space level, fundamentally improving the stability and uniqueness of the estimation results.

[0138] The method for measuring the external field parameters of a superconducting quantum system provided in this application has at least the following characteristics: 1. Reduced hardware dependence and implementation complexity: This application uses open-loop data acquisition, which avoids real-time feedback control, reduces the requirements for control system latency and real-time computing capabilities, and improves engineering feasibility and scalability.

[0139] 2. It can solve the problem of posterior multi-peak structure and improve the stability of estimation: This application can effectively suppress false peaks by using the complementary information of dynamics at different time points through joint estimation in the time domain, and ensure that the estimation results converge stably to a single global optimal solution.

[0140] 3. High-precision measurement can be achieved under realistic constraints: This application can achieve high-precision measurement through time-domain information fusion under the constraints of fixed measurement base, finite coherence time and measurement resources.

[0141] 4. Enhanced robustness in real noise environments: This application uses a time-domain data fusion mechanism to average the effects of random noise and transient interference, making the final estimation results insensitive to experimental fluctuations and noise, thus exhibiting good robustness.

[0142] According to another aspect of this application, this application also provides a superconducting quantum system external field parameter measurement system for measuring external field parameters.

[0143] For example, a superconducting quantum system external field parameter measurement system may include a superconducting quantum system and a classical computing system. The superconducting quantum system may include a superconducting quantum processor.

[0144] For example, external field parameters refer to the strength or amplitude parameters of the physical field applied outside the superconducting quantum system that affects its dynamic behavior. In applications, it typically refers to the strength of the real-world physical field (such as a magnetic field or electric field) being measured. For example, external field parameters may include a linear gradient in the potential field.

[0145] As an example, the external field parameters may include a linear gradient in the potential field.

[0146] It is understood that, in addition to superconducting quantum processors, this application can also be applied to programmable quantum simulation platforms such as ion traps, cold atoms, and solid-state spin, as long as the corresponding system modeling, initial state preparation, and evolution control are realized according to the physical characteristics of the platform. This application does not impose any restrictions on this.

[0147] According to the example embodiment, such as Figure 9 As shown, the superconducting quantum system external field parameter measurement system 1 includes an initialization processing module 10, a data processing module 20, and an external field parameter measurement module 30.

[0148] According to an example embodiment, the initialization processing module 10 performs initialization processing via a superconducting quantum processor to enter a reference state.

[0149] For example, the initialization processing module 10 can respond to user instructions and perform initialization processing through the superconducting quantum processor in a low-temperature dilution cooling environment, such as configuring the frequency of the qubits and calibrating the parameters of the superconducting quantum processor, so that the superconducting quantum system external field parameter measurement system enters the reference state, thereby enabling the measurement system to be in a reference state with high consistency and low noise.

[0150] For example, the initialization process includes, but is not limited to, closed-loop automated optimization of key quantum control parameters such as calibrating the transmission parameters of the readout link, coarsely calibrating the qubit frequency, determining the excitation pulse amplitude, calibrating the reference point of the fundamental quantum state in the IQ plane (the IQ plane: a two-dimensional signal coordinate system plane used to characterize, calibrate, and read out the state of qubits), and frequency. With this configuration, this application allows all qubits to be placed at a preset idle frequency point and suppresses crosstalk between qubits by keeping the coupler channels of the superconducting quantum processor switched off.

[0151] Optionally, during the initialization process, the initialization processing module 10 can also respond to user instructions and perform environmental stability control to suppress the interference of thermal fluctuations and external noise on the initialization consistency.

[0152] For example, environmental stability control includes, but is not limited to, controlling the current ambient temperature within a preset range (e.g., controlling the base temperature of the dilution chiller below 20mK), applying multi-layer electromagnetic shielding, and optimizing filter configuration, etc., and this application does not limit these aspects.

[0153] This application, through initialization processing, establishes a highly reliable quantum state manipulation and measurement benchmark via an integrated calibration protocol and automated optimization program. This provides highly repeatable and low-error starting conditions for subsequent external field parameter measurements and dynamic experiments. Furthermore, through initialization processing and environmental stabilization control, this application maintains high consistency and low noise levels during subsequent external field parameter measurements and dynamic experiments, reducing systematic errors caused by long-term drift of the measurement system or initial configuration deviations.

[0154] According to an example embodiment, based on a baseline state, the data processing module 20 constructs the target Hamiltonian and initial state of the target simulation model using a superconducting quantum processor.

[0155] For example, the target simulation model can be a mathematical model of the physical system to be simulated. The data processing module 20 can use a superconducting quantum processor to control the parameters related to the Hamiltonian, thereby preparing the target Hamiltonian of the target simulation model. Furthermore, the data processing module 20 can apply high-fidelity parameters to the target qubit using the superconducting quantum processor. Pulses are used to prepare the initial state of the target simulation model. .

[0156] For example, the parameter adjustment methods include, but are not limited to, adjusting the operating frequency of each quantum bit and adjusting the frequency of the coupler between neighboring quantum bits, etc., and this application does not limit them.

[0157] As an example, the target simulation model can be a one-dimensional chain lattice system. Taking linear in-potential gradient estimation in a one-dimensional chain lattice system as an example, this one-dimensional chain lattice system consists of L lattice points. Considering only nearest-neighbor interactions, the target Hamiltonian can be defined as:

[0158] in, For the j-th lattice point, For the decrease operator at the j-th lattice point, Let be the nearest neighbor interaction strength between the j-th grid point and the (j+1)-th grid point. Let be the potential strength at the j-th lattice point.

[0159] For example, such as Figure 2a As shown, the target simulation model is a one-dimensional qubit array containing 9 qubits (Q1-Q9), and the size of the target simulation model is denoted as L=9. . Figure 2a In the diagram, the horizontal axis represents the spatial location of the qubit, and the vertical axis (height) represents the applied linear Stark potential. This results in a potential strength of [value missing]. satisfy , The linear gradient in the potential field represents the unknown external field parameter to be measured. The physical system's Hamiltonian will change with... An increase in the ratio, undergoing a transition from the extended phase to the Stark-Wannier localized phase, can contain a wealth of physical phenomena.

[0160] Optionally, in addition to linear in-potential gradient estimation in a one-dimensional chain lattice, the external field parameters to be measured can also be the interaction strength, disorder potential amplitude, amplitude of applied magnetic field or electric field, etc. High-precision estimation of other physical parameters can be achieved simply by adjusting the form of Hamiltonian and the parameter scanning range. This application does not impose any restrictions on this.

[0161] In this embodiment, the data processing module 20 can employ a one-dimensional chain-like superconducting quantum processor with a built-in coupler, and prepare the target Hamiltonian in an analogous quantum simulation manner.

[0162] For example, the data processing module 20 can achieve the potential strength by precisely setting the operating frequency of each quantum bit. Regulation, such as: First, determine a reference frequency. ( (Using the reference frequency), then through frequency biasing, the operating frequency of the j-th qubit is made to satisfy... (in (where j is the operating frequency of the j-th qubit), where , For the first The potential strength of each qubit This represents the linear gradient in the potential field. With this setting, the linear gradient in the potential field... It can be encoded into the frequency space of qubits.

[0163] For example, the data processing module 20 can fix the nearest-neighbor exchange interaction strength by adjusting the frequency of the coupler between nearest-neighbor qubits. With this configuration, the data processing module 20 processes the potential intensity... Exchange interaction strength with nearest neighbor The target Hamiltonian can be prepared by regulating the parameters.

[0164] In this embodiment, the data processing module 20 can also prepare the initial state in a single excitation space using a superconducting quantum processor. That is, a superconducting quantum processor can excite only the qubit located in the middle position. It controls the remaining qubits to be in a certain state. This initial state can be obtained by applying a high-fidelity [condition] to the target qubit. The pulse is obtained.

[0165] Alternatively, in addition to the above initial state Furthermore, any non-equilibrium quantum state that can be easily prepared on a superconducting quantum processor can serve as the initial state. For example, the initial state excited at the end of the chain. The initial state, or the initial state of multiple qubits being excited (in which case a model needs to be built and data processed in the corresponding multi-excitation subspace). The choice of the initial state will affect the specific dynamic path, but as long as its evolution is sensitive to the target parameters, it can be applied to this application, and this application does not impose any restrictions on it.

[0166] According to the example embodiment, the data processing module 20 constructs a Bayesian estimation framework based on Bayes' theorem:

[0167] in, The first preset external field parameters, Let be the linear gradient of the potential field corresponding to the i-th parameter in the target domain. The value is known. For the gradient in the linear potential field The next The in-situ potential strength of each qubit; For the first One qubit was measured to be in an excited state, i.e., the measurement result was... The number of times; It is a posterior probability distribution, which integrates prior knowledge and experimental observations to characterize the probability distribution of a given event. The final output of the selected value; It is the likelihood function, which quantifies the likelihood at... When a specific value is taken, the entire dataset is observed. The conditional probability; To represent the prior probability distribution of the external field parameters to be measured, we need to characterize the prior probability distribution of the parameters before acquiring the measurement data. Initial understanding of the value; This is the normalization factor.

[0168] It is understandable that an accurate likelihood function is crucial for achieving high-precision external field parameter estimation. However, in superconducting quantum systems, because the evolution of quantum states often exhibits periodicity or symmetry with parameter changes, at a single evolution time point... Above, different This can lead to identical or extremely similar observation probability distributions, resulting in a "many-to-one" mapping from observation data to the parameter space. Under finite sample conditions, the likelihood function constructed based on data from a single time point... and its corresponding posterior probability distribution It often exhibits multiple local maxima (i.e., multimodal structure), meaning that there are multiple candidate parameter values ​​that are highly compatible with the current data. This multimodal structure directly leads to unstable field parameter measurement results, poor repeatability, and even erroneous convergence that deviates significantly from the true values.

[0169] According to the example embodiment, the data processing module 20 performs quantum evolution at multiple preset evolution times on multiple first preset external field parameters based on the target Hamiltonian and the initial state, so as to determine the first quantum state data.

[0170] For example, the data processing module 20 can be at a series of preset evolution times. Above, each first preset external field parameter is collected. The first quantum state data of the next quantum evolution. The first quantum state data includes the quantum state data of all qubits under this quantum evolution.

[0171] As an example, multiple preset evolution times It can be Time points with uniform intervals. First preset external field parameters. The target domain can be denoted as Furthermore, the preset resolution for discrete sampling in quantum evolution can be... That is, in this embodiment, 30 first preset external field parameters are set. The choice of this domain can fully cover the extended phase and the critical region, and can also involve local phases.

[0172] Data processing module 20 uses a superconducting quantum processor to perform discrete sampling at a preset resolution based on the defined domain, and performs time-dependent evolution on each sample. This is achieved by traversing all the first preset external field parameters within the defined domain. This yields the first quantum state data, which includes all quantum state data.

[0173] Optionally, this application may employ heuristic rules based on dynamic characteristics to determine the evolution time point array. In other embodiments, a preset evolution time may also be generated using uniform time intervals, random sampling, or offline optimization methods based on information gain indices; this application does not impose any limitations on this.

[0174] Optionally, the data processing module 20 performs quantum evolution at each preset evolution time for each first preset external field parameter based on the initial state and the target Hamiltonian.

[0175] For example, the data processing module 20 uses a superconducting quantum processor to process data from the initial state. Initially, under the condition of achieving the target Hamiltonian, each first preset external field parameter is subjected to a time period of [duration missing]. Free quantum evolution.

[0176] For each preset evolution time, the data processing module 20 performs a preset number of measurements on all qubits under a fixed computational basis to determine the first quantum state data.

[0177] For example, the data processing module 20 uses a superconducting quantum processor to process data under a fixed computational basis (i.e., the computational basis is...). Projection measurements are performed on all qubits. Each projection measurement yields a single excited quantum state. This represents the detection of an excitation at the j-th qubit. For each preset evolution time... The data processing module 20 performs M projection measurements, and the measurement results include the quantum state data of all qubits, thereby determining the first quantum state data.

[0178] Optionally, the value of M can be much greater than 2. L As an example, M can be 45000.

[0179] According to an example embodiment, the data processing module 20 determines a target probability set based on the first quantum state data. The target probability set includes the probability data of the target measurement result at each preset evolution time for each first preset external field parameter.

[0180] For example, the data processing module 20 uses a superconducting quantum processor to record probability data and construct the target probability set. The superconducting quantum processor can statistically obtain the target measurement result at each preset evolution time based on the first quantum state data (e.g., the measurement result satisfies the quantum state condition). The occurrence count of ) is used to construct probability data at the preset evolution time based on the occurrence count.

[0181] Optionally, the data processing module 20 determines the number of times the target measurement result appears at each preset evolution time for each first preset external field parameter based on the first quantum state data.

[0182] The data processing module 20 determines the probability data corresponding to the first preset external field parameter and each preset evolution time based on the number of occurrences.

[0183] The data processing module 20 iterates through the probability data of all the first preset external field parameters to determine the target probability set based on the probability data of all the first preset external field parameters.

[0184] For example, the data processing module 20 determines the target measurement result based on the first quantum state data. Number of times The total number of measurement data is recorded as follows: Then the data processing module 20 can calculate the preset evolution time. The empirical probability of each measurement result satisfy:

[0185] Big In the limit, empirical probability This can be considered as true probability data. .like Figure 2b As shown, the horizontal axis represents the preset evolution time, and the vertical axis represents the number of the qubit.

[0186] Figure 2b Demonstrated in the form of a two-dimensional quantum walk Under these conditions, all qubits at all predetermined evolution times probability data The current measurement system is in a local phase and exhibits significant Bloch oscillations.

[0187] Finally, the data processing module 20 can process the probability data of all the first preset external field parameters. Construct the target probability set .

[0188] It is understandable here that, due to readout errors during quantum evolution, multiple qubits may be in different states. In the case of a state where the particle number is conserved, it is necessary to remove these data through a post-selection process. This would reduce the total number of data available for constructing the target probability set. satisfy: .

[0189] According to the example embodiment, the data processing module 20 performs quantum evolution at multiple preset evolution times on the second preset external field parameters based on the target Hamiltonian and the initial state, so as to determine the second quantum state data.

[0190] For example, the second preset field parameters For unknown parameters, the second preset external field parameters This is the linear gradient in the potential field that needs to be estimated.

[0191] For example, the second preset field parameters This is a subset of the target domain. Second preset external field parameters. This is selected based on user requirements within the target domain.

[0192] For example, based on the same measurement principle as the first quantum state data, the data processing module 20 can perform data processing at a series of preset evolution times. Above, collect the second preset external field parameters. The second quantum state data of the next quantum evolution. The second quantum state data includes the quantum state data of all qubits under this quantum evolution.

[0193] It can be understood here that the quantum evolution and the measurement process of the second quantum state data are the same as those of the first quantum state data. Both involve performing free quantum evolution at a preset evolution time and measuring all qubits a preset number of times under a fixed computational basis. This will not be elaborated further here.

[0194] Alternatively, unlike the measurement of first quantum state data, the dynamic evolution of the measurement system is determined by the unknown parameters to be measured. This ensures that the measurement data fully carries the characteristic information of the parameter. Since Bayesian estimation does not require a high number of samples, the number of measurement repetitions M in the measurement of the second quantum state data does not need to be much greater than 2. L .

[0195] Optionally, since the theoretical modeling and analysis of this application are both limited to a single excitation subspace, the measurement system will perform a post-selection operation on the original measurement data to eliminate measurement results that do not conform to the single excitation constraint.

[0196] This setting ensures that the filtered valid count data is strictly confined to the target Hilbert subspace, thus guaranteeing the physical consistency of the subsequent likelihood function construction and effectively avoiding model mismatch problems caused by non-ideal transitions or experimental noise.

[0197] According to the example embodiment, the external field parameter measurement module 30 performs joint Bayesian estimation in the time domain based on the target probability set, the second quantum state data and the Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameters.

[0198] For example, the external field parameter measurement module 30 uses a classical computing system to integrate measurement information from multiple moments into the same Bayesian estimation framework based on the target probability set, the second quantum state data, and the Bayesian estimation framework, through a combination of sequential updates and iterative loops. This enables high-precision estimation of unknown second preset external field parameters.

[0199] Optionally, this application uses the explicit form of Bayesian estimation for joint estimation in the time domain. However, without changing the principle of "jointly utilizing likelihood information across time points", this application can also use numerical inference methods such as numerical maximum a posteriori estimation, importance sampling, and Markov chain Monte Carlo to determine the external field parameters. This application does not impose any restrictions on this.

[0200] Optionally, the field parameter measurement module 30 determines the initial prior probability distribution in the Bayesian estimation framework.

[0201] For example, the field parameter measurement module 30 can be located in the parameter space (i.e., the target domain). Initialize a prior probability distribution Because the external field parameter measurement module 30 has limitations on the external field parameters to be measured. Since there is no prior knowledge, the external parameter measurement module 30 can use a uniform distribution as an uninformative prior:

[0202] As an example, , Then the initial prior distribution .

[0203] Alternatively, in addition to a uniform distribution (without prior information), if there is some prior knowledge about the external field parameters to be measured (e.g., preliminary estimates from other low-precision measurements), a Gaussian distribution or other forms of parameterized distribution can be used as the prior distribution, which may accelerate the convergence of the posterior distribution. This application does not impose any restrictions on this.

[0204] The external parameter measurement module 30 determines the target time. Target time It is a subset of multiple preset evolution times.

[0205] Target time At least including the first target moment Second target time It can also include the third target moment. Fourth target time This application does not impose any restrictions on this.

[0206] For example, the external parameter measurement module 30 at a preset evolution time Select at least one target time The target time Used for Bayesian iterative updates. With this configuration, this application uses preset and selected target times. This approach eliminates the need for real-time feedback and enables open-loop data acquisition, fundamentally reducing the dependence of field parameter measurements on real-time hardware control performance.

[0207] What is understandable here is that, for the target time... The selection of [aspect name] must fully consider the time-varying characteristics of the non-equilibrium dynamics of the quantum system. In the initial stage of evolution (target time...) (The system is relatively small), and its state has not been fully developed. Its dynamic response to parameters is weak, resulting in highly similar quantum state probability distributions corresponding to different values. If data is introduced at this stage, the constructed likelihood function will have a flat shape and weak discriminative ability, contributing limitedly to the update of the posterior distribution, making it difficult to effectively distinguish and suppress multimodal structures that may appear in subsequent evolution.

[0208] Optionally, the field parameter measurement module 30 determines the target time based on the principles of avoiding initial ambiguity intervals and temporal diversity. .

[0209] For example, based on the principle of avoiding the initial ambiguity interval, the external parameter measurement module 30 can actively skip the "response sluggish region" in the early stage of evolution. This avoidance threshold can be determined through pre-calibration or numerical simulation, thereby avoiding periods with low information density. Based on the principle of temporal diversity, to ensure that the joint likelihood function can effectively dismantle the multi-peak structure, the selected target time... By maintaining appropriate dispersion in the time domain, characteristic responses at different stages of dynamic evolution (such as diffusion, interference, oscillation, etc.) can be captured, and their complementary discriminative capabilities in the parameter space can be utilized.

[0210] With this setup, this application can effectively improve the information efficiency of data collection, laying the foundation for the rapid construction of a discriminative and unambiguous posterior probability distribution through subsequent joint temporal Bayesian estimation.

[0211] The external parameter measurement module 30 measures the parameters based on the first target time. Second quantum state data and target probability set and initial prior probability distribution Determine the first target time The second preset field parameters The first posterior probability distribution.

[0212] For example, the external parameter measurement module 30 measures the first target time. Second quantum state data, target probability set and initial prior probability distribution Determine the first target time likelihood function The external parameter measurement module 30 measures the parameters based on the first target time. likelihood function Determine the second preset external field parameters The first posterior probability distribution.

[0213] For example, at the first target time In the second quantum state data below, each quantum state The number of times it appears is The field parameter measurement module 30 measures the target probability set. probability data in The first preset external field parameters can be obtained and the first target moment Quantum states are obtained from Therefore, the field parameter measurement module 30 combines the current sampling results with the probability data to calculate the probability data at the first target time. likelihood function .

[0214] First target moment likelihood function It can satisfy:

[0215] Subsequently, the field parameter measurement module 30 will measure the first target time. likelihood function Substituting these parameters into the Bayesian estimation framework described above, the current second preset external field parameters can be calculated. The posterior probability. The external parameter measurement module traverses all parameters within the target domain. to obtain all The corresponding posterior probabilities, to form the first posterior probability distribution. .

[0216] The external parameter measurement module 30 will measure the first posterior probability distribution. As the second target moment The prior probability distribution is used to determine the time of the second target. The second preset field parameters The second posterior probability distribution.

[0217] For example, the external parameter measurement module 30 will use the first posterior probability distribution As the second target moment The prior probability distribution is used to perform a new round of iterative updates within the Bayesian estimation framework.

[0218] The external parameter measurement module 30 measures the parameters according to the second target time. Second quantum state data, target probability set and the first posterior probability distribution Determine the second target time The likelihood function. The external field parameter measurement module 30 measures the value based on the second target time. The likelihood function determines the second preset external field parameters. Second posterior probability distribution .

[0219] Similarly, the second posterior probability distribution The calculation process and the first posterior probability distribution The same applies, so I will not repeat it here.

[0220] The external parameter measurement module 30 iterates through all target times, performing multiple iterations on the second preset external parameter. The posterior probability distribution is determined until the target posterior probability distribution is determined.

[0221] For example, the field parameter measurement module 30 uses the posterior probability distribution obtained in the previous iteration as the prior probability distribution for the next iteration. Through multiple iterations at different target times, the target posterior probability distribution can finally be obtained. .

[0222] According to the example embodiment, the field parameter measurement module 30 determines the target field parameters based on the target posterior probability distribution and the second preset field parameters.

[0223] For example, if the maximum value of the target posterior probability distribution is consistent with the second preset field parameter, it indicates that the current parameter estimation has high accuracy. Then, the field parameter measurement module 30 determines the second preset field parameter as the target field parameter, thereby enabling the measurement of the field parameter.

[0224] If the maximum value of the target posterior probability distribution is inconsistent with the second preset external field parameter, it indicates that the current parameter estimation accuracy is poor. In this case, the external field parameter measurement module 30 selects another second preset external field parameter in the target domain and determines the second quantum state data and performs time-domain joint Bayesian estimation again until the external field parameter measurement module 30 determines the target external field parameter.

[0225] The dynamical response of a quantum system to its parameters varies at different evolutionary moments. One such system, at the first target moment... A candidate parameter value compatible with the data (i.e., a spurious peak) is very likely to be present at the second target time. This application exhibits a very low probability. Through the fusion iteration mechanism within the aforementioned Bayesian estimation framework, sequential updates and probability multiplication across time points amplify and confirm the probability near the true parameter value using complementary information from multiple time points, while effectively suppressing and eliminating probabilities at spurious peaks. This application can transform an initial, flat, uniform distribution into a concentrated and sharp unimodal distribution.

[0226] This application can acquire dynamic data at multiple preset evolution times under a fixed measurement basis and perform joint Bayesian estimation in the time domain using a classical computing system. This solves the problems of high dependence on real-time feedback control and convergence instability caused by multi-peak posterior distribution. This application can achieve stable and high-precision measurement of unknown external field parameters.

[0227] This application abandons the complex and demanding real-time feedback loop, and adopts a strategy of pre-defining a set of target times and performing parallel or sequential open-loop measurements. This open-loop acquisition mode can reduce the dependence on the real-time performance of hardware and avoid the accumulation of feedback errors.

[0228] This application utilizes Bayes' theorem to multiply the likelihood functions of measurement data obtained at different evolutionary times to construct a joint posterior distribution. By leveraging the information complementarity of quantum dynamics in the time dimension, it effectively suppresses the multimodal structure caused by information ambiguity in the posterior probability distribution at a single objective time, ensuring that the joint posterior probability distribution retains only a single globally optimal peak near the true parameters under the common constraint of data from multiple objective times. Unlike estimation methods that simply weight and average independent estimation results at different time points, this application achieves rigorous cross-time point joint inference at the probability space level, fundamentally improving the stability and uniqueness of the estimation results.

[0229] The method for measuring the external field parameters of a superconducting quantum system provided in this application has at least the following characteristics: 1. Reduced hardware dependence and implementation complexity: This application uses open-loop data acquisition, which avoids real-time feedback control, reduces the requirements for control system latency and real-time computing capabilities, and improves engineering feasibility and scalability.

[0230] 2. It can solve the problem of posterior multi-peak structure and improve the stability of estimation: This application can effectively suppress false peaks by using the complementary information of dynamics at different time points through joint estimation in the time domain, and ensure that the estimation results converge stably to a single global optimal solution.

[0231] 3. High-precision measurement can be achieved under realistic constraints: This application can achieve high-precision measurement through time-domain information fusion under the constraints of fixed measurement base, finite coherence time and measurement resources.

[0232] 4. Enhanced robustness in real noise environments: This application uses a time-domain data fusion mechanism to average the effects of random noise and transient interference, making the final estimation results insensitive to experimental fluctuations and noise, thus exhibiting good robustness.

[0233] According to another aspect of this application, an electronic device is also provided. The electronic device includes: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, enable the one or more processors to implement the method for measuring the external field parameters of a superconducting quantum system as described above.

[0234] According to another aspect of this application, a non-volatile computer-readable storage medium is also provided. This storage medium stores a computer program that, when executed by a processor, enables the implementation of the method for measuring the external field parameters of a superconducting quantum system as described above.

[0235] Finally, it should be noted that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions of the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for measuring external field parameters of a superconducting quantum system, characterized in that, include: Initialization is performed using a superconducting quantum processor to enter the baseline state; Based on the baseline state, the target Hamiltonian and initial state of the target simulation model are constructed using the superconducting quantum processor; Based on the target Hamiltonian and the initial state, quantum evolution is performed at multiple preset evolution times on multiple first preset external field parameters to determine the first quantum state data; A target probability set is determined based on the first quantum state data. The target probability set includes the probability data of the target measurement result at each preset evolution time for each first preset external field parameter. Based on the target Hamiltonian and the initial state, quantum evolution is performed on the second preset external field parameters at multiple preset evolution times to determine the second quantum state data; Based on the target probability set, the second quantum state data, and the Bayesian estimation framework, perform joint Bayesian estimation in the time domain to determine the target posterior probability distribution corresponding to the second preset external field parameters; The target external field parameters are determined based on the target posterior probability distribution and the second preset external field parameters.

2. The method for measuring external field parameters of a superconducting quantum system according to claim 1, characterized in that, The process of performing quantum evolution at multiple preset evolution times on multiple first preset external field parameters based on the target Hamiltonian and the initial state to determine the first quantum state data includes: Based on the initial state and the target Hamiltonian, quantum evolution is performed at each preset evolution time for each of the first preset external field parameters; For each preset evolution time, all qubits are measured a preset number of times under a fixed computational basis to determine the first quantum state data.

3. The method for measuring external field parameters of a superconducting quantum system according to claim 1, characterized in that, The step of determining the target probability set based on the first quantum state data includes: Based on the first quantum state data, determine the number of times the target measurement result appears at each of the first preset external field parameters at each preset evolution time; Based on the number of occurrences, the probability data corresponding to the first preset external field parameter and each preset evolution time are determined; The probability data of all first preset external field parameters are traversed to determine the target probability set based on the probability data of all first preset external field parameters.

4. The method for measuring external field parameters of a superconducting quantum system according to claim 1, characterized in that, The step of performing joint Bayesian estimation in the time domain based on the target probability set, the second quantum state data, and the Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameters includes: Determine the initial prior probability distribution in the Bayesian estimation framework; A target time is determined, wherein the target time is a subset of the plurality of preset evolution times, and the target time includes at least a first target time and a second target time; Based on the second quantum state data at the first target time, the target probability set, and the initial prior probability distribution, the first posterior probability distribution of the second preset external field parameters at the first target time is determined. Using the first posterior probability distribution as the prior probability distribution of the second target time, the second posterior probability distribution of the second preset external field parameters at the second target time is determined. The posterior probability distribution of the second preset external field parameters is iterated multiple times through all target time points until the target posterior probability distribution is determined.

5. A system for measuring external field parameters of a superconducting quantum system, characterized in that, include: The initialization processing module performs initialization processing through a superconducting quantum processor to enter the reference state; The data processing module, based on the reference state, constructs the target Hamiltonian and initial state of the target simulation model using the superconducting quantum processor. Based on the target Hamiltonian and the initial state, it performs quantum evolution at multiple preset evolution times on multiple first preset external field parameters to determine the first quantum state data. Based on the first quantum state data, it determines the target probability set, which includes the probability data of the target measurement result at each preset evolution time for each first preset external field parameter. Based on the target Hamiltonian and the initial state, it performs quantum evolution at multiple preset evolution times on the second preset external field parameter to determine the second quantum state data. The external field parameter measurement module performs joint Bayesian estimation in the time domain based on the target probability set, the second quantum state data, and the Bayesian estimation framework to determine the target posterior probability distribution corresponding to the second preset external field parameter, and determines the target external field parameter based on the target posterior probability distribution and the second preset external field parameter.

6. The superconducting quantum system external field parameter measurement system according to claim 5, characterized in that, The data processing module performs quantum evolution at each preset evolution time for each of the first preset external field parameters based on the initial state and the target Hamiltonian. For each preset evolution time, the data processing module performs a preset number of measurements on all qubits under a fixed computational basis to determine the first quantum state data.

7. The superconducting quantum system external field parameter measurement system according to claim 5, characterized in that, The data processing module determines the number of times the target measurement result appears at each preset evolution time for each of the first preset external field parameters based on the first quantum state data. The data processing module determines the probability data corresponding to the first preset external field parameter and each preset evolution time based on the number of occurrences. The data processing module iterates through the probability data of all the first preset external field parameters to determine the target probability set based on the probability data of all the first preset external field parameters.

8. The superconducting quantum system external field parameter measurement system according to claim 5, characterized in that, The field parameter measurement module determines the initial prior probability distribution in the Bayesian estimation framework; The field parameter measurement module determines the target time, which is a subset of the plurality of preset evolution times, and the target time includes at least a first target time and a second target time; The external field parameter measurement module determines the first posterior probability distribution of the second preset external field parameter at the first target time based on the second quantum state data at the first target time, the target probability set, and the initial prior probability distribution; The field parameter measurement module uses the first posterior probability distribution as the prior probability distribution of the second target time to determine the second posterior probability distribution of the second preset field parameter at the second target time. The field parameter measurement module iterates through all target times, repeatedly iterating the posterior probability distribution of the second preset field parameter until the target posterior probability distribution is determined.

9. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method for measuring the external field parameters of a superconducting quantum system as described in any one of claims 1-4.

10. A non-volatile computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for measuring the external field parameters of the superconducting quantum system as described in any one of claims 1-4.

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