Quantum state tomography method and apparatus, storage medium

Abstract

This application proposes a quantum state tomography method, apparatus, and storage medium. The quantum state tomography method includes: receiving quantum system specifications and measurement constraints; preparing multiple quantum state replicas based on the quantum system specifications and measurement constraints; analyzing the multiple quantum state replicas based on Hamiltonian evolution to obtain a manifold of a predetermined quantum state; selecting an optimal measurement basis according to the manifold of the predetermined quantum state; acquiring measurement data of the multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set; and generating a compressed measurement protocol based on the compressed measurement set, including: selecting a preset reconstruction algorithm and reconstructing the quantum state density matrix based on the compressed measurement set and the preset reconstruction algorithm. Based on this, this application can exponentially reduce the amount of measurement data, achieve complete state reconstruction of large-scale quantum systems, and ensure reconstruction fidelity.

Description

Technical Field

[0001] This application relates to the field of quantum state tomography (QST), specifically to a quantum state tomography method, apparatus, and storage medium. Background Technology

[0002] Quantum state tomography (QST) is a technique for reconstructing the quantum states of a quantum system through experimental measurements. Its core idea is to statistically analyze the measurement results of a large number of quantum systems prepared under identical conditions to derive the density matrix describing the quantum states, i.e., the quantum state density matrix, thus providing a complete characterization of the quantum system's state. QST is widely used in quantum computing, quantum communication, and quantum sensing, for example, to verify the performance of quantum processors, characterize entangled states, or optimize quantum algorithms. However, traditional QST methods involve measurements under all measurement bases and reconstructing the quantum state density matrix from the obtained measurement data. This leads to the problem that the measurement data for QST grows exponentially with the system size, making the complete reconstruction of the state of large-scale quantum systems impractical. Summary of the Invention

[0003] In view of this, this application provides a quantum state tomography method, apparatus, and storage medium, which can improve the problem that the amount of measurement data in existing quantum state tomography methods increases exponentially with the system size.

[0004] This application provides a quantum state tomography method, comprising: Receive quantum system specifications and measurement constraints; Multiple copies of the quantum state were prepared based on the quantum system specifications and measurement constraints. Based on Hamiltonian evolution principle, multiple quantum state copies are analyzed to obtain the manifold of the predetermined quantum state; The optimal measurement basis is selected based on the manifold of the preset quantum state; Acquire measurement data from multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set; The compressed measurement protocol is generated based on the compressed measurement set, including: selecting a preset reconstruction algorithm, and reconstructing the quantum state density matrix based on the compressed measurement set and the preset reconstruction algorithm.

[0005] Optionally, the preparation of multiple quantum state copies based on the quantum system specifications and measurement constraints includes: The type of quantum platform is determined and the physical parameters of the quantum system are obtained according to the quantum system specification. The environmental control parameters are obtained based on the measurement constraints. The quantum platforms of the type described above simulate the quantum states of various quantum sources under the physical and environmental control parameters to generate multiple independent copies of quantum states, wherein the quantum states of the same quantum source are identical. Select quantum state replicas that meet the replica quality index from the generated quantum state replicas.

[0006] Optionally, the physical parameters include at least one of decoherence time, energy level structure, and entanglement characteristics.

[0007] Optionally, the environmental control parameters include at least one of temperature, electromagnetic shielding parameters, and frequency stability.

[0008] Optionally, the replica quality metrics include at least one of quantum state fidelity, trace distance, and average fidelity.

[0009] Optionally, the step of analyzing multiple quantum state copies based on the Hamiltonian evolution principle to obtain the manifold of the predetermined quantum state includes: Acquire measurement data for each quantum state replica across multiple measurement bases; A density matrix is ​​reconstructed based on the measurement data; Based on the Hamiltonian evolution principle, predetermined quantum states with the smallest distance between each other are selected from the density matrix to form the Hamiltonian density matrix; The manifold obtained through the Hamiltonian density matrix is ​​used as the manifold for the predetermined quantum state.

[0010] Optionally, the predetermined quantum state is a state in which the quantum state is collapsed to a neighboring ground state and excited state by a microwave pulse.

[0011] Optionally, selecting the optimal measurement basis based on the manifold of the preset quantum state includes: The manifold of the preset quantum state is represented as real parameters; Fisher information is calculated based on the real parameters; Multiple measurement bases are used as points on the Stiefel manifold; Riemann gradient ascent is performed on the Stiefel manifold to obtain the measurement basis when Fisher information is maximized, and this basis is used as the optimal measurement basis.

[0012] Optionally, acquiring measurement data from multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set includes: Measurement data of multiple quantum state replicas under the optimal measurement basis are acquired, and measurement data corresponding to the quantum state density matrix that can achieve quantum state fidelity are selected to form a compressed measurement set.

[0013] Optionally, the preset reconstruction algorithm includes at least one of the following: a classical reconstruction algorithm based on linear regression estimation, a reconstruction algorithm based on quantum parallelism for linear regression, a Bayesian inference algorithm, and a minimum variance estimation algorithm.

[0014] This application provides a quantum state tomography device, including a processor and a memory. The memory stores a quantum state tomography program, which, when executed by the processor, is used to implement the steps of the quantum state tomography method described above.

[0015] This application provides a storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-described quantum state tomography methods.

[0016] As described above, this application obtains measurement data of multiple quantum state replicas under the optimal measurement basis to reconstruct the quantum state density matrix. That is, measurements are performed only under the optimal measurement basis, rather than reconstructing the quantum state density matrix based on measurement data under all measurement basis. Therefore, the amount of measurement data can be reduced exponentially, which is beneficial for achieving complete state reconstruction of large-scale quantum systems. In addition, this application analyzes multiple quantum state replicas based on the Hamiltonian evolution principle to obtain the manifold of the predetermined quantum state. The Hamiltonian evolution principle uses the shortest path to simulate and reconstruct the manifold of the predetermined quantum state based on multiple quantum state replicas. The resulting manifold is smaller and can completely represent the quantum state of the entire system. The optimal measurement basis selected based on the manifold of the predetermined quantum state is smaller and can completely cover the entire Hilbert space, thereby completely reconstructing the quantum state information. Attached Figure Description

[0017] Figure 1 This is a schematic flowchart of a quantum state tomography method according to an embodiment of this application; Figure 2 This is a schematic diagram of the process for obtaining a copy of a quantum state according to an embodiment of this application; Figure 3 This is a schematic flowchart illustrating the process of obtaining a manifold of a predetermined quantum state according to an embodiment of this application; Figure 4 This is a schematic diagram of the process for selecting the optimal measurement base according to an embodiment of this application; Figure 5 This is a schematic diagram of the structure of a quantum state tomography apparatus according to an embodiment of this application. Detailed Implementation

[0018] Traditional quantum state tomography methods perform measurements across all measurement bases, resulting in an exponential increase in measurement data with system size. Consequently, the computational complexity for reconstructing the quantum state density matrix from this data is enormous. To address the aforementioned problems in the prior art, this application provides a quantum state tomography method, apparatus, and storage medium. These protected subjects are based on the same concept, and their principles for solving the problems are essentially the same or similar. The implementation methods of each protected subject can be referred to mutually, and repeated details are omitted.

[0019] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly described below in conjunction with specific embodiments and corresponding drawings. Obviously, the embodiments described below are only a part of the embodiments of this application, and not all of them. Unless otherwise specified, the following embodiments and their technical features can be combined with each other, and also belong to the technical solutions of this application.

[0020] Figure 1 This is a schematic flowchart of a quantum state tomography method according to an embodiment of this application. The quantum state tomography method can also be simply referred to as a "method" or "tomography method". The execution subject of each step of the method can be an appropriate quantum state tomography device, an electronic terminal such as a computer that performs quantum state tomography, or a storage medium, processor, controller, etc. with quantum state tomography function.

[0021] like Figure 1 As shown, the method includes at least the following steps S1 to S6.

[0022] S1, receiving quantum system specifications and measurement constraints.

[0023] The so-called quantum system specification refers to a series of standard frameworks and requirements for building quantum systems that meet the requirements, including but not limited to quantum hardware specifications, quantum software and algorithm standards, quantum network and communication specifications, quantum security standards, and testing, verification and application frameworks.

[0024] Quantum hardware specifications define the design requirements for qubit selection, quantum processor architecture, and coupling methods between qubits. They also specify the physical parameters of the quantum system (such as the number of qubits, decoherence time of quantum states, error rate or fault tolerance, energy level structure, and entanglement properties) and the type of quantum platform (i.e., the physical implementation platform). A qubit, also known as a physical qubit, is the fundamental information unit in a quantum system. Quantum systems record information through the quantum states (i.e., superposition states) and entanglement properties of qubits. Unlike traditional bits, which can only be in a single state of 0 or 1, a qubit can simultaneously represent a superposition state of 0 and 1, i.e., |ψ|. = α|0 + β|1 , where α and β are complex probability amplitudes, satisfying |α| 2 + |β| 2 = 1. This superposition property allows a single qubit to encode multiple information states in parallel, thus far exceeding the information storage density of classical storage devices. Taking quantum memory as an example, a quantum system can include multiple storage units, and a single storage unit has multiple qubits. Therefore, the physical parameters of a quantum system include at least the storage capacity of the quantum memory to be designed, through which the number of qubits can be determined. The coherence time of the quantum state refers to the duration for which the quantum state of the qubit remains stable. The error rate refers to the minimum error rate operation allowed to maintain the integrity of quantum information. Generally, the error rate can be less than 0.1%. The physical implementation platform refers to the hardware device that can store quantum states (such as a superposition of 0 and 1) in a real physical system. This hardware device needs to meet two core conditions: first, there are two mutually orthogonal quantum states, i.e., |0| = 1. and |1 Secondly, it can prepare and maintain any superposition state of these two quantum states. In practical scenarios, the physical realization platform can trap ions with electromagnetic fields, use their energy levels as qubits, and achieve storage through laser manipulation, or construct qubits based on solid-state devices such as Josephson junctions.

[0025] The quantum software and algorithm standard specifies the design, optimization, and evaluation of quantum algorithms to improve their efficiency and versatility. It also specifies the standardized quantum programming languages ​​and development tools to ensure cross-platform portability and provides performance evaluation and optimization strategies.

[0026] Quantum network and communication specifications define communication and collaboration between quantum computers, including requirements for qubit transmission and entanglement sharing. For example, in quantum communication, the security principle of quantum key distribution (QKD) is emphasized, key generation is achieved using the superposition and entanglement properties of quantum states, and standards for constructing quantum channels are specified to address channel loss and noise issues.

[0027] Quantum security standards specify measures such as quantum key distribution and quantum cryptography to prevent information leakage and attacks. For example, based on the principle of quantum state collapse, any eavesdropping will be detected.

[0028] The testing, verification, and application framework specifies the testing methods, verification procedures, and application scenarios for quantum systems.

[0029] The measurement constraint refers to the external environmental parameters specified for the constructed quantum system. The measurement constraint at least specifies the external environment in which the constructed quantum system operates. The external environmental parameters include, but are not limited to, at least one of temperature, electromagnetic shielding parameters, and frequency stability.

[0030] S2. Multiple copies of quantum states are prepared based on quantum system specifications and measurement constraints.

[0031] A quantum state replica is a set of multiple identical and independent quantum states created from an unknown quantum state. Due to the collapse effect of quantum states, quantum measurements are irreversible; therefore, a single measurement cannot obtain complete information about the quantum state, and parallel measurements must be performed using a large number of identical and independent quantum state replicas. Figure 2 As shown, the method for obtaining a copy of the quantum state includes the following steps S21 to S24.

[0032] S21. Determine the type of quantum platform and obtain the physical parameters of the quantum system according to the quantum system specification. The physical parameters include at least one of the following: decoherence time, energy level structure, and entanglement properties.

[0033] S22. Obtain environmental control parameters based on measurement constraints. These environmental control parameters include, but are not limited to, temperature, electromagnetic shielding parameters (e.g., setting up a shield to attenuate the external electromagnetic field by 99% or more), and frequency stability (e.g., less than 1*10). -12 At least one of the following: (per second) and vacuum degree.

[0034] S23. Using a quantum platform of the type described above, the quantum states of each quantum source are simulated under the physical and environmental control parameters to generate multiple independent copies of the quantum states, wherein the quantum states of the same quantum source are identical. In other words, the constructed quantum state generator precisely replicates the initial quantum state to be measured under the same physical and environmental control parameters.

[0035] S24. From the generated quantum state replicas, select quantum state replicas that meet the replica quality index. The replica quality index includes at least one of quantum state fidelity, trace distance, and average fidelity.

[0036] Through relational formulas This is used to measure the similarity between the quantum state of the copy (which can be called the experimental state) and the target quantum state (which can be called the target state) to determine the quantum state fidelity. Indicating similarity, It is an abbreviation for Trace, which represents the summation of the diagonal elements of a square matrix in linear algebra. It reflects the degree of overlap between the experimental state and the target state in Hilbert space. The density matrix representing the target quantum state. The density matrix representing the quantum states of a copy. The closer the value is to 1, the higher the fidelity of the quantum state. Therefore, a value close to 1 is set as the corresponding replica quality index.

[0037] Through relational formulas This is used to obtain the trace distance. This represents the trace distance between the experimental state and the target state, with values ​​ranging from 0 to 1. Smaller values ​​indicate closer proximity between the two states. , and The mathematical definition of is similar to the aforementioned calculation. The same applies at that time. Therefore, a value between 0 and 1 is set as the corresponding replica quality indicator.

[0038] Average fidelity refers to the average fidelity of possible initial quantum states in quantum state space (i.e., Hilbert space).

[0039] This replica quality index ensures the fidelity of the quantum state replica obtained in step S2, thereby ensuring the fidelity of the final compressed measurement protocol.

[0040] S3. Analyze multiple quantum state copies based on the Hamiltonian evolution principle to obtain the manifold of the predetermined quantum state.

[0041] S4. Select the optimal measurement basis based on the manifold of the preset quantum state.

[0042] In one example, the predetermined quantum state is a state in which the quantum state is collapsed into the neighboring ground and excited states by a microwave pulse.

[0043] Combination Figure 3 As shown, the method for obtaining a manifold with a predetermined quantum state includes the following steps S31 to S34.

[0044] S31. Obtain measurement data for each quantum state replica under multiple measurement bases; S32. Reconstruct a density matrix based on the measurement data; S33. Based on the Hamiltonian evolution principle, select the predetermined quantum states with the smallest distance between each other from the density matrix to form the Hamiltonian density matrix; S34. The manifold obtained through the Hamiltonian density matrix is ​​used as the manifold of the predetermined quantum state.

[0045] Multiple measurement bases are a set of reference standards used to reconstruct a preset quantum state, or in other words, measurement methods selected when reconstructing the preset quantum state. These include, but are not limited to, any combination of Pauli bases (including Pauli-X, Pauli-Y, and Pauli-Z bases) and computational bases. The reference standards are used to determine the size, shape, and position of each quantum state replica under each reference standard. Step S31 involves performing corresponding measurements (i.e., calculations) under these reference standards, specifically the results obtained by performing projection measurements on the quantum state replica using multiple different measurement bases, which serve as measurement data. The principles and processes of measuring the quantum state replica under multiple measurement bases can be found in existing technologies in this field.

[0046] In step S32, through the relational expression The density matrix is ​​obtained, where, This represents the probability of the i-th measurement data, with a value ranging from 0 to 1, i.e., within the measurement baseline. The measurement basis is obtained when a copy of the quantum state is measured. The corresponding statistical probability value describes the measurement basis when multiple copies of the same quantum state are repeatedly measured. The statistical frequency of obtaining a specific result. This represents the projection operator corresponding to the i-th measurement basis. Represents the density matrix, Indicates measurement base The expected value under a quantum state copy. This is determined by different measurement bases. } The probability of obtaining { Construct a system of linear equations and solve it inversely. This allows the expected value in the quantum state copy to match the experimental data, thus enabling the reconstruction of the quantum state.

[0047] In step S33, the Hamiltonian evolution principle refers to selecting a preset quantum state with the shortest path from the density matrix. Then, a density matrix, called the Hamiltonian density matrix, is reconstructed based on the measurement data corresponding to the selected preset quantum state. The process of the Hamiltonian evolution principle can be found in existing technologies in this field.

[0048] In step S34, the set of Hamiltonian density matrices constitutes the manifold of the predetermined quantum states. The construction of this manifold is a mathematical process that transitions from algebraic representation (i.e., density matrix) to geometric and topological structures. This process can be performed using existing techniques in the art, such as differential geometry or Lie group theory. The manifold of the predetermined quantum states is a mathematical abstract description of the spatial structure formed by all predetermined quantum states. It is a complex projective space spanned by normalized state vectors in Hilbert space. The geometric space defined by this manifold represents the distances, curvatures, and topological properties between predetermined quantum states. Each copy of a quantum state is a physical realization of each point on the manifold (i.e., the complex projective space).

[0049] This application compresses the manifold obtained based on multiple quantum state copies through step S3.

[0050] Combination Figure 4 As shown, step S4, which selects the optimal measurement basis, includes the following steps S41 to S44.

[0051] S41. Represent the manifold of the preset quantum state as real parameters; S42. Calculate Fisher information based on the real parameters; S43. Treat multiple measurement bases as points on the Stiefel manifold; S44. Perform Riemann gradient ascent on the Stiefel manifold to obtain the measurement basis when Fisher information is maximized, and use it as the optimal measurement basis.

[0052] Step S41 involves parameterizing the density matrix corresponding to the manifold of the preset quantum state, representing it as multiple real parameters, thereby obtaining a real parameter space of a preset dimension, which constitutes the local coordinate system of the manifold; Step S42 calculates the Fisher information matrix based on these real parameters. The trace of this Fisher information matrix can directly quantify the estimation accuracy of the measurement basis for the real parameters and is a mathematical tool for measuring the information gain of the measurement basis; the measurement basis set { The array, composed of unitary operators, forms a Stiefel manifold; therefore, step S43 involves combining multiple measurement bases. } are considered as points on the Stiefel manifold; in order to maintain the unitary constraint, step S44 uses Riemann optimization, which can be regarded as using Riemann gradient ascent to optimize the Stiefel manifold and obtain the measurement basis when the Fisher information is maximized (i.e. the trace of the Fisher information matrix is ​​maximized), which is used as the optimal measurement basis.

[0053] S5. Obtain measurement data of multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set.

[0054] In one example, measurement data of multiple quantum state replicas are acquired under the optimal measurement basis, and measurement data corresponding to the quantum state density matrix that achieves quantum state fidelity are selected to form a compressed measurement set. That is, after obtaining measurement data under the optimal measurement basis, the corresponding quantum state fidelity is calculated based on the density matrix of each preset quantum state, for example, through the aforementioned relationship. The results are calculated, and then each quantum state fidelity is compared with the target quantum state fidelity. The quantum state fidelity that achieves the target quantum state fidelity is selected, and finally the measurement data corresponding to the density matrix is ​​used to form a compressed measurement set.

[0055] Therefore, through the aforementioned screening, the fidelity of the measurement data obtained in step S5 can be ensured, thereby ensuring the fidelity of the final compressed measurement protocol. Furthermore, the compressed measurement set obtained through screening is a specific set of measurement data obtained under the premise of satisfying quantum state sparsity, which is far less than the measurement data obtained by traditionally using all measurement bases, thus exponentially reducing the amount of measurement data.

[0056] S6. Generate a compressed measurement protocol based on the compressed measurement set, including: selecting a preset reconstruction algorithm, and reconstructing the quantum state density matrix based on the compressed measurement set and the preset reconstruction algorithm.

[0057] In one example, the preset reconstruction algorithm includes, but is not limited to, at least one of the following: a classical reconstruction algorithm based on linear regression estimation, a reconstruction algorithm based on quantum parallelism for linear regression, a Bayesian inference algorithm, and a minimum variance estimation algorithm. The principles and processes by which these algorithms construct the quantum density of states matrix can be found in existing technologies.

[0058] Based on steps S1 to S6 above, this application obtains measurement data of multiple quantum state replicas under the optimal measurement basis to reconstruct the quantum state density matrix. That is, measurements are performed only under the optimal measurement basis, rather than reconstructing the quantum state density matrix based on measurement data under all measurement basis. Therefore, the measurement data can be reduced exponentially, which is beneficial for realizing the complete state reconstruction of large-scale quantum systems. In practical scenarios, the quantum state tomography method executed based on the compressed measurement protocol of this application can reduce the measurement data by at least 60% compared with the traditional quantum state tomography method. In addition, this application analyzes multiple quantum state replicas based on the Hamiltonian evolution principle to obtain the manifold of the predetermined quantum state. The Hamiltonian evolution principle uses the shortest path to simulate and reconstruct the manifold of the predetermined quantum state based on multiple quantum state replicas. The manifold obtained in this way is smaller and can completely represent the quantum state of the entire system. The optimal measurement basis selected based on the manifold of the predetermined quantum state is smaller and can completely cover the entire Hilbert space, thereby completely reconstructing the quantum state information.

[0059] This application embodiment also provides a storage medium storing a quantum state tomography program, which is essentially a computer program, and when executed by a processor, implements the steps of a quantum state tomography method as in any example.

[0060] The storage medium includes, but is not limited to, any one of read-only memory (ROM), random access memory (RAM), magnetic disk, and optical disk.

[0061] Since the program stored in the storage medium can execute the steps in the quantum state tomography method of any embodiment provided in this application, the beneficial effects that the quantum state tomography method of any of the foregoing embodiments can achieve can be realized, as detailed in the foregoing embodiments, which will not be repeated here.

[0062] This application also provides a quantum state tomography device or chip, including a memory and a processor. The memory stores a quantum state tomography program, which, when executed by the processor, implements the steps of the quantum state tomography method of any of the foregoing embodiments; and / or, the quantum state tomography device or chip is provided with a storage medium as shown in the above example, and the processor loads the storage medium to execute the steps of the quantum state tomography method, thereby achieving the beneficial effects that the quantum state tomography method of the corresponding embodiment can achieve.

[0063] Figure 5 This is a schematic diagram of the structure of a quantum state tomography device provided in an embodiment of this application. Figure 5 As shown, the quantum state tomography device 50, which can also be simply referred to as device 50, includes: Receiver module 51 is used to receive quantum system specifications and measurement constraints; The first generation module 52 is used to prepare multiple copies of quantum states based on quantum system specifications and measurement constraints; The second generation module 53 is used to analyze multiple quantum state copies based on the Hamiltonian evolution principle to obtain a manifold of a predetermined quantum state; Selection module 54 is used to select the optimal measurement basis according to the manifold of the preset quantum state; Measurement module 55 is used to acquire measurement data of multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set; The reconstruction module 56 is used to generate a compressed measurement protocol based on the compressed measurement set, including: selecting a preset reconstruction algorithm, and reconstructing the quantum state density matrix based on the compressed measurement set and the preset reconstruction algorithm.

[0064] It should be understood that the various modules of the device 50 described above can be represented as physical devices or virtual modules (i.e., modules in general) in a real-world scenario. A module can be implemented by a single physical device or by two or more physical devices working together. Similarly, the function performed by a module can be implemented by a single physical device or by two or more physical devices working together. Furthermore, the functions corresponding to each module can be implemented by the corresponding steps of the quantum state tomography method of any of the foregoing embodiments.

[0065] The above are only some embodiments of this application and do not limit the patent scope of this application. For those skilled in the art, any equivalent structural transformations made using the content of this specification and drawings are similarly included within the patent protection scope of this application.

[0066] The use of step designations such as S1 and S2 in this document is intended to more clearly and concisely describe the corresponding content and does not constitute a substantial restriction on the order. In specific implementation, those skilled in the art may execute S2 first and then S1, etc., but these should all be within the scope of protection of this application.

[0067] Although this document uses terms such as "first," "second," etc., to describe various types of information, this information should not be limited to these terms. These terms are only used to distinguish information of the same type from one another. Furthermore, the singular forms "a," "an," and "the" are intended to also include the plural forms. The terms "or" and "and / or" are interpreted as inclusive, or meaning either one or any combination thereof. Exceptions to this definition only arise when combinations of elements, functions, steps, or operations are inherently mutually exclusive in some way.

Claims

1. A quantum state tomography method, characterized in that, include: Receive quantum system specifications and measurement constraints; Multiple copies of the quantum state were prepared based on the quantum system specifications and measurement constraints. Based on Hamiltonian evolution principle, multiple quantum state copies are analyzed to obtain the manifold of the predetermined quantum state; The optimal measurement basis is selected based on the manifold of the preset quantum state; Acquire measurement data from multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set; The compressed measurement protocol is generated based on the compressed measurement set, including: selecting a preset reconstruction algorithm, and reconstructing the quantum state density matrix based on the compressed measurement set and the preset reconstruction algorithm.

2. The method according to claim 1, characterized in that, The preparation of multiple quantum state copies based on the quantum system specifications and measurement constraints includes: The type of quantum platform is determined and the physical parameters of the quantum system are obtained according to the quantum system specification. The environmental control parameters are obtained based on the measurement constraints. The quantum platforms of the type described above simulate the quantum states of various quantum sources under the physical and environmental control parameters to generate multiple independent copies of quantum states, wherein the quantum states of the same quantum source are identical. Select quantum state replicas that meet the replica quality index from the generated quantum state replicas.

3. The method according to claim 2, characterized in that, The physical parameters include at least one of decoherence time, energy level structure, and entanglement properties; The environmental control parameters include at least one of temperature, electromagnetic shielding parameters, and frequency stability. The replica quality metrics include at least one of quantum state fidelity, trace distance, and average fidelity.

4. The method according to claim 1, characterized in that, The method of analyzing multiple quantum state copies based on the Hamiltonian evolution principle to obtain a manifold of a predetermined quantum state includes: Acquire measurement data for each quantum state replica across multiple measurement bases; A density matrix is ​​reconstructed based on the measurement data; Based on the Hamiltonian evolution principle, predetermined quantum states with the smallest distance between each other are selected from the density matrix to form the Hamiltonian density matrix; The manifold obtained through the Hamiltonian density matrix is ​​used as the manifold for the predetermined quantum state.

5. The method according to claim 4, characterized in that, The predetermined quantum state is a state in which the quantum state is collapsed into the neighboring ground state and excited state by microwave pulses.

6. The method according to any one of claims 1, 4, and 5, characterized in that, The step of selecting the optimal measurement basis based on the manifold of the preset quantum state includes: The manifold of the preset quantum state is represented as real parameters; Fisher information is calculated based on the real parameters; Multiple measurement bases are used as points on the Stiefel manifold; Riemann gradient ascent is performed on the Stiefel manifold to obtain the measurement basis when Fisher information is maximized, and this basis is used as the optimal measurement basis.

7. The method according to claim 1, characterized in that, The step of acquiring measurement data from multiple quantum state replicas under the optimal measurement basis to form a compressed measurement set includes: Measurement data of multiple quantum state replicas under the optimal measurement basis are acquired, and measurement data corresponding to the quantum state density matrix that can achieve quantum state fidelity are selected to form a compressed measurement set.

8. The method according to claim 1 or 7, characterized in that, The preset reconstruction algorithm includes at least one of the following: a classical reconstruction algorithm based on linear regression estimation, a reconstruction algorithm based on quantum parallelism for linear regression, a Bayesian inference algorithm, and a minimum variance estimation algorithm.

9. A quantum state chromatography apparatus, characterized in that, It includes a processor and a memory, the memory storing a quantum state tomography program, which, when executed by the processor, implements the steps of the quantum state tomography method as described in any one of claims 1 to 8.

10. A storage medium, characterized in that, The device contains a computer program that, when executed by a processor, implements the steps of the method as described in any one of claims 1 to 8.

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