Quantum state chromatography method and device, electronic equipment and computer readable storage medium
By selecting measurement operators and using gradient descent to update the complex matrix, the problems of high computational cost and low accuracy in high-dimensional quantum systems are solved, achieving efficient quantum state reconstruction, which is applicable to high-dimensional quantum systems.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-11-13
- Publication Date
- 2026-03-13
AI Technical Summary
Existing quantum state tomography methods are computationally expensive, have slow convergence, and are complex to handle physical constraints in high-dimensional systems, resulting in low reconstruction accuracy. Traditional reconstruction algorithms do not consider error models and are susceptible to decoherence and control errors.
We employ a method of selecting a set of measurement operators for qubit measurement, randomly initializing the complex matrix, calculating the density matrix, updating the complex matrix using a loss function and gradient descent, constructing the density matrix, introducing a sparse regularization term to improve noise resistance, avoiding projection operations, and reducing computational complexity.
It reduces computational costs, improves computational speed and reconstruction accuracy, and is suitable for efficient quantum state reconstruction in high-dimensional quantum systems.
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Figure CN121660118A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of quantum computing technology, and in particular to a quantum state tomography method, apparatus, electronic device, and computer-readable storage medium. Background Technology
[0002] Quantum state tomography is a method that reconstructs the complete state (density matrix) of an unknown quantum system through experimental measurements. The core idea is to use the principle of linear superposition of quantum states and the statistical nature of measurement to infer all the information of the quantum state from the measurement data under multiple measurement bases (measurement operators).
[0003] Quantum state tomography plays a crucial role in quantum computing, serving as a core tool for performance diagnosis and quality control. It directly impacts the research, optimization, and practical application of quantum processors. For example, quantum state tomography can precisely quantize the coherence and decoherence of qubits, assess the fidelity of quantum gate operations, diagnose qubit crosstalk and crosstalk suppression, verify the evolution of quantum states, evaluate the performance of quantum error correction codes, guide iterative optimization of quantum hardware, and accelerate the expansion of multi-qubit systems. Through the complete characterization of quantum states, quantum state tomography provides end-to-end support from qubit quality control to algorithm verification and hardware iterative optimization, making it indispensable in quantum computing.
[0004] In existing quantum state tomography methods, the parameters of the density matrix grow exponentially with the dimension of the quantum system, resulting in high time complexity for traditional reconstruction algorithms. Furthermore, high-dimensional systems require more measurement data to suppress statistical noise; if the number of measurements is insufficient, the reconstructed density matrix may contain non-physical eigenvalues (such as negative eigenvalues), necessitating additional correction by projection onto a positive definite cone, further increasing computational time. Finally, the physical realization of high-dimensional systems is susceptible to decoherence and control errors, leading to systematic errors in the measurement data. Traditional reconstruction algorithms do not consider error models, further reducing reconstruction accuracy. Therefore, existing quantum state tomography methods suffer from high computational cost, slow convergence, and complex handling of physical constraints in high-dimensional systems. Summary of the Invention
[0005] This application provides a quantum state tomography method, apparatus, electronic device, and computer-readable storage medium, which can reduce the computational cost of quantum state tomography, improve computational speed, and enhance reconstruction accuracy.
[0006] A first aspect of this application provides a quantum state tomography method, the method comprising: The expected experimental measurement value is obtained by measuring the qubit according to a selected set of measurement operators; Randomly initialize a complex matrix, and calculate a density matrix based on the complex matrix; The loss function value is calculated based on the density matrix, the measurement operator, and the expected value of the experimental measurement. If the loss function value is less than the preset loss function convergence threshold, then a density matrix is constructed based on the complex matrix.
[0007] Optionally, the method further includes: If the loss function value is greater than or equal to a preset loss function convergence threshold, then the complex matrix is updated based on the loss function value and gradient descent, and the step of calculating the density matrix based on the complex matrix is executed.
[0008] Optionally, updating the complex matrix based on the loss function value and gradient descent includes: The momentum estimate in the current iteration step is calculated based on the preset momentum decay coefficient, the momentum estimate in the previous iteration step, and the gradient corresponding to the loss function value. The second moment estimate in the current iteration step is calculated based on the preset root mean square propagation attenuation coefficient, the second moment estimate in the previous iteration step, and the gradient corresponding to the loss function value. The momentum estimate and second moment estimate in the current iteration step are corrected respectively; The complex matrix in the current iteration step is calculated based on the corrected momentum estimate and second moment estimate, the preset numerical stability constant and learning rate, and the complex matrix in the previous iteration step. The complex matrix in the current iteration step is used as the complex matrix in the previous iteration step to update the complex matrix.
[0009] Optionally, the method further includes: The number of iterations is determined based on the current iteration step number; If the number of iterations is greater than the preset number of iterations, then a density matrix is constructed based on the complex matrix in the previous iteration step.
[0010] Optionally, the density matrix is calculated using the following formula:
[0011] in, Here is the density matrix. It is a complex matrix.
[0012] Optionally, the loss function can be calculated using the following formula: , in, For loss function, Let i be the expected experimental measurement value corresponding to the i-th measurement operator. , For the i-th measurement operator, is the regularization coefficient.
[0013] Optionally, the update formula for the complex matrix is: , in, Let be the complex matrix in the current iteration step. The complex matrix from the previous iteration step, For learning rate, , These are the corrected momentum estimate and the second moment estimate, respectively. This is a preset numerical stability constant; The correction formulas for the momentum estimate and the second moment estimate are as follows: , in, , These are the momentum estimate and the second moment estimate before correction, respectively. , These are the correction factors for the momentum estimate and the second moment estimate, respectively; The formulas for calculating the momentum estimate and the second moment estimate are as follows: , , in, It is the momentum decay coefficient. It is the attenuation coefficient of root mean square propagation.
[0014] A second aspect of this application provides a quantum state tomography apparatus, characterized in that the apparatus comprises: The expectation value determination unit is used to measure the qubit according to a selected set of measurement operators to obtain the expected value of the experimental measurement; A density matrix calculation unit is used to randomly initialize a complex matrix and calculate a density matrix based on the complex matrix. The loss function calculation unit is used to calculate the loss function value based on the density matrix, the measurement operator, and the expected value of the experimental measurement. The density matrix construction unit is used to construct a density matrix based on the complex matrix if the loss function value is less than a preset loss function convergence threshold.
[0015] A third aspect of this application provides an electronic device, including: a processor and a memory; The processor is connected to a memory, wherein the memory is used to store computer programs and the processor is used to invoke the computer programs to execute the methods as described in the first aspect of the embodiments of this application.
[0016] A fourth aspect of this application provides a computer-readable storage medium storing a computer program, the computer program including program instructions, which, when executed by a processor, perform the method as described in the first aspect of this application.
[0017] The quantum state tomography method, apparatus, electronic device, and computer-readable storage medium provided in this application measure qubits according to a selected set of measurement operators to obtain the expected experimental measurement value; randomly initialize a complex matrix and calculate a density matrix based on the complex matrix; calculate a loss function value based on the density matrix, measurement operators, and the expected experimental measurement value; if the loss function value is less than a preset loss function convergence threshold, construct the density matrix based on the complex matrix. It can be seen that the embodiments of this application do not require projection operations, and the computational complexity is lower than that of traditional positive semidefinite programming methods, thereby reducing computational costs and increasing computational speed; in addition, the loss function supports the introduction of correlation terms to improve noise resistance, thereby improving reconstruction accuracy. Therefore, the embodiments of this application are suitable for efficient quantum state reconstruction of high-dimensional quantum systems. Attached Figure Description
[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0019] Figure 1 An example system block diagram for quantum state tomography provided in one embodiment of this application is shown; Figure 2 A flowchart illustrating a quantum state tomography method provided in one embodiment of this application is shown; Figure 3 This diagram illustrates how the loss function varies with iteration steps according to an embodiment of this application; Figure 4 This diagram illustrates how the residual changes with the iteration step according to an embodiment of this application; Figure 5 This diagram illustrates how the fidelity varies with iteration steps according to one embodiment of this application. Figure 6 A schematic diagram of the structure of a quantum state tomography apparatus provided in one embodiment of this application is shown; Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of this application is shown. Detailed Implementation
[0020] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.
[0021] Classical computers use transistors to encode information in binary data, such as bits, where each bit can represent a value of 1 or 0. These 1s and 0s act as switches to drive the functions of a classical computer. If there are n bits of data, there are 2^n possible classical states, and one state is represented at a time.
[0022] Quantum computers use quantum processors that operate on data represented by qubits, also known as quantum bits. A single qubit can represent the classical binary states "0" or "1", or a superposition of "0" and "1". Because it can represent a superposition of "0" and "1", a qubit can represent both "0" and "1" states simultaneously. For example, if there are n bits of data, then... A quantum state can be represented simultaneously. Furthermore, qubits in a superposition can be correlated with each other, a phenomenon known as entanglement, where the state of one qubit (whether 1, 0, or both) depends on the state of another qubit, and more information can be encoded within two entangled qubits. Based on the principles of superposition and entanglement, qubits enable quantum computers to perform functions that might be relatively complex and time-consuming for classical computers.
[0023] Please refer to Figure 1 This illustrates an example system block diagram of quantum state tomography provided in one embodiment of this application. System 100 may be a hybrid computing system comprising a combination of one or more quantum computers, quantum systems, and / or classical computers. Figure 1 In the example shown, system 100 may include a quantum system 110 and a classical computer 120. In one implementation, the quantum system 110 and the classical computer 120 may be configured to communicate via one or more wired and / or wireless connections (e.g., wireless networks). The quantum system 110 may include a quantum chipset consisting of one or more quantum chips, comprising various hardware components for processing data encoded in qubits. The quantum chipset may be a quantum computing core surrounded by infrastructure to protect the quantum chips from electromagnetic noise sources, mechanical vibration sources, heat sources, and other noise sources that can degrade the performance of the quantum chips. The classical computer 120 may be electronically integrated with the quantum system 110 via any suitable wired and / or wireless electronic connection.
[0024] exist Figure 1In the example shown, quantum system 110 can be any suitable set of components capable of performing quantum operations on a physical system. Quantum operations, such as quantum gate operations, manipulate the quantum states of qubits to evolve and / or become entangled. Figure 1 In the illustrated example embodiment, the quantum system 110 may include a measurement and control unit 111, an interface 112, and a quantum chip 113. In some embodiments, all or part of each of the measurement and control unit 111, interface 112, and quantum chip 113 may be located in a cryogenic environment to facilitate the performance of quantum operations. The quantum chip 113 may be any hardware capable of processing information using quantum states. This hardware may include multiple qubits and means for coupling or entanglement of the qubits to process information using quantum states. Qubits may include, but are not limited to, charge qubits, flux qubits, phase qubits, spin qubits, and ion qubits. The quantum chip may include a set of quantum logic gates configured to perform quantum logic operations on the qubits stored in a quantum register. The quantum gates may include one or more single-qubit gates, two-qubit gates, and / or other multi-qubit gates.
[0025] The measurement and control unit 111 can be any combination of digital computing devices capable of performing quantum computing (e.g., executing quantum circuits) in conjunction with interface 112. This digital computing device may include a digital processor and memory for storing and executing quantum instructions using interface 112. The digital computing device may also include a communication protocol device for receiving instructions and sending the results of the performed quantum computing to a classical computer. Additionally, the digital computing device may include a communication interface with interface 112. In one embodiment, the measurement and control unit 111 may be configured to receive classical instructions (e.g., from classical computer 120) and convert these classical instructions into measurement and control instructions for interface 112. The measurement and control instructions provided by the measurement and control unit 111 to interface 112 may be, for example, digital signals indicating which quantum gates in a quantum system need to be applied to the qubits to perform a specific function. Interface 112 may be configured to convert these digital signals into analog signals (e.g., analog pulses of microwave pulses), which can be used to apply quantum gates to the qubits to manipulate the interactions between them.
[0026] Interface 112 may be a classical-quantum interface, comprising a combination of devices capable of receiving instructions from the integrated measurement and control unit 111 and converting those instructions into a means for implementing quantum operations. In one embodiment, interface 112 may convert instructions from the integrated measurement and control unit 111 into drive signals capable of driving or manipulating qubits, and / or applying quantum gates to qubits. Additionally, interface 112 may be configured to convert signals received from the quantum chip 113 into digital signals capable of being processed and transmitted by the integrated measurement and control unit 111. Devices included in interface 112 may include, but are not limited to, digital-to-analog converters, analog-to-digital converters, waveform generators, attenuators, amplifiers, optical fibers, lasers, and filters. Interface 112 may further include circuitry configured to measure multiple qubits after the application of quantum gates, wherein the measurements may produce results represented in classical bits. Each measurement performed by interface 112 may be read out to a device connected to the quantum system 110, such as a classical computer 120. The multiple measurement results provided by interface 112 may represent probabilistic results.
[0027] The classical computer 120 can include hardware components such as a processor and storage devices (e.g., including memory devices and classical registers) for processing data encoded in classical bits. In one embodiment, the classical computer 120 can be configured to provide the quantum system 110 with various control signals, instructions, and data encoded in classical bits. Further, quantum states measured by the quantum system 110 can be read out by the classical computer 120, and the classical computer 120 can store the measured quantum states as classical bits in classical registers. In one embodiment, the classical computer 120 can be any suitable combination of computer-executable hardware and / or computer-executable software capable of executing the preparation module 121 to perform quantum computation using data stored in the data storage module 122 as part of the construction and computation. The data storage module 122 can be a repository for data to be analyzed using quantum computing algorithms and the results of that analysis. The preparation module 121 can be a program or module capable of preparing classical data from the data storage module 122 as part of a quantum circuit implementation. Preparation module 121 can be instantiated as part of a larger algorithm, such as an application programming interface (API) function call, or by resolving hybrid classical-quantum computing into aspects of quantum and classical computing. For example, preparation module 121 can generate instructions for creating quantum circuits using quantum gates. In an embodiment, such instructions can be stored by the measurement and control unit 111 and can be instantiated by components of interface 112 to execute, enabling quantum operations of quantum gates to be performed on quantum chip 113.
[0028] The classic computer 120 may be a laptop computer, desktop computer, vehicle-integrated computer, smart mobile device, tablet device, and / or any other suitable classic computing device. Additionally or alternatively, the classic computer 120 may also operate as part of a cloud computing service model, such as Software as a Service (SaaS), Platform as a Service (PaaS), or Infrastructure as a Service (IaaS). The classic computer 120 may also reside in a cloud computing deployment model, such as a private cloud, community cloud, public cloud, or hybrid cloud.
[0029] Please refer to Figure 2 This illustration shows a flowchart of a quantum state tomography method provided in one embodiment of this application. The method can be applied to computer devices, which refer to electronic devices capable of data computation and processing. The method may include the following steps: Step 201: Measure the qubit according to the selected set of measurement operators to obtain the expected experimental measurement value.
[0030] In quantum computing, a qubit is the fundamental unit, and its state is described by a unit vector in a two-dimensional complex Hilbert space. ,satisfy (Probability normalization). The density matrix is in the form of...
[0031] Quantum measurement consists of a set of orthogonal projection operators. Description, satisfy (Projectivity) and (Completeness, (This is the identity matrix). For qubits, common measurement operators correspond to a Pauli matrix basis (X, Y, Z) or an arbitrary orthogonal basis.
[0032] Among them, the expected value of the experiment: for a certain observable... The average value of multiple measurements in the experiment is theoretically equal to the expected value of the quantum state. .
[0033] Step 202: Randomly initialize the complex matrix and calculate the density matrix based on the complex matrix.
[0034] Any density matrix can be parameterized using Cholesky decomposition. For example, the formula for calculating the density matrix is as follows:
[0035] in, Here is the density matrix. It is a complex matrix.
[0036] According to the formula for calculating the density matrix, if the complex matrix can be determined, the density matrix can be determined.
[0037] It can be seen that the Cholesky decomposition of the parameterized density matrix ensures the physical validity (positive definiteness, Hermitian property, unit trace) of the density matrix, avoiding non-physical problems in traditional linear inversion. Furthermore, by adjusting the dimension of matrix T... This enables flexible reconstruction from a pure state (m=1) to a full-rank mixed state, significantly reducing the parameter space.
[0038] Step 203: Calculate the loss function value based on the density matrix, the measurement operator, and the expected value of the experimental measurement.
[0039] The formula for calculating the loss function is as follows: , in, For loss function, Let i be the expected experimental measurement value corresponding to the i-th measurement operator. , For the i-th measurement operator, is the regularization coefficient.
[0040] It can be seen that the loss function supports the introduction of sparse regularization terms (regularization coefficients) to improve noise resistance and is suitable for efficient state reconstruction of high-dimensional quantum systems.
[0041] Step 204: If the loss function value is less than the preset loss function convergence threshold, then construct the density matrix based on the complex matrix.
[0042] Furthermore, the method also includes: If the loss function value is greater than or equal to a preset loss function convergence threshold, then the complex matrix is updated based on the loss function value and gradient descent, and the step of calculating the density matrix based on the complex matrix is executed.
[0043] Gradient descent is an iterative optimization algorithm whose core objective is to find the minimum (or local minimum) of the loss function by progressively adjusting the parameters in the opposite direction of the gradient (the direction in which the function value changes the fastest). Common gradient descent methods include batch gradient descent, stochastic gradient descent, mini-batch gradient descent, momentum descent, and adaptive learning rate methods.
[0044] For example, the update formula for the standard gradient descent method is: , in, Here, the gradient of the loss function is given with respect to step t. That is, T. Let be the learning rate. The gradient of the loss function is: , , Let i be the expected experimental measurement value corresponding to the i-th measurement operator. , For the i-th measurement operator, is the regularization coefficient. yes The norm term is the gradient direction matrix of the density matrix, and each element of it is... The "phase", that is .
[0045] matrix The norm is defined as: .
[0046] in It is the modulus of a complex number.
[0047] The quantum state tomography method provided in this application measures a qubit using a selected set of measurement operators to obtain the expected experimental measurement value; a complex matrix is randomly initialized, and a density matrix is calculated based on this complex matrix; a loss function value is calculated based on the density matrix, the measurement operators, and the expected experimental measurement value; if the loss function value is less than a preset loss function convergence threshold, the density matrix is constructed based on the complex matrix. It can be seen that the embodiments of this application do not require projection operations, and the computational complexity is lower than that of traditional positive semidefinite programming methods, thereby reducing computational costs and increasing computational speed. Furthermore, the loss function supports the introduction of correlation terms (regularization coefficients) to improve noise resistance, thereby improving reconstruction accuracy. Therefore, the embodiments of this application are suitable for efficient quantum state reconstruction of high-dimensional quantum systems.
[0048] Furthermore, gradient descent can also be used for the Adam optimization algorithm, wherein updating the complex matrix based on the loss function value and gradient descent includes: The momentum estimate in the current iteration step is calculated based on the preset momentum decay coefficient, the momentum estimate in the previous iteration step, and the gradient corresponding to the loss function value. The second moment estimate in the current iteration step is calculated based on the preset root mean square propagation attenuation coefficient, the second moment estimate in the previous iteration step, and the gradient corresponding to the loss function value. The momentum estimate and second moment estimate in the current iteration step are corrected respectively; The complex matrix in the current iteration step is calculated based on the corrected momentum estimate and second moment estimate, the preset numerical stability constant and learning rate, and the complex matrix in the previous iteration step. The complex matrix in the current iteration step is used as the complex matrix in the previous iteration step to update the complex matrix.
[0049] In the Adam optimization algorithm, the update formula for the complex matrix is: , in, Let be the complex matrix in the current iteration step. The complex matrix from the previous iteration step, For learning rate, , These are the corrected momentum estimate and the second moment estimate, respectively. This is a preset numerical stability constant; The correction formulas for the momentum estimate and the second moment estimate are as follows: , in, , These are the momentum estimate and the second moment estimate before correction, respectively. , These are the correction factors for the momentum estimate and the second moment estimate, respectively; The formulas for calculating the momentum estimate and the second moment estimate are as follows: , , in, It is the momentum decay coefficient. It is the attenuation coefficient of root mean square propagation.
[0050] Furthermore, the method also includes: The number of iterations is determined based on the current iteration step number; If the number of iterations is greater than the preset number of iterations, then a density matrix is constructed based on the complex matrix in the previous iteration step.
[0051] To verify the beneficial effects of the embodiments of this application, low-rank quantum state density matrices with dimensions of 4, 8, 16, 32, and 64 are randomly generated as the true states, and the expected value of the true state density matrix measured in Paulige is calculated. Randomly initialize T. =0.9, =0.999, =0, =0, =10−8, =0, maximum iteration steps are set to 2000, and the loss function convergence threshold is set to... =1E−6, =0.05. See the experimental results below. Figures 3-5 . Figure 3 This diagram illustrates how the loss function varies with iteration steps according to an embodiment of this application. Figure 4 This diagram illustrates how the residual changes with iteration steps according to an embodiment of this application. Figure 5 This diagram illustrates the fidelity variation with iteration steps according to an embodiment of this application. The left diagram shows the Adam optimization algorithm, and the right diagram shows the standard gradient descent method. The results show that the technical solution in this embodiment can obtain its density matrix based on the measured expected value, and the fidelity can reach 1 after a certain number of iterations. Furthermore, the Adam optimization algorithm in this solution has higher efficiency and accuracy than the classic gradient descent method.
[0052] Figure 6 A schematic diagram of a quantum state tomography apparatus according to an embodiment of this application is shown. The apparatus includes: The expectation value determination unit 601 is used to measure the qubit according to a selected set of measurement operators to obtain the experimental measurement expectation value; The density matrix calculation unit 602 is used to randomly initialize a complex matrix and calculate a density matrix based on the complex matrix. The loss function calculation unit 603 is used to calculate the loss function value based on the density matrix, the measurement operator, and the expected value of the experimental measurement. The density matrix construction unit 604 is used to construct a density matrix based on the complex matrix if the loss function value is less than a preset loss function convergence threshold.
[0053] Figure 7 A schematic diagram of the structure of a computer device provided in one embodiment of this application is shown, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the functions of the computer system of the quantum state tomography method in any of the above embodiments.
[0054] This application also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a computer, causes the computer to perform the functions of the computer system of the quantum state tomography method in any of the above embodiments.
[0055] This application also provides a computer program product containing instructions that, when executed by a computer, cause the computer to perform the functions of the computer system of the quantum state tomography method in any of the above embodiments.
[0056] It is understood that the specific examples in this application are only intended to help those skilled in the art better understand the implementation methods of this application, and are not intended to limit the scope of the invention.
[0057] It is understood that in the various embodiments of this application, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not limit the implementation process of the embodiments of this application in any way.
[0058] It is understood that the various implementation methods described in this application can be implemented individually or in combination, and the implementation methods in this application are not limited in this respect.
[0059] Unless otherwise stated, all technical and scientific terms used in the embodiments of this application have the same meaning as commonly understood by one of ordinary skill in the art. The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to limit the scope of this application. The term "and / or" as used in this application includes any and all combinations of one or more of the associated listed items. The singular forms "a," "the," and "the" as used in the embodiments of this application and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.
[0060] It is understood that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuits in the processor's hardware or by instructions in software form. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied in the execution of a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory; the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method.
[0061] It is understood that the memory in the embodiments of this application may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Specifically, non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may be random access memory (RAM). It should be noted that the memory in the systems and methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.
[0062] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.
[0063] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the aforementioned method implementations, and will not be repeated here.
[0064] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the mutual coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.
[0065] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.
[0066] In addition, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.
[0067] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.
[0068] The above are merely specific embodiments of this application, but the scope of protection of this invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this invention should be determined by the scope of the claims.
Claims
1. A quantum state tomography method, characterized in that, The method includes: The expected experimental measurement value is obtained by measuring the qubit according to a selected set of measurement operators; Randomly initialize a complex matrix, and calculate a density matrix based on the complex matrix; The loss function value is calculated based on the density matrix, the measurement operator, and the expected value of the experimental measurement. If the loss function value is less than the preset loss function convergence threshold, then a density matrix is constructed based on the complex matrix.
2. The method according to claim 1, characterized in that, The method further includes: If the loss function value is greater than or equal to a preset loss function convergence threshold, then the complex matrix is updated based on the loss function value and gradient descent, and the step of calculating the density matrix based on the complex matrix is executed.
3. The method according to claim 2, characterized in that, The step of updating the complex matrix based on the loss function value and gradient descent includes: The momentum estimate in the current iteration step is calculated based on the preset momentum decay coefficient, the momentum estimate in the previous iteration step, and the gradient corresponding to the loss function value. The second moment estimate in the current iteration step is calculated based on the preset root mean square propagation attenuation coefficient, the second moment estimate in the previous iteration step, and the gradient corresponding to the loss function value. The momentum estimate and second moment estimate in the current iteration step are corrected respectively; The complex matrix in the current iteration step is calculated based on the corrected momentum estimate and second moment estimate, the preset numerical stability constant and learning rate, and the complex matrix in the previous iteration step. The complex matrix in the current iteration step is used as the complex matrix in the previous iteration step to update the complex matrix.
4. The method according to claim 3, characterized in that, The method further includes: The number of iterations is determined based on the current iteration step number; If the number of iterations is greater than the preset number of iterations, then a density matrix is constructed based on the complex matrix in the previous iteration step.
5. The method according to claim 4, characterized in that, The formula for calculating the density matrix is: in, Here is the density matrix. It is a complex matrix.
6. The method according to claim 5, characterized in that, The formula for calculating the loss function is: ， in, For loss function, Let i be the expected experimental measurement value corresponding to the i-th measurement operator. , For the i-th measurement operator, This is the regularization coefficient.
7. The method according to claim 6, characterized in that, The update formula for the complex matrix is: ， in, Let be the complex matrix in the current iteration step. The complex matrix from the previous iteration step, For learning rate, , These are the corrected momentum estimate and the second moment estimate, respectively. This is a preset numerical stability constant; The correction formulas for the momentum estimate and the second moment estimate are as follows: ， in, , These are the momentum estimate and the second moment estimate before correction, respectively. , These are the correction factors for the momentum estimate and the second moment estimate, respectively; The formulas for calculating the momentum estimate and the second moment estimate are as follows: ， ， in, It is the momentum decay coefficient. It is the attenuation coefficient of root mean square propagation.
8. A quantum state tomography apparatus, characterized in that, The device includes: The expectation value determination unit is used to measure the qubit according to a selected set of measurement operators to obtain the expected value of the experimental measurement; A density matrix calculation unit is used to randomly initialize a complex matrix and calculate a density matrix based on the complex matrix. The loss function calculation unit is used to calculate the loss function value based on the density matrix, the measurement operator, and the expected value of the experimental measurement. The density matrix construction unit is used to construct a density matrix based on the complex matrix if the loss function value is less than a preset loss function convergence threshold.
9. An electronic device, characterized in that, include: Processor and memory; The processor is connected to a memory, wherein the memory is used to store a computer program, and the processor is used to invoke the computer program to perform the method as described in any one of claims 1-7.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions that, when executed by a processor, perform the method as described in any one of claims 1-7.