Non-sparse quantum state data tomography method and related apparatus

Abstract

The embodiment of the application discloses a non-sparse quantum state data tomography method and related device, the method comprises the following steps: n rounds of sampling are performed on a sparse quantum state to obtain n sampling results; from the first sampling result, each sampling result is summed with the previous convolution result as a convolution image, and a convolution operation is performed on the convolution image, and the previous convolution result of the first sampling result is 0; and the nth convolution result is taken as a data tomography result of the non-sparse quantum state. The embodiment of the application applies the idea of multiple diffusion, superimposes the sampling result of this time on the convolution result of the last time for reconvolution, realizes the re-diffusion of the data stored by the sparse quantum state in space, a small amount of sampling is performed in each round, and the process is repeated for n rounds, so that the kernel estimation can be quickly diffused to the amplitudes corresponding to all basis vectors, and thus the data tomography of the non-sparse quantum state is realized.

Description

Technical Field

[0001] This invention relates to the field of quantum computing technology, and in particular to a method and apparatus for non-sparse quantum state data tomography. Background Technology

[0002] Quantum state pointer Where |i> is the selected expansion basis vector, x i Let |i> be the amplitude, and N be the number of basis vectors. In quantum computing, information is stored in the quantum computer in the form of quantum states; for example, using |i> as an index and x as the basis vector. i Store the information corresponding to the index |i>. When utilizing the information, it must first be extracted. Extraction of information stored in quantum state form is called quantum state tomography. For a given precision 0 < ∈ < 1, if there are s |x i If |≥∈, then s is called the sparsity of the quantum state |x> with precision ∈. If s<<N, then the quantum state |x> is said to be sparse, meaning that a small number of amplitudes are sufficient to accurately describe the entire quantum state. The totem complexity of sparse quantum state data is O(∈ -2 The tomographic complexity of non-sparse quantum state data is at least O(log N), where log N is the log N). -2 Therefore, how to reduce the tomography complexity of non-sparse quantum state data, thereby improving the extraction speed of non-sparse quantum state data and reducing the storage resource requirements during the tomography process of non-sparse quantum state data, is an urgent technical problem to be solved. Summary of the Invention

[0003] This application provides a method and related apparatus for tomography of non-sparse quantum state data, which helps to reduce the tomography complexity of non-sparse quantum state data, thereby improving the extraction speed of non-sparse quantum state data and reducing the storage resource requirements during the tomography process of non-sparse quantum state data.

[0004] The first aspect of this application provides a method for non-sparse quantum state data tomography, including:

[0005] The sparse quantum state is sampled in n rounds to obtain n sampling results, where n is a positive integer greater than 0;

[0006] Starting from the first sampling result, each sampling result is summed with the previous convolution result to form a convolution image, and a convolution operation is performed on the convolution image, wherein the previous convolution result of the first sampling result is 0;

[0007] The nth convolution result is used as the data tomography result of the non-sparse quantum state.

[0008] Optionally, performing a convolution operation on the convolutional image includes:

[0009] The convolution kernel is determined based on the obtained kernel function, and the convolution operation is performed on the convolution image based on the convolution kernel.

[0010] Optionally, determining the convolution kernel based on the obtained kernel function includes:

[0011] Determine the size of the convolution kernel;

[0012] The number of elements in the convolution kernel is determined based on the size of the convolution kernel;

[0013] Determine the distance between each element and the preset origin;

[0014] Substituting the distance into the obtained kernel function, the value of each element is obtained;

[0015] The convolution kernel is determined based on the normalized value of each of the elements.

[0016] Optionally, the kernel function is a spline kernel function.

[0017] Optionally, determining the convolution kernel based on the normalized value of each element includes:

[0018] Candidate convolution kernels are determined based on the normalized values ​​of each of the elements;

[0019] Based on the overlapping region between the candidate convolution kernel and the convolution image;

[0020] The values ​​of elements in the candidate convolution kernel other than the overlapping region are set to 0, and the values ​​of elements within the overlapping region of the candidate convolution kernel are normalized to obtain the convolution kernel.

[0021] Optionally, summing each of the sampling results with the previous convolution result to obtain the convolutional image includes:

[0022] Determine a first weight for each of the sampling results and a second weight for the previous convolution result, wherein the sum of the first weight and the second weight is 1;

[0023] Determine a first product of each of the sampling results with the first weight, and determine a second product of the previous convolution result with the second weight;

[0024] The first product and the second product are used as a convolutional image.

[0025] Optionally, each sampling result includes multiple basis vector labels and the amplitude corresponding to each basis vector label. Each basis vector label is used to characterize each mesh label in the finite element method, and the amplitude corresponding to each basis vector label is used to characterize the physical quantity at each mesh label.

[0026] A second aspect of this application provides a non-sparse quantum state data tomography apparatus, comprising:

[0027] A sampling unit is used to perform n rounds of sampling on a sparse quantum state to obtain n sampling results, where n is a positive integer greater than 0;

[0028] A convolutional unit is configured to, starting from the first sampling result, sum each sampling result with the previous convolution result to obtain a convolutional image, and perform a convolution operation on the convolutional image, wherein the previous convolution result of the first sampling result is 0;

[0029] A tomography unit is used to take the nth convolution result as the data tomography result of the non-sparse quantum state.

[0030] A third aspect of this application provides an electronic device, including: a processor and a memory;

[0031] 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.

[0032] 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.

[0033] In this embodiment, the sparse quantum state is first sampled n times to obtain n sampling results. Then, starting from the first sampling result, each sampling result is summed with the previous convolution result to obtain a convolution image, and a convolution operation is performed on the convolution image. In this way, the nth sampling result is summed with the (n-1)th convolution result to obtain the final convolution image. A convolution operation is performed on the final convolution image, and the nth convolution result is used as the data tomography result of the non-sparse quantum state.

[0034] As can be seen, this tomography method applies the idea of ​​multiple diffusion, superimposing the current sampling result with the previous convolution result for reconvolution, thereby realizing the spatial re-diffusion of the data stored in the sparse quantum state. A small amount of sampling is performed in each round, and this is repeated n times. This can quickly diffuse the kernel estimate to the amplitude corresponding to all basis vectors, thereby realizing the tomography of non-sparse quantum state data. Using the embodiments of this application is beneficial to reducing the tomography complexity of non-sparse quantum state data, thereby improving the extraction speed of non-sparse quantum state data and reducing the storage resource requirements during the tomography of non-sparse quantum state data. Attached Figure Description

[0035] 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.

[0036] Figure 1 An example system block diagram of a non-sparse quantum state data tomography method provided in one embodiment of this application is shown;

[0037] Figure 2 A flowchart illustrating a non-sparse quantum state data tomography method provided in one embodiment of this application is shown;

[0038] Figure 3 A schematic diagram comparing direct quantum sampling results, theoretical values ​​of quantum state data, and results based on a convolutional quantum state tomography method provided in one embodiment of this application is shown.

[0039] Figure 4 This paper shows a schematic diagram of the structure of a non-sparse quantum state data tomography apparatus provided in one embodiment of the present application;

[0040] Figure 5 A schematic diagram of the structure of a computer device provided in one embodiment of this application is shown. Detailed Implementation

[0041] 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.

[0042] 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.

[0043] 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 2^n qubits can represent n bits of data. nA 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.

[0044] Please refer to Figure 1 This illustrates an example system block diagram of a non-sparse quantum state data tomography method 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.

[0045] exist Figure 1 In 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.

[0046] 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 having 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 gate array 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 the qubits.

[0047] 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.

[0048] 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.

[0049] 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.

[0050] Quantum state pointer Where |i> is the selected expansion basis vector, x i Let |i> be the amplitude, and N be the number of basis vectors. In quantum computing, information is stored in the quantum computer in the form of quantum states; for example, using |i> as an index and x as the basis vector. i Store the information corresponding to the index |i>. When utilizing the information, it must first be extracted. Extraction of information stored in quantum state form is called quantum state tomography. For a given precision 0 < ∈ < 1, if there are s |x iIf |≥∈, then s is called the sparsity of the quantum state |x> at the precision ∈. If s << N, then the quantum state |x> is called sparse, meaning that very few amplitudes are sufficient to accurately describe the entire quantum state. The tomography complexity of sparse quantum state data is O(∈ - 2 logN), and the tomography complexity of non-sparse quantum state data is at least O(∈ -2 N).

[0051] For example, for a 3-qubit system, it can include 8 basis vectors and corresponding amplitudes. For example, this quantum state is a sparse quantum state:

[0052] x = [0.7, 0.7, a, a, a, a, a, a],

[0053] where a represents a very small amplitude. If the above |x> is sampled, it will be found that the basis vectors of the observed quantum state are either 000 or 001, because the amplitudes corresponding to other basis vectors are too small to be observed almost. Therefore, the final sampling result can basically be considered as:

[0054] y = [0.707, 0.707, 0, 0, 0, 0, 0, 0],

[0055] It can be seen that y is a very good approximation of the real data x, and only O(∈ -2 ) observations are required. If this quantum state is a non-sparse quantum state:

[0056]

[0057] Then the probability of each basis vector being observed is equal, meaning that at least O(∈ -2 N) observations are expected to complete the extraction of all data. However, for a computer, the number of observations is usually limited. Assuming that the maximum number of observations is 1000 times, for a sparse quantum state, theoretically the number of observations of 000 and 001 is about 500 each, and its fluctuation is small, and the theoretical and actual results are not very different; but for a non-sparse quantum state, theoretically the number of observations of each basis vector is about 125. Due to the limitation of the number of observations, the number of observations is small, and its fluctuation will be large, resulting in a large difference between the theoretical and actual results, and thus this tomography method cannot effectively extract non-sparse quantum state data.

[0058] Based on this, the embodiments of this application provide a non-sparse quantum state data tomography method and related devices, hoping to reduce the tomography complexity of non-sparse quantum state data, thereby improving the extraction speed of non-sparse quantum state data and reducing the storage resource requirements during the tomography of non-sparse quantum state data.

[0059] Please refer to Figure 2 This illustration shows a flowchart of a non-sparse quantum state data 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:

[0060] Step 201: Perform n rounds of sampling on the sparse quantum state to obtain n sampling results, where n is a positive integer greater than 0.

[0061] Each sampling result includes multiple basis vector labels and the amplitude corresponding to each basis vector label. For example, for a 3-qubit system, after 1000 samplings, the measured basis vectors and their corresponding frequencies are {"000": s1, "001": s2, "010": s3, "011": s4, "100": s5, "101": s6, "110": s7, "111": s8}. Dividing the corresponding frequency by the total frequency gives the probability, and the square root of the probability is the amplitude. Therefore, the sampling result can be expressed as...

[0062] Of course, the basis vector label can also be represented in decimal, then the sampling result can be represented as:

[0063] Furthermore, each of the aforementioned basis vector labels is used to characterize each mesh label in the finite element method, and the amplitude corresponding to each basis vector label is used to characterize the physical quantity at each mesh label. For example, when performing quantum computational fluid dynamics (QCFD) simulations using quantum computing, the flow field result is a solution to the Navier-Stokes equations (NS). The solution to each equation in the NS equations corresponds to a mesh point in the finite element method. The mesh label can be represented by a basis vector label, and the physical quantity at that mesh label can be represented by an amplitude. The solution is the numerical value of that physical quantity. Physical quantities can be, for example, pressure, density, flow velocity, temperature, etc., and need to be determined in conjunction with the specific physical quantities to be solved in the system.

[0064] It should be noted that the number of samples in each round can be the same or different, and no limitation is made here.

[0065] Step 202: Starting from the first sampling result, sum each sampling result with the previous convolution result to obtain a convolution image, and perform a convolution operation on the convolution image, wherein the previous convolution result of the first sampling result is 0.

[0066] Specifically, for the first sampling result, it is directly used as a convolutional image for convolution to obtain the first convolution result; then the second sampling result is summed with the first convolution result and used as a convolutional image for convolution to obtain the second convolution result; and so on, until the nth sampling result is summed with the (n-1)th convolution result and used as a convolutional image for convolution to obtain the nth convolution result.

[0067] Specifically, each sampling result includes multiple basis vector labels and the amplitude corresponding to each basis vector label. Each amplitude can be arranged according to the order of its basis vector labels to obtain a one-dimensional array. It is then determined whether each element in this one-dimensional array is a square. If not, it is padded with zero elements to obtain a square. The padded one-dimensional array is then reconstructed into a matrix with dimension equal to the square root of the square. This matrix can be directly subjected to convolution operations, for example, when it is the first sampling result. Alternatively, the elements in this matrix can be added to the corresponding elements in the convolution result before performing a convolution operation, for example, when it is not the first sampling result.

[0068] Step 203: Use the nth convolution result as the data tomography result of the non-sparse quantum state.

[0069] Specifically, the nth convolution result, which is the sum of the nth sampling result and the (n-1)th convolution result, is used as the convolution result obtained by convolving the convolution image. This result can also be represented in the form of a matrix. By deconstructing this matrix, a one-dimensional array can be obtained. Then, the supplementary elements in this one-dimensional array, namely each basis vector label and the amplitude corresponding to each basis vector label, are deleted, which is the data that needs to be tomographically analyzed.

[0070] As can be seen, the non-sparse quantum state data tomography method of this application applies the idea of ​​multiple diffusion, superimposing the current sampling result with the previous convolution result for re-convolution, realizing the spatial re-diffusion of the data stored in the sparse quantum state. A small amount of sampling is performed in each round, and this is repeated n times, which can quickly diffuse the kernel estimate to the amplitude corresponding to all basis vectors, thereby realizing the tomography of non-sparse quantum state data. Using the embodiments of this application is beneficial to reducing the tomography complexity of non-sparse quantum state data, thereby improving the extraction speed of non-sparse quantum state data and reducing the storage resource requirements during the tomography of non-sparse quantum state data.

[0071] In one embodiment provided in this application, the convolution operation on the convolutional image includes:

[0072] The convolution kernel is determined based on the obtained kernel function, and the convolution operation is performed on the convolution image based on the convolution kernel.

[0073] Specifically, determining the convolution kernel based on the obtained kernel function includes:

[0074] Determine the size of the convolution kernel;

[0075] The number of elements in the convolution kernel is determined based on the size of the convolution kernel;

[0076] Determine the distance between each element and the preset origin;

[0077] Substituting the distance into the obtained kernel function, the value of each element is obtained;

[0078] The convolution kernel is determined based on the normalized value of each of the elements.

[0079] Furthermore, the grid step size can be a time step size or a spatial step size, thereby determining the distance between each element and the preset origin based on the grid step size.

[0080] For example, if the selected convolution kernel size is 3×3, then the kernel includes 9 elements. Before using this kernel for convolution, it is necessary to first determine the value of each element. If the middle element of the second row and second column of the kernel is set as the origin, the distance between the origin and the kernel can be determined based on the basis vector label corresponding to each element. Assuming the grid shape is also 3×3, with equal horizontal and vertical strides, and the sampling results are represented according to the arrangement of grid points, then the distance between the origin and the four grid points before, after, to the left, and to the right of the origin is equal to one grid stride, and the distance between the origin and the four grid points at the top left, top right, bottom left, and bottom right is equal to... Each grid step size.

[0081] Kernel functions are tools that map low-dimensional data to high-dimensional features, used in machine learning and statistics to measure the similarity between two variables. Common kernel functions include:

[0082] The Gaussian kernel function has the following general expression:

[0083]

[0084] In one-dimensional problems In the two-dimensional problem, a = 1 / (πh) 2 In the three-dimensional problem, a = 3 / (2πh) 3 ).

[0085] The general expression for a cubic spline function is:

[0086]

[0087] In a one-dimensional problem, a = 1 / h; in a two-dimensional problem, a = 15 / (7πh) 2 In the three-dimensional problem, a = 3 / (2πh) 3 Other kernel functions will not be introduced here.

[0088] Where h is the smooth length of the kernel function.

[0089] For example, taking the spline kernel function as an example, in two dimensions, a = 15 / (7πh) 2 If the horizontal and vertical step sizes are both h and 1, then the function value at the origin is... The function values ​​of the four grid points in front of, behind, to the left and right of the origin are... The function values ​​for the top left, top right, bottom left, and bottom right grid points are... Normalizing the values ​​of the above 9 points, we can obtain the convolution kernel as follows:

[0090]

[0091] In one embodiment provided in this application, determining the convolution kernel based on the normalized value of each element includes:

[0092] Candidate convolution kernels are determined based on the normalized values ​​of each of the elements;

[0093] Based on the overlapping region between the candidate convolution kernel and the convolution image;

[0094] The values ​​of elements in the candidate convolution kernel other than the overlapping region are set to 0, and the values ​​of elements within the overlapping region of the candidate convolution kernel are normalized to obtain the convolution kernel.

[0095] Specifically, for pixels on the boundary of a convolutional image, if the aforementioned convolution kernel is still used for convolution, since there are no pixels outside the boundary, this part will not contribute to the points that need to be calculated for convolution, resulting in an overall contribution rate that is not 1. For example, consider the following convolutional image:

[0096]

[0097] The convolution at point a is 0.4543a + 0.1136b + 0.1136d + 0.0228, and its overall contribution rate is 0.4543 + 0.1136 + 0.1136 + 0.0228, which is less than 1. Therefore, this embodiment only considers the overlapping region of K and I (0.4543, 0.1136, 0.1136, 0.0228), sets the values ​​of elements outside the overlapping region to 0, and normalizes the values ​​of elements within the overlapping region.

[0098]

[0099] K ′As the convolution kernel at point a, the convolution kernels of the other pixels on the boundary can be determined with reference to the embodiments of this application, so that for the pixels on the boundary, the surrounding pixels can contribute to it, and the total contribution rate is 1, realizing the spatial re-diffusion of the data stored in the sparse quantum state.

[0100] In one embodiment provided in this application, summing each sampling result with the previous convolution result to obtain a convolutional image includes:

[0101] Determine a first weight for each of the sampling results and a second weight for the previous convolution result, wherein the sum of the first weight and the second weight is 1;

[0102] Determine a first product of each of the sampling results with the first weight, and determine a second product of the previous convolution result with the second weight;

[0103] The first product and the second product are used as a convolutional image.

[0104] Specifically, when summing each sampling result with the previous convolution result to obtain the convolutional image, weights can be assigned to the sampling and convolution results to adjust their contributions to quantum state data tomography. Generally, newly sampled data contributes more to quantum state data tomography than the previous convolution result; therefore, the first weight is greater than the second weight. For example, the first weight can be set to 1 / (1+n), and the second weight can be set to n / (1+n), thus ensuring that the contribution rate of each sampling to the final result is consistent.

[0105] To verify the embodiments of this application, taking velocity data stored in quantum states as an example, direct quantum state tomography (Experiment A) and tomography using the method in the embodiments of this application (Experiment B) were performed. The sum of the absolute differences between the theoretical quantum state and the tomographic quantum state, as well as the fidelity, were used as reference indicators. Experiment A involved 10,000 measurements to sample the velocity data of the flow field; Experiment B involved applying the convolution-based QCFD tomography method in the embodiments of this application, measuring and convolving 10 times, with each measurement consisting of 1,000 measurements, for a total of 10,000 measurements. The diffusion coefficient was equal to the grid step size.

[0106] The qualitative results of Experiment A and Experiment B are as follows: Figure 3 As shown, where, Figure 3 The left side shows the direct quantum sampling results, the middle side shows the theoretical values, and the right side shows the sampling results applied to the embodiments of this application. In the figure, the horizontal and vertical axes represent the grid number 126*126, and the colors represent the magnitude of the velocity.

[0107] The quantitative results are as follows: the fidelity of Experiment A is 0.768905662882023, and the sum of absolute differences is 73.66350140851171; the fidelity of Experiment B is 0.986342095454255, and the sum of absolute differences is 14.40023553944089. It can be seen that using the embodiments of this application for non-sparse quantum state data tomography can improve the fidelity of data extraction and obtain more accurate data.

[0108] Figure 4 A schematic diagram of a non-sparse quantum state data tomography apparatus according to an embodiment of this application is shown. The apparatus includes:

[0109] The sampling unit 401 is used to perform n rounds of sampling on the sparse quantum state to obtain n sampling results, where n is a positive integer greater than 0;

[0110] Convolution unit 402 is configured to, starting from the first sampling result, sum each sampling result with the previous convolution result to obtain a convolution image, and perform a convolution operation on the convolution image, wherein the previous convolution result of the first sampling result is 0;

[0111] The tomography unit 403 is used to take the nth convolution result as the data tomography result of the non-sparse quantum state.

[0112] Figure 5 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 non-sparse quantum state data tomography method in any of the above embodiments.

[0113] 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 non-sparse quantum state data tomography method in any of the above embodiments.

[0114] 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 non-sparse quantum state data tomography method in any of the above embodiments.

[0115] 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.

[0116] 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.

[0117] 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.

[0118] 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.

[0119] 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.

[0120] 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.

[0121] 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.

[0122] 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.

[0123] 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.

[0124] 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.

[0125] 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.

[0126] 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.

[0127] 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 method for tomography of non-sparse quantum state data, characterized in that, include: The sparse quantum state is sampled in n rounds to obtain n sampling results, where n is a positive integer greater than 0; Starting from the first sampling result, each sampling result is summed with the previous convolution result to form a convolution image, and a convolution operation is performed on the convolution image, wherein the previous convolution result of the first sampling result is 0; The nth convolution result is used as the data tomography result of the non-sparse quantum state.

2. The method according to claim 1, characterized in that, The convolution operation on the convolutional image includes: The convolution kernel is determined based on the obtained kernel function, and the convolution operation is performed on the convolution image based on the convolution kernel.

3. The method according to claim 2, characterized in that, The step of determining the convolution kernel based on the obtained kernel function includes: Determine the size of the convolution kernel; The number of elements in the convolution kernel is determined based on the size of the convolution kernel; Determine the distance between each element and the preset origin; Substituting the distance into the obtained kernel function, the value of each element is obtained; The convolution kernel is determined based on the normalized value of each of the elements.

4. The method according to claim 3, characterized in that, The kernel function is a spline kernel function.

5. The method according to claim 3, characterized in that, Determining the convolution kernel based on the value of each normalized element includes: Candidate convolution kernels are determined based on the normalized values ​​of each of the elements; Based on the overlapping region between the candidate convolution kernel and the convolution image; The values ​​of elements in the candidate convolution kernel other than the overlapping region are set to 0, and the values ​​of elements within the overlapping region of the candidate convolution kernel are normalized to obtain the convolution kernel.

6. The method according to any one of claims 1-5, characterized in that, The step of summing each sampling result with the previous convolution result to obtain the convolutional image includes: Determine a first weight for each of the sampling results and a second weight for the previous convolution result, wherein the sum of the first weight and the second weight is 1; Determine a first product of each of the sampling results with the first weight, and determine a second product of the previous convolution result with the second weight; The first product and the second product are used as a convolutional image.

7. The method according to any one of claims 1-5, characterized in that, Each sampling result includes multiple basis vector labels and the amplitude corresponding to each basis vector label. Each basis vector label is used to characterize each mesh label in the finite element method, and the amplitude corresponding to each basis vector label is used to characterize the physical quantity at each mesh label.

8. A non-sparse quantum state data tomography device, characterized in that, include: A sampling unit is used to perform n rounds of sampling on a sparse quantum state to obtain n sampling results, where n is a positive integer greater than 0; A convolutional unit is configured to, starting from the first sampling result, sum each sampling result with the previous convolution result to obtain a convolutional image, and perform a convolution operation on the convolutional image, wherein the previous convolution result of the first sampling result is 0; A tomography unit is used to take the nth convolution result as the data tomography result of the non-sparse quantum state.

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.

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