CN114579926B

CN114579926B - Reduced density matrix reconstruction method, apparatus, device, medium and program product

Info

Publication number: CN114579926B
Application number: CN202210169008.5A
Authority: CN
Inventors: 辛涛; 魏超
Original assignee: Southern University of Science and Technology
Current assignee: Southern University of Science and Technology
Priority date: 2022-02-23
Filing date: 2022-02-23
Publication date: 2024-09-27
Anticipated expiration: 2042-02-23
Also published as: CN114579926A

Abstract

The present application relates to a reduced density matrix reconstruction method, apparatus, computer device, storage medium and computer program product. The method comprises the following steps: splitting the n-bit quantum system to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical; judging whether each coefficient corresponding to the k-order Paulownia matrix of each k-bit sub-quantum system can be determined by coefficient measurement result distribution information corresponding to the n-order Paulownia matrix of the n-bit sub-quantum system; determining a target n-order Paully matrix according to the judgment result, and measuring the coefficient of the target n-order Paully matrix by utilizing a superconducting platform; and determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set based on the measurement result so as to reconstruct a reduced density matrix corresponding to each k-bit sub-quantum system. The method can optimize the measurement work of the reconstruction of the reduced density matrix.

Description

Reduced density matrix reconstruction method, apparatus, device, medium and program product

Technical Field

The present application relates to the field of quantum information technology, and in particular, to a reduced density matrix reconstruction method, apparatus, computer device, storage medium, and computer program product.

Background

The reduced density matrix refers to the description of the quantum state of a k-bit sub-quantum system in an n-bit quantum system, is an indispensable tool for analyzing the quantum system, and plays an important role in the development of quantum signals and quantum technologies.

In the prior art, when obtaining the reduced density matrix corresponding to each k-bit sub-quantum system in the n-bit quantum system, the coefficient measurement work is respectively executed on the coefficients containing the k-order Paulownia matrix in the reduced density matrix corresponding to each k-bit sub-quantum system by means of the superconducting platform.

However, by adopting the method, the measurement workload is huge, the laboratory resource consumption is large, and the measurement efficiency is low.

Disclosure of Invention

In view of the foregoing, it is desirable to provide a reduced density matrix reconstruction method, apparatus, computer device, computer-readable storage medium, and computer program product that can improve the measurement efficiency of reduced density matrix reconstruction work.

In a first aspect, the present application provides a reduced density matrix reconstruction method. The method comprises the following steps:

Splitting n-bit quantum systems to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not completely identical;

judging whether each coefficient corresponding to a k-order Paulownia matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to an n-order Paulownia matrix of the n-bit sub-quantum system;

According to the judging result of the target sub-quantum system set, determining a target n-order Brix matrix which needs to be measured by utilizing a superconducting platform in coefficients corresponding to the n-order Brix matrix, and measuring the coefficients of the target n-order Brix matrix by utilizing the superconducting platform;

based on the measurement result, determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set, and reconstructing a reduced density matrix corresponding to each k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients.

In one embodiment, determining whether each coefficient corresponding to a k-order berkovich matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to an n-order berkovich matrix of the n-bit sub-quantum system includes:

For an ith n-order Pauloy matrix of the n-bit quantum system, acquiring a first operation composition element set corresponding to the ith n-order Pauloy matrix;

For a jth k-order Paulownia matrix corresponding to the target sub-quantum system set, obtaining a second operation composition element set corresponding to the jth k-order Paulownia matrix;

If the second operation component element set is a subset of the first operation component element set, the coefficient corresponding to the jth k-order Paulownia matrix can be determined by the coefficient measurement result distribution information corresponding to the ith n-order Paulownia matrix;

If the second operation component element set is not a subset of the first operation component element set, the coefficient corresponding to the jth k-order Paulownia matrix cannot be determined by the coefficient measurement result distribution information corresponding to the ith n-order Paulownia matrix.

In one embodiment, the determination result of the target sub-quantum system set includes a target matrix, and the size of the target matrix isThe matrix element a _ij in the target matrix is used for representing whether the corresponding coefficient of the jth k-order bubble-benefit matrix corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order bubble-benefit matrix of the n-bit quantum system, and determining the target n-order bubble-benefit matrix which needs to be measured by using the superconducting platform in the coefficients corresponding to the n-order bubble-benefit matrix according to the judgment result of the target sub-quantum system set, including:

According to a target matrix corresponding to the target sub-quantum system set, calculating to obtain a target vector corresponding to the target sub-quantum system set, wherein the size of the target vector is 3 ⁿ multiplied by 1, and the vector elements of the target vector are 0 or 1;

and determining a target n-order Brix matrix which needs to be measured by utilizing a superconducting platform in coefficients corresponding to the n-order Brix matrix according to the positions of non-zero vector elements in the target vector corresponding to the target sub-quantum system set.

In one embodiment, according to a target matrix corresponding to the target sub-quantum system set, calculating to obtain a target vector corresponding to the target sub-quantum system set includes:

Calculating a target vector corresponding to the target sub-quantum system set based on the target constraint condition and a target matrix corresponding to the target sub-quantum system set; the target constraint includes that the target sub-quantum system set corresponds to a minimum of non-zero vector elements of the target vector.

In one embodiment, the target constraint comprises:

subject to:A^Tx≥1and x_i＝{0,1}，

Where x represents the target vector, x _i represents the i-th vector element of the target vector x, and a represents the target matrix.

In one embodiment, determining, according to a position of a non-zero vector element in a target vector corresponding to a target sub-quantum system set in the target vector, a target n-order berm to be measured by using a superconducting platform in coefficients corresponding to the n-order berm includes:

According to the position of the non-zero vector element in the target vector, determining an n-bit ternary number corresponding to the non-zero vector element;

and determining a target n-order Brix matrix which needs to be measured by using the superconducting platform in coefficients corresponding to the n-order Brix matrix based on the n-bit ternary number.

In a second aspect, the present application also provides a reduced density matrix apparatus. The device comprises:

The splitting module is used for executing splitting processing on the n-bit quantum system to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not completely identical;

the judging module is used for judging whether each coefficient corresponding to the k-order Paulownia matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to the n-order Paulownia matrix of the n-bit sub-quantum system;

The determining module is used for determining a target n-order Paully matrix which needs to be measured by utilizing the superconducting platform in coefficients corresponding to the n-order Paully matrix according to the judging result of the target sub-quantum system set, and measuring the coefficients of the target n-order Paully matrix by utilizing the superconducting platform;

And the reconstruction module is used for determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set based on the measurement result, and reconstructing a reduced density matrix corresponding to each k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients.

In one embodiment, the judging module is specifically configured to:

For a j-th k-order Paulownia matrix of a k-bit sub-quantum system corresponding to the target sub-quantum system set, acquiring a second operation composition element set corresponding to the j-th k-order Paulownia matrix;

In one embodiment, the determination result of the target sub-quantum system set includes a target matrix, and the size of the target matrix isThe matrix element a _ij in the target matrix is used for characterizing whether the corresponding coefficient of the jth k-order berkovich matrix corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order berkovich matrix of the n-bit quantum system, and the determining module is specifically configured to:

In one embodiment, the determining module is further specifically configured to:

In one embodiment, the target constraint comprises:

subject to:A^Tx≥1and x_i＝{0,1}，

In a third aspect, the present application also provides a computer device. The computer device comprises a memory storing a computer program and a processor implementing the reduced density matrix reconstruction method according to any one of the first aspects above when the computer program is executed by the processor.

In a fourth aspect, the present application also provides a computer-readable storage medium. The computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements a reduced density matrix reconstruction method as described in any one of the first aspects above.

In a fifth aspect, the present application also provides a computer program product. The computer program product comprising a computer program which, when executed by a processor, implements a reduced density matrix reconstruction method as described in any one of the first aspects above.

The reduced density matrix reconstruction method, the reduced density matrix reconstruction device, the computer equipment, the storage medium and the computer program product perform multiple splitting treatment on the n-bit quantum system to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not completely identical; judging whether each coefficient corresponding to a k-order Paulownia matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to an n-order Paulownia matrix of the n-bit sub-quantum system; according to the judging result of the target sub-quantum system set, determining a target n-order Brix matrix which needs to be measured by utilizing a superconducting platform in coefficients corresponding to the n-order Brix matrix, and measuring the coefficients of the target n-order Brix matrix by utilizing the superconducting platform; based on the measurement result, determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set, and reconstructing a reduced density matrix corresponding to each k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients. And the measurement of all k-order Paulownia matrix coefficients corresponding to a plurality of k-bit sub-quantum systems in the target subsystem set is realized only by selecting a group of n-order Paulownia matrices, the measurement work is not required to be executed for the coefficients of each k-order Paulownia matrix, the number of times of executing the coefficient measurement work is reduced as much as possible, the reconstruction work of the reduced density matrix is optimized, and the efficiency of the measurement work is improved.

Drawings

FIG. 1 is a flow chart of a method for reconstructing a reduced density matrix in one embodiment;

FIG. 2 is a flow chart of step 102 in one embodiment;

FIG. 3 is a flow chart of step 103 in one embodiment;

FIG. 4 is a flow chart of step 302 in one embodiment;

FIG. 5 is a flow chart of a method for reconstructing a reduced density matrix according to another embodiment;

FIG. 6 is a block diagram of an apparatus for reconstructing a reduced density matrix in one embodiment;

fig. 7 is an internal structural diagram of a computer device in one embodiment.

Detailed Description

The present application will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present application more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the application.

The quantum state reconstruction is carried out by continuously measuring and reading out partial information and recombining the partial information to obtain the complete information of the quantum state in the quantum system. The state of the quantum system is generally described by a density matrix ρ. Any density Matrix can be considered as a linear combination of a set of Pauli matrices (Pauli Matrix). The berlite matrix is a set of 2 x 2 matrices defined as follows:

the form of expansion of ρ (2 ⁿ×2ⁿ) for an n-bit system is as follows:

Where P _i is the direct product of the Pauloian matrix, referred to herein as the n-th order Pauloian matrix. For an n-bit system, V _i is the expansion coefficient for P _i, such unknown coefficients v _i together being 4 ⁿ -1.

The density matrix of the system quantum state can be calculated according to the formula as long as all expansion coefficients are obtained through measurement. All coefficients are obtained through multiple measurements and a density matrix is obtained through calculation, namely quantum state reconstruction.

All the information of the density matrix ρ cannot be read out through one measurement, so that the information of ρ needs to be measured and read out step by using a plurality of different measurement experiments, and the experimental data is processed to calculate the complete density matrix ρ. In this process, different brix matrix expansion coefficients are measured by modifying the experimental setup for each measurement.

The reduced density matrix refers to the description of the quantum state of a k-bit sub-quantum system in an n-bit quantum system, is an indispensable tool for analyzing the quantum system, and plays an important role in the development of quantum signals and quantum technologies. In the prior art, when obtaining the reduced density matrix corresponding to each k-bit sub-quantum system in the n-bit quantum system, coefficient measurement is performed on the expansion coefficients of the k-order berm matrix (i.e., the measurement expected values corresponding to the berm matrix when the berm matrix is used as an observably measured operator) included in the reduced density matrix corresponding to each k-bit sub-quantum system by means of the superconducting platform. In the conventional QST method, only the superconducting platform is needed to be used for theAnd (3) respectively measuring coefficients corresponding to the k-order Paulownian matrix to obtain coefficients corresponding to all the n-order Paulownian matrices in the density matrix rho. The coefficient measurement work for each k-th order berm needs to be performed M times, so the number of measurements required for only a certain k-bit quantum system of the n-bit quantum systems is 3 ^k ×m times.

But the n-bit quantum system is commonly included withA k-bit quantum system. And the coefficient measurement work is respectively executed aiming at the coefficient of the k-order Pauloy matrix contained in each k-bit quantum system, so that the measurement workload is huge, the laboratory resource requirement is huge, and the measurement efficiency is low.

In view of this, the embodiment of the application provides a reduced density matrix reconstruction method, which can improve the measurement efficiency of the reduced density matrix reconstruction measurement work.

It should be noted that, in the reduced density matrix reconstruction method provided by the embodiment of the present application, the execution body may be a reduced density matrix reconstruction device, and the reduced density matrix reconstruction device may be implemented in a manner of software, hardware, or a combination of software and hardware to form part or all of the terminal.

In the following method embodiments, the execution subject is a terminal, which may be a personal computer, a notebook computer, a media player, a smart television, a smart phone, a tablet computer, a portable wearable device, etc., and it is understood that the method may also be applied to a server, and may also be applied to a system including the terminal and the server, and implemented through interaction between the terminal and the server.

Referring to fig. 1, a flowchart of a reduced density matrix reconstruction method according to an embodiment of the application is shown. As shown in fig. 1, the reduced density matrix reconstruction method may include the steps of:

And step 101, splitting the n-bit quantum system to obtain a target sub-quantum system set.

The target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical.

Alternatively, a k (k < n) is determined, and a k-bit sub-quantum system is formed by optionally k quantum bits from n quantum bits in the n-bit sub-quantum system by adopting a random sampling method, thereby obtainingAnd k-bit sub-quantum systems which form a target sub-quantum system set.

Step 102, determining whether each coefficient corresponding to the k-order bubble-benefit matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the n-order bubble-benefit matrix of the n-bit sub-quantum system.

Optionally, for each k-order pauli matrix in a k-bit sub-quantum system, it is determined whether the coefficient corresponding to the k-order pauli matrix can not be obtained by the coefficient measurement result distribution information corresponding to the n-order pauli matrix of the n-bit sub-quantum system, if so, the coefficient corresponding to the k-order pauli matrix can be determined by the coefficient measurement result distribution information corresponding to the n-order pauli matrix of the n-bit sub-quantum system, otherwise, the coefficient corresponding to the k-order pauli matrix can not be determined by the coefficient measurement result distribution information corresponding to the n-order pauli matrix of the n-bit sub-quantum system.

And step 103, determining a target n-order Paully matrix which needs to be measured by using a superconducting platform in coefficients corresponding to the n-order Paully matrix according to a judging result of the target sub-quantum system set, and measuring the coefficients of the target n-order Paully matrix by using the superconducting platform.

Optionally, the superconducting platform has XYZ volume, including an X-axis, a Y-axis, and a Z-axis. For a certain n-order Paully matrix needing coefficient measurement by utilizing a superconducting platform The corresponding poultice matrix element set b= { B ₁,B₂,…,B_n }, according to the poultice matrix type corresponding to each element of the poultice matrix element set b= { B ₁,B₂,…,B_n }, determining the direction in which each qubit in the n-order poultice matrix should rotate, for example, when the poultice matrix type corresponding to the ith poultice matrix element B _i is X, rotating the ith qubit to the X axis; when the type of the Baoli matrix corresponding to the ith Baoli matrix element B _i is Y, rotating the ith quantum bit to a Y axis; when the type of the bubble matrix corresponding to the ith bubble matrix element B _i is Z, the ith qubit is rotated to the Z axis.

The superconducting platform determines the type of the pulse signal to be reflected according to the obtained rotation direction of each qubit. A pulse signal of this pulse signal type is then sent to enable each qubit to rotate to the corresponding axis. However, the positions where the qubits finally stop on the axes have randomness, and the qubits can stop on a positive half shaft and a negative half shaft. Therefore, the final stop position of each qubit corresponding to the n-order brix matrix is 2 ⁿ. For these 2 ⁿ cases, the number of times of each case was determined.

With a certain Brix matrix in a 3-bit sub-system(Abbreviated as t=xyz) for example, which may occur includes ：X_↑Y_↑Z_↑,X_↑Y_↑Z_↓,X_↑Y_↓Z_↑,X_↑Y_↓Z_↓,X_↓Y_↑Z_↑,X_↓Y_↑Z_↓,X_↓Y_↓Z_↑,X_↓Y_↓Z_↓, where ∈indicates that the qubit is stopped on the positive half-axis, ∈r indicates that the qubit is stopped on the negative half-axis, i.e., X _↑ indicates that the qubit is stopped on the positive half-axis of the X-axis.

Optionally, after determining the target n-order pauli matrix, performing M measurement operations with the superconducting platform for each target n-order pauli matrix. And counting probability distribution conditions of various conditions in M times of measurement operation aiming at each target n-order Paully matrix to obtain coefficient measurement result distribution information corresponding to the target n-order Paully matrix.

Step 104, determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set based on the measurement result, and reconstructing a reduced density matrix corresponding to each k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients.

Optionally, determining the target situation according with the k-order Paulownia matrix measurement scenario from the 2 ⁿ situations, counting the times of each target situation, and finally calculating to obtain the coefficient corresponding to the k-order Paulownia matrix according to the times of each target situation.

Taking the 3-bit quantum system to reconstruct the reduced density matrix of any 2-bit sub-quantum system as an example, aiming at a certain 2-order Paul matrix corresponding to a certain 2-bit sub-quantum system(Abbreviated as s=xy), the target cases of the above 2 ⁿ cases that fit the k-order berkovich matrix measurement scenario include ：X_↑Y_↑Z_↑,X_↑Y_↑Z_↓,X_↑Y_↓Z_↑,X_↑Y_↓Z_↓,X_↓Y_↑Z_↑,X_↓Y_↑Z_↓,X_↓Y_↓Z_↑,X_↓Y_↓Z_↓. where, for the 2-order berkovich matrix XY, the case where X _↑Y_↑ occurs includes: x _↑Y_↑Z_↑,X_↑Y_↑Z_↓. Then, the coefficient corresponding to the 2 nd order berlite matrix s=xy can be calculated by using the following formula:

Wherein N is the total number of measurements; the j eigenvalue corresponding to the Pauloy matrix represented by a _ij is only 1 or-1 for the Pauloy matrix; n _ij represents the number of occurrences of the corresponding eigenvalue. For a _ij, assuming that when measuring the coefficients of some n-th order brix matrix of an n-bit quantum system, the mth qubit finally stops at the positive half-axis of each axis, a _m =1, otherwise a _m = -1. Thus, a _ij＝a₁*a₂*…*a_n.

That is, the above calculation formula of the coefficient corresponding to the 2 nd order bery matrix s=xy can be converted into:

wherein, The number of occurrences of X _↑Y_↑Z_↑ is indicated,The number of occurrences of X _↑Y_↑Z_↓ is indicated,The number of occurrences of X _↑Y_↓Z_↑ is indicated,The number of occurrences of X _↑Y_↓Z_↓ is indicated,The number of occurrences of X _↓Y_↑Z_↑ is indicated,The number of occurrences of X _↓Y_↑Z_↓ is indicated,The number of occurrences of X _↓Y_↓Z_↑ is indicated,Indicating the number of times X _↓Y_↓Z_↓ occurs.

Optionally, for each k-bit sub-quantum system, calculating to obtain coefficients corresponding to each k-order Paulownian matrix contained in the k-bit sub-quantum system, and obtaining a reduced density matrix corresponding to the k-bit sub-quantum system according to the coefficients corresponding to each k-order Paulownian matrix.

In the reduced density matrix reconstruction method, the n-bit quantum system is split for multiple times to obtain the target sub-quantum system set, and the target n-order Pauloy matrix which is required to be measured by utilizing the superconducting platform in the coefficients corresponding to the n-order Pauloy matrix is determined according to the judging result of the target sub-quantum system set, so that the purpose of selecting a group of n-order Pauloy matrices to be used for measuring all k-order Pauloy matrix coefficients in the target sub-quantum system set is realized, the measurement work is not required to be respectively carried out for the coefficients of each k-order Pauloy matrix, the times for carrying out the coefficient measurement work are reduced as much as possible, the reduced density matrix work is optimized, and the efficiency of the measurement work is improved.

In the implementation of the present application, referring to fig. 2, based on the embodiment shown in fig. 1, the present embodiment relates to determining, in step 102, whether each coefficient corresponding to a k-order berkovich matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to an n-order berkovich matrix of an n-bit sub-system, including the following steps:

step 201, for the ith n-order bubble matrix of the n-bit quantum system, obtaining a first operation element set corresponding to the ith n-order bubble matrix.

Optionally, each qubit of the N-bit quantum system is numbered to obtain a set of qubit numbers N ₁＝{D₁,D₂,…,D_n of the N-bit quantum system, where D _n represents the number of the N-th qubit. For any n-th order Paully matrixWherein the method comprises the steps ofRepresenting the type of the berk matrix corresponding to the nth qubit.

The method comprises the steps of obtaining a Paully matrix element set B= { B ₁,B₂,…,B_n } and numbers of all quantum bits of T _n for direct product operation, combining the numbers corresponding to all the quantum bits with the Paully matrix types to form elements of a first operation component element set, for example, the representation form of an nth element in the first operation component element set is B _n -Dn, and then the corresponding first operation component element set S ₁＝{B₁·D1,B₂·D2,…,B_n -Dn.

Step 202, for the jth k-order bubble-benefit matrix corresponding to the target sub-quantum system set, obtaining a second operation composition element set corresponding to the jth k-order bubble-benefit matrix.

Optionally, all k-order bubble-benefit matrixes contained in all k-bit sub-quantum systems in the target sub-quantum system set are formed into a k-order bubble-benefit matrix set, and the j element in the k-order bubble-benefit matrix set is used as the j k-order bubble-benefit matrix.

Optionally, since the k-bit sub-quantum system is formed by selecting k quantum bits from N quantum bits in the N-bit sub-quantum system, obtaining numbers corresponding to the N-bit sub-quantum system of each quantum bit in the k-bit sub-quantum system to obtain a number set N ₂＝{E₁,E₂,…,E_k }, whereFor the k-th order Paully matrix Wherein the method comprises the steps ofThe set of the Paul matrix elements C= { C ₁,C₂,…,C_k } for which the direct product operation is performed is obtained.

Similarly, the number corresponding to each qubit of the k-bit sub-quantum system is combined with the Paulori matrix type to form an element of the second operation component element set, and the representation form of the kth element in the second operation component element set is B _k·E_k, so that the corresponding second operation component element set S ₁＝{B_k·E₁,B₂·E₂,…,B_k·E_k is formed.

In step 203, if the second operation component element set is a subset of the first operation component element set, the coefficient corresponding to the kth order k-ary berm can be determined by the coefficient measurement result distribution information corresponding to the ith n-ary berm.

Optionally, by means of a character recognition algorithm, whether each element in the second set of operation constituent elements is a constituent element in the first set of operation constituent elements, and if each element in the second set of operation constituent elements is an element in the first set of operation constituent elements, then the second set of operation constituent elements is said to be a subset of the first set of operation constituent elements.

In step 204, if the second operation component element set is not a subset of the first operation component element set, the coefficient corresponding to the kth order k-ary berm cannot be determined by the coefficient measurement result distribution information corresponding to the ith n-ary berm.

Optionally, if there is an element in the certain second set of operation constituent elements that is not an element in the first set of operation constituent elements, it is indicated that the second set of operation constituent elements is not a subset of the first set of operation constituent elements.

In this embodiment, by acquiring the first operation component element set corresponding to the ith n-order bubble-benefit matrix in the n-bit quantum system and the second operation component element set corresponding to the jth k-order bubble-benefit matrix corresponding to the target sub-quantum system set, and determining that the coefficient corresponding to the jth k-order bubble-benefit matrix can be determined by the coefficient measurement result distribution information corresponding to the ith n-order bubble-benefit matrix when the second operation component element set is the subset of the first operation component element set, the determination method is simple and has a small calculation amount, and it is realized whether each coefficient corresponding to the k-order bubble-benefit matrix of each k-bit sub-quantum system in the target sub-quantum system set can be determined by the coefficient corresponding to the n-order bubble-benefit matrix of the n-bit quantum system.

In the implementation of the present application, the judgment result of the target sub-quantum system set includes a target matrix, and the size of the target matrix isMatrix element a _ij in the target matrix is used to characterize whether the corresponding coefficient of the jth k-order berm corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order berm of the n-bit quantum system. As shown in fig. 3, based on the embodiment shown in fig. 1, the present embodiment relates to determining, in step 103, a target n-order berkovich matrix that needs to be measured by using a superconducting platform, from coefficients corresponding to the n-order berkovich matrix according to a determination result of the target sub-quantum system set, including the following steps:

step 301, calculating to obtain a target vector corresponding to the target sub-quantum system set according to the target matrix corresponding to the target sub-quantum system set.

The size of the target vector is 3 ⁿ ×1, and the vector element of the target vector is 0 or 1.

Optionally, the a _ij element of the target matrix is 0 or 1. And determining the coefficient corresponding to the j-th order k-ary bubble matrix in all k-ary bubble matrices contained in the target sub-quantum system set by the coefficient corresponding to the i-th order n-ary bubble matrix, wherein a _ij =1, otherwise a _ij =0.

Optionally, when the number of non-zero elements in the vector corresponding to the target sub-quantum system set obtained by calculation is smaller than a preset threshold value according to the target matrix corresponding to the target sub-quantum system set, the vector is used as the target vector.

Step 302, determining a target n-order Paul matrix which needs to be measured by using a superconducting platform in coefficients corresponding to the n-order Paul matrix according to positions of non-zero vector elements in target vectors corresponding to the target sub-quantum system set.

Optionally, the terminal stores a mapping relation table of positions of non-zero elements in the target vector and the n-order berkovich matrix. And the terminal obtains the position of the non-zero element in the target vector, and obtains an n-order Paulownia matrix corresponding to the position in a table look-up mode, namely the target n-order Paulownia matrix.

In this embodiment, the target vector corresponding to the target sub-quantum system set is obtained by calculation according to the target matrix corresponding to the target sub-quantum system set, and the target n-order berkovich matrix, which needs to be measured by using the superconducting platform, in the coefficients corresponding to the n-order berkovich matrix is determined according to the position of the non-zero vector element in the target vector corresponding to the target sub-quantum system set, so that the reconstruction work of the reduced density matrix is optimized, and the efficiency of measurement work is improved.

In the embodiment of the present application, based on the embodiment shown in fig. 3, the embodiment relates to a process of calculating, in step 301, a target vector corresponding to a target sub-quantum system set according to a target matrix corresponding to the target sub-quantum system set, where the implementing process includes:

Optionally, the target constraint includes:

subject to:A^Tx≥1and x_i＝{0,1}，

In the embodiment of the application, the target vector corresponding to the sub-quantum system set is calculated based on the target constraint condition and the target matrix corresponding to the target sub-quantum system set, so that the minimum measurement object corresponding to the target sub-quantum system set is obtained, the reduced density matrix reconstruction work is optimized, and the efficiency of the measurement work is improved.

In the embodiment of the present application, as shown in fig. 4, based on the embodiment shown in fig. 3, the embodiment relates to a process for implementing a target n-order berkovich matrix, which needs to be measured by using a superconducting platform, in determining coefficients corresponding to the n-order berkovich matrix according to positions of non-zero vector elements in target vectors corresponding to a target sub-quantum system set in the target vector in step 302, where the implementing process includes:

Step 401, determining an n-bit ternary number corresponding to the non-zero vector element according to the position of the non-zero vector element in the target vector.

The position of the non-zero vector element in the target vector refers to the number of vector elements in the whole target vector.

Optionally, for a certain non-zero vector element, determining what number of vector elements is in the whole target vector, assuming that the non-zero vector element is the i-th vector element in the whole target vector, subtracting 1 from i to obtain a k value, converting the k value into a ternary number, and representing the ternary number as an n-bit ternary number, wherein if the L-th bit number of the ternary number is 0, the L-th bubble matrix element in the n-order bubble matrix is taken as X; if the L-th digit of the ternary number is 1, taking the L-th Pauloy matrix element as Y; if the L-th digit of the ternary number is 2, the L-th Pauloy matrix element is taken as Z. And determining the target coefficient for executing the measurement according to the obtained ternary number. For example, the k=1, then converted to a ternary number of 0001, then the n-order brix matrix is needed to perform the coefficient measurement operation

Step 402, determining a target n-order Paullian matrix to be measured by using a superconducting platform in coefficients corresponding to the n-order Paullian matrix based on the n-bit ternary number.

In this embodiment, the n-order bubble-benefit matrix of the target n-order bubble-benefit matrix, which needs to be measured by using the superconducting platform, is determined according to the position of the non-zero vector element in the target vector, the n-bit ternary number corresponding to the non-zero vector element is determined, and based on the n-bit ternary number, the n-order bubble-benefit matrix of the target n-order bubble-benefit matrix, which needs to be measured by using the superconducting platform, is determined, so that the method is simple and the calculation amount is small.

In an embodiment of the present application, as shown in fig. 5, a reduced density matrix reconstruction method is provided, including the following steps:

step 501, performing multiple splitting processing on the n-bit quantum system to obtain a target sub-quantum system set.

Step 502, for an ith n-order bubble matrix of the n-bit quantum system, obtaining a first operation element set corresponding to the ith n-order bubble matrix.

Step 503, for the jth k-th order bubble-benefit matrix corresponding to the target sub-quantum system set, obtaining a second operation component element set corresponding to the jth k-th order bubble-benefit matrix.

In step 504, if the second operation component element set is a subset of the first operation component element set, the coefficient corresponding to the kth order k-ary berm can be determined by the coefficient measurement result distribution information corresponding to the ith n-ary berm.

In step 505, if the second operation component element set is not a subset of the first operation component element set, the coefficient corresponding to the kth order k-ary berm cannot be determined by the coefficient measurement result distribution information corresponding to the ith n-ary berm.

And step 506, generating a target matrix corresponding to the target sub-quantum system set according to the judgment result.

Wherein the size of the target matrix isMatrix element a _ij in the target matrix is used to characterize whether the corresponding coefficient of the jth k-order berm corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order berm of the n-bit quantum system.

Step 507, calculating a target vector corresponding to the target sub-quantum system set based on the target constraint condition and a target matrix corresponding to the target sub-quantum system set.

Wherein, the size of the target vector is 3 ⁿ ×1, the vector element of the target vector is 0 or 1, and the target constraint condition includes:

subject to:A^Tx≥1and x_i＝{0,1}，

Step 508, determining an n-bit ternary number corresponding to the non-zero vector element according to the position of the non-zero vector element in the target vector.

Step 509, determining a target n-order bubble matrix to be measured by using the superconducting platform in coefficients corresponding to the n-order bubble matrix based on the n-bit ternary number.

Step 510, measuring coefficients of the target n-order berkovich matrix by using a superconducting platform, and determining coefficients corresponding to each k-order berkovich matrix in the target sub-quantum system set based on a measurement result.

And step 511, reconstructing a reduced density matrix corresponding to each k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients.

In the reduced density matrix reconstruction method, the measurement of all k-order Paulownia matrix coefficients corresponding to a plurality of k-bit sub-quantum systems in the target sub-quantum system set is realized by selecting a group of n-order Paulownia matrices, the measurement work is not required to be executed for the coefficients of each k-order Paulownia matrix, the times for executing the coefficient measurement work are reduced as much as possible, the reduced density matrix work is optimized, and the efficiency of the measurement work is improved; and the objective of selecting a group of n-order Paulownia matrixes containing the least number for measuring all k-order Paulownia matrix coefficients is realized by calculating the objective vector corresponding to the target sub-quantum system set based on the target constraint condition and the objective matrix corresponding to the target sub-quantum system set, so that the number of n-order Paulownia matrixes needing to execute coefficient measurement is reduced, the reduced density matrix reconstruction is greatly optimized, the measurement times are further reduced, and the efficiency of the measurement is improved.

The following is an experimental case for verifying the reduced density matrix reconstruction method according to the embodiment of the present application.

The scheme can reconstruct the reduced density matrix of any k-bit quantum system in the n-bit quantum system, and the number of used measurement settings is greatly reduced. Applying this scheme in 4-bit, 5-bit, 6-bit, 7-bit, 8-bit, 9-bit, 10-bit systems optimizes the number of measurement settings they need to reconstruct any 2-bit reduced density matrix, resulting in the following:

Number of bits	4	5	6	7	8	9	10
								Traditional QST	54	90	135	189	252	324	405
The proposal is that	9	11	12	12	14	15	16

It can be seen that our method has a significant reduction in the number of measurements compared to conventional QST measurements.

The following illustrates the advantages of our approach over the traditional QST approach with the reconstruction of an arbitrary 2-bit reduced density matrix in a 4-bit quantum system:

the unknown coefficients to be measured for the 2-bit quantum state total 16 are:

P_i∈S_p＝{II,IX,IY,IZ,XI,XX,XY,XZ,YI,YX,YY,YZ,ZI,ZX,ZY,ZZ}

the measurements required for a conventional QST are set to (containing 9 measurements):

{XX,XY,XZ,YX,YY,YZ,ZX,ZY,ZZ}

All the above 9 measurements must be used to measure 16 unknown coefficients, which is not necessary.

And two bits are arbitrarily selected in the 4-bit quantum system, and there are 6 possible selection combinations, so that 54 measurements are required in total.

(2) According to the scheme, after optimization, only 9 4-order Paulownia matrixes needing coefficient measurement are measured and set, and the elements are respectively:

{XXXZ,XYYX,XZZY,YXYY,YYZZ,YZXX,ZXZX,ZYXY,ZZYZ}

the function is as follows:

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix XXXZ ：{X₁X₂,X₁X₃,X₁Z₄,X₂X₃,X₂Z₄,X₃Z₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix XYYX ：{X₁Y₂,X₁Y₃,X₁X₄,Y₂Y₃,Y₂X₄,Y₃X₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix XZZY ：{X₁Z₂,X₁Z₃,X₁Y₄,Z₂Z₃,Z₂Y₄,Z₃Y₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix YXYY ：{Y₁X₂,Y₁Y₃,Y₁Y₄,X₂Y₃,X₂Y₄,Y₃Y₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix YYZZ ：{Y₁Y₂,Y₁Z₃,Y₁Z₄,Y₂Z₃,Y₂Z₄,Z₃Z₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix YZXX ：{Y₁Z₂,Y₁X₃,Y₁X₄,Z₂X₃,Z₂X₄,X₃X₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix ZXZX ：{Z₁X₂,Z₁Z₃,Z₁X₄,X₂Z₃,X₂X₄,Z₃X₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix ZYXY ：{Z₁Y₂,Z₁X₃,Z₁Y₄,Y₂X₃,Y₂Y₄,X₃Y₄};

The coefficients of the following 6 2-order Brix matrices can be measured under the 4-order Brix matrix ZZYZ ：{Z₁Z₂,Z₁Y₃,Z₁Z₄,Z₂Y₃,Z₂Z₄,Y₃Z₄}.

Wherein X ₁X₂ represents that the type of the brix matrix corresponding to the first quantum bit is X and the type of the brix matrix corresponding to the second quantum bit is X, and so on, and no description is given.

The 9 4 th order bery matrices comprise all 54 second order bery matrices of 6 2-bit reduced density matrices. It can be seen that the above 9 measurements can measure all 54 unknown coefficients, and thus reconstruct all 2-bit reduced density matrices.

It should be understood that, although the steps in the flowcharts related to the embodiments described above are sequentially shown as indicated by arrows, these steps are not necessarily sequentially performed in the order indicated by the arrows. The steps are not strictly limited to the order of execution unless explicitly recited herein, and the steps may be executed in other orders. Moreover, at least some of the steps in the flowcharts described in the above embodiments may include a plurality of steps or a plurality of stages, which are not necessarily performed at the same time, but may be performed at different times, and the order of the steps or stages is not necessarily performed sequentially, but may be performed alternately or alternately with at least some of the other steps or stages.

Based on the same inventive concept, the embodiment of the application also provides a reduced density matrix reconstruction device for realizing the above related reduced density matrix reconstruction method. The implementation of the solution provided by the apparatus is similar to the implementation described in the above method, so the specific limitations in the embodiments of one or more reduced density matrix reconstruction apparatuses provided below may be referred to above for the limitations of the reduced density matrix reconstruction method, which are not repeated here.

In one embodiment, as shown in fig. 6, there is provided a reduced density matrix reconstruction apparatus comprising: splitting module, judging module, determining module and reconstructing module, wherein:

the splitting module is used for executing splitting processing on the n-bit quantum systems to obtain a target sub-quantum system set, wherein the target sub-system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical;

In one embodiment, the judging module is specifically configured to:

In one embodiment, the target constraint includes:

subject to:A^Tx≥1and x_i＝{0,1}，

The various modules in the reduced density matrix reconstruction device described above may be implemented in whole or in part by software, hardware, and combinations thereof. The above modules may be embedded in hardware or may be independent of a processor in the computer device, or may be stored in software in a memory in the computer device, so that the processor may call and execute operations corresponding to the above modules.

In one embodiment, a computer device is provided, which may be a terminal, and the internal structure of which may be as shown in fig. 7. The computer device includes a processor, a memory, a communication interface, a display screen, and an input device connected by a system bus. Wherein the processor of the computer device is configured to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The communication interface of the computer device is used for carrying out wired or wireless communication with an external terminal, and the wireless mode can be realized through WIFI, a mobile cellular network, NFC (near field communication) or other technologies. The computer program is executed by a processor to implement a reduced density matrix reconstruction method. The display screen of the computer equipment can be a liquid crystal display screen or an electronic ink display screen, and the input device of the computer equipment can be a touch layer covered on the display screen, can also be keys, a track ball or a touch pad arranged on the shell of the computer equipment, and can also be an external keyboard, a touch pad or a mouse and the like.

It will be appreciated by those skilled in the art that the structure shown in FIG. 7 is merely a block diagram of some of the structures associated with the present inventive arrangements and is not limiting of the computer device to which the present inventive arrangements may be applied, and that a particular computer device may include more or fewer components than shown, or may combine some of the components, or have a different arrangement of components.

In one embodiment, a computer device is provided comprising a memory and a processor, the memory having stored therein a computer program, the processor when executing the computer program performing the steps of:

According to the judging result of the target sub-quantum system set, determining a target n-order Brix matrix which needs to be measured by using a superconducting platform in coefficients corresponding to the n-order Brix matrix, and measuring the coefficients of the target n-order Brix matrix by using the superconducting platform;

In one embodiment, the processor when executing the computer program further performs the steps of:

For an ith n-order Pauloy matrix of the n-bit quantum system, acquiring a first operation composition element set corresponding to the ith n-order Pauloy matrix; for a jth k-order Paulownia matrix corresponding to the target sub-quantum system set, obtaining a second operation composition element set corresponding to the jth k-order Paulownia matrix; if the second operation component element set is a subset of the first operation component element set, the coefficient corresponding to the jth k-order Paulownia matrix can be determined by the coefficient measurement result distribution information corresponding to the ith n-order Paulownia matrix; if the second operation component element set is not a subset of the first operation component element set, the coefficient corresponding to the jth k-order Paulownia matrix cannot be determined by the coefficient measurement result distribution information corresponding to the ith n-order Paulownia matrix.

According to a target matrix corresponding to the target sub-quantum system set, calculating to obtain a target vector corresponding to the target sub-quantum system set, wherein the size of the target vector is 3 ⁿ multiplied by 1, and vector elements of the target vector are 0 or 1, the judgment result of the target sub-quantum system set comprises a target matrix, and the size of the target matrix is Matrix element A _ij in the target matrix is used for representing whether the corresponding coefficient of the jth k-order Pauloside matrix corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order Pauloside matrix of the n-bit quantum system; and determining a target n-order Brix matrix which needs to be measured by utilizing a superconducting platform in coefficients corresponding to the n-order Brix matrix according to the positions of non-zero vector elements in the target vector corresponding to the target sub-quantum system set.

The target constraint includes:

subject to:A^Tx≥1and x_i＝{0,1}，

According to the position of the non-zero vector element in the target vector, determining an n-bit ternary number corresponding to the non-zero vector element; and determining a target n-order Brix matrix which needs to be measured by using the superconducting platform in coefficients corresponding to the n-order Brix matrix based on the n-bit ternary number.

In one embodiment, a computer readable storage medium is provided having a computer program stored thereon, which when executed by a processor, performs the steps of:

In one embodiment, the computer program when executed by the processor further performs the steps of:

The target constraint includes:

subject to:A^Tx≥1and x_i＝{0,1}，

In one embodiment, a computer program product is provided comprising a computer program which, when executed by a processor, performs the steps of:

splitting the n-bit quantum system to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical;

The target constraint includes:

subject to:A^Tx≥1and x_i＝{0,1}，

Those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by way of a computer program stored on a non-transitory computer readable storage medium, which when executed, may comprise the steps of the embodiments of the methods described above. Any reference to memory, database, or other medium used in embodiments provided herein may include at least one of non-volatile and volatile memory. The nonvolatile Memory may include Read-Only Memory (ROM), magnetic tape, floppy disk, flash Memory, optical Memory, high density embedded nonvolatile Memory, resistive random access Memory (ReRAM), magneto-resistive random access Memory (Magnetoresistive Random Access Memory, MRAM), ferroelectric Memory (Ferroelectric Random Access Memory, FRAM), phase change Memory (PHASE CHANGE Memory, PCM), graphene Memory, and the like. Volatile memory can include random access memory (Random Access Memory, RAM) or external cache memory, and the like. By way of illustration, and not limitation, RAM can be in various forms such as static random access memory (Static Random Access Memory, SRAM) or dynamic random access memory (Dynamic Random Access Memory, DRAM), etc. The databases referred to in the embodiments provided herein may include at least one of a relational database and a non-relational database. The non-relational database may include, but is not limited to, a blockchain-based distributed database, and the like. The processor referred to in the embodiments provided in the present application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic unit, a data processing logic unit based on quantum computing, or the like, but is not limited thereto.

The technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be considered as the scope of the description.

The foregoing examples illustrate only a few embodiments of the application and are described in detail herein without thereby limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of the application should be assessed as that of the appended claims.

Claims

1. A method of reduced density matrix reconstruction, the method comprising:

splitting n-bit quantum systems to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical;

judging whether each coefficient corresponding to a k-order Paulownia matrix of each k-bit sub-quantum system in the target sub-quantum system set can be obtained from coefficient measurement result distribution information corresponding to an n-order Paulownia matrix of the n-bit sub-quantum system;

Based on a measurement result, determining coefficients corresponding to the k-order Paul matrix in the target sub-quantum system set, and reconstructing a reduced density matrix corresponding to the k-bit sub-quantum system in the target sub-quantum system set based on the determined coefficients;

wherein the judging result of the target sub-quantum system set comprises a target matrix, and the size of the target matrix is that The matrix element a _ij in the target matrix is used for characterizing whether the corresponding coefficient of the jth k-order berkovich matrix corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order berkovich matrix of the n-bit quantum system, and determining, according to the judgment result of the target sub-quantum system set, a target n-order berkovich matrix which needs to be measured by using a superconducting platform from the coefficients corresponding to the n-order berkovich matrix, where the method includes:

Determining a target n-order Paully matrix which needs to be measured by using a superconducting platform in coefficients corresponding to the n-order Paully matrix according to the positions of non-zero vector elements in target vectors corresponding to the target sub-quantum system set;

the calculating to obtain the target vector corresponding to the target sub-quantum system set according to the target matrix corresponding to the target sub-quantum system set includes:

Calculating a target vector corresponding to the target sub-quantum system set based on a target constraint condition and a target matrix corresponding to the target sub-quantum system set; the target constraint condition includes that non-zero vector elements of a target vector corresponding to the set of target sub-quantum systems are at a minimum.

2. The method according to claim 1, wherein the determining whether each coefficient corresponding to the k-order berm of each k-bit sub-quantum system in the target sub-quantum system set can be determined by coefficient measurement result distribution information corresponding to the n-order berm of the n-bit sub-quantum system includes:

for a jth k-order Paulownia matrix corresponding to the target sub-quantum system set, acquiring a second operation composition element set corresponding to the jth k-order Paulownia matrix;

If the second operation component element set is not a subset of the first operation component element set, the coefficient corresponding to the jth k-order berkovich matrix cannot be determined by the coefficient measurement result distribution information corresponding to the ith n-order berkovich matrix.

3. The method of claim 1, wherein the target constraint comprises:

subject to:A^Tx≥1and x_i＝{0,1}，

4. The method according to claim 1, wherein the determining, according to the positions of non-zero vector elements in the target vectors corresponding to the target sub-quantum system set, a target n-order berkovich matrix, which needs to be measured by using a superconducting platform, in coefficients corresponding to the n-order berkovich matrix includes:

and determining the target n-order Paul matrix which needs to be measured by using a superconducting platform in coefficients corresponding to the n-order Paul matrix based on the n-bit ternary number.

5. A reduced density matrix reconstruction apparatus, the apparatus comprising:

The splitting module is used for executing splitting processing on the n-bit quantum systems to obtain a target sub-quantum system set, wherein the target sub-quantum system set comprises a plurality of k-bit sub-quantum systems, and k quantum bits contained in each k-bit sub-quantum system are not identical;

The judging module is used for judging whether each coefficient corresponding to the k-order Paulownia matrix of each k-bit sub-quantum system in the target sub-quantum system set can be obtained from coefficient measurement result distribution information corresponding to the n-order Paulownia matrix of the n-bit sub-quantum system;

the determining module is used for determining a target n-order Brix matrix which needs to be measured by utilizing a superconducting platform in coefficients corresponding to the n-order Brix matrix according to the judging result of the target sub-quantum system set, and measuring the coefficients of the target n-order Brix matrix by utilizing the superconducting platform;

The reconstruction module is used for determining coefficients corresponding to the k-order Paulownia matrixes in the target sub-quantum system set based on a measurement result, and reconstructing a reduced density matrix corresponding to the k-bit sub-quantum systems in the target sub-quantum system set based on the determined coefficients;

wherein the judging result of the target sub-quantum system set comprises a target matrix, and the size of the target matrix is that The matrix element a _ik in the target matrix is used for characterizing whether the corresponding coefficient of the jth k-order berkovich matrix corresponding to the target sub-quantum system set can be determined by the coefficient measurement result distribution information corresponding to the ith n-order berkovich matrix of the n-bit quantum system, and determining, according to the judgment result of the target sub-quantum system set, a target n-order berkovich matrix which needs to be measured by using a superconducting platform from the coefficients corresponding to the n-order berkovich matrix, where the method includes:

6. A computer device comprising a memory and a processor, the memory storing a computer program, characterized in that the processor implements the steps of the method of any of claims 1 to 4 when the computer program is executed.

7. A computer readable storage medium, on which a computer program is stored, characterized in that the computer program, when being executed by a processor, implements the steps of the method of any of claims 1 to 4.

8. A computer program product comprising a computer program, characterized in that the computer program, when executed by a processor, implements the steps of the method of any of claims 1 to 4.