Optimization method of single-quantum-bit 4-element rank-1 positive operator value measurement circuit

Abstract

The invention provides an optimization method for a single-quantum-bit 4-element rank 1 positive operator value measurement circuit. The optimization method comprises the following steps: S1, compiling a single-quantum-bit 4-element rank 1 positive operator value measurement scheme # imgabs0 # to be realized into an initial and unoptimized quantum circuit matrix which is expressed as UP; s2, judging the type of the measurement scheme, and dividing the measurement scheme into symmetrical information complete positive operator value measurement or other types of positive operator value measurement; s3, for symmetrical information complete positive operator value measurement, calculating to-be-compiled parameters US and c, and substituting US into the designed fixed line structure to complete compiling; s4, for other types of positive operator value measurement, optimizing the matrix form UP through an iterative algorithm for adjusting redundant parameters until an optimized matrix form # imgabs1 # is obtained, and then executing conventional quantum line compiling on # imgabs2 #; and S5, constructing and executing quantum measurement, obtaining original measurement data, and adjusting an original measurement result according to the compilation parameter c, thereby effectively reducing the noise influence in a measurement circuit.

Description

Technical Field

[0001] The present invention relates to the field of quantum information, and in particular to an optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit. Background Art

[0002] Estimating the properties of quantum systems is a core task in fields such as quantum physics and quantum information processing. As the number of degrees of freedom of a quantum system increases, such as the number of qubits, the dimensionality of the Hilbert space grows exponentially, which poses a huge challenge to quantum measurement and benchmarking. In addition, efficient characterization of noise and performance in quantum computing platforms has become an urgent need.

[0003] In this area, an important recent research advance is shadow estimation technology. This technology uses a set of shadows obtained by random measurements to obtain Multiple properties of the quantum state ρ can be estimated simultaneously. Specifically, each shadow generated is an unbiased estimate of ρ based on the random unitary ensemble from a tomographically complete or overcomplete A randomly selected unitary matrix U i The determined base, the result b obtained by projection measurement on this base i The applications of this framework are very wide, including quantum error mitigation, quantum correlation detection, and quantum chaos diagnosis. However, the process of sampling from a random unitary ensemble also brings about implementation complexity: on the one hand, random sampling requires a lot of resources to generate randomness and compile random circuits; on the other hand, frequent changes in experimental settings or circuit parameters also bring inconvenience to experimental operations. In addition, the shadow generated by each measurement is highly correlated with the corresponding quantum state, so frequent changes in the basis may introduce noise related to the gate operation, thereby affecting the accuracy of the shadow estimation.

[0004] To address these issues, researchers introduced IC-POVMs that go beyond projection measurements, realizing a real-time shadow estimation framework without frequent changes to circuit configurations. However, optimizing the circuit implementation of IC-POVM remains a critical but unsolved problem, especially when considering the noise in quantum hardware. In conventional compilation schemes, three CNOT gates are often required to implement a single-qubit POVM, and CNOT gates are particularly susceptible to noise in short-range quantum devices, with error rates typically much higher than single-qubit gates. Therefore, reducing the use of CNOT gates becomes critical. The goal of the present invention is to improve the practicality of POVM-based shadow estimation, reduce the impact of noise, and enhance compatibility with related algorithms. Summary of the invention

[0005] In view of the shortcomings of the prior art mentioned above, the purpose of the present invention is to provide an optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit, so as to solve the problems of resource consumption, inconvenient experimental operation and noise introduction in the prior art.

[0006] To achieve the above objectives and other related objectives, the present invention provides the following technical solutions:

[0007] A method for optimizing a single quantum bit 4-element rank 1 positive operator value measurement circuit comprises the following steps:

[0008] S1: The single-qubit 4-element rank-1 positive operator value measurement scheme to be implemented Compile to the initial, unoptimized quantum circuit matrix denoted as U P ;

[0009] S2: Determine the type of the measurement scheme and classify it into symmetric information complete positive operator valued measurement (SIC-POVM) or other types of positive operator valued measurement;

[0010] S3: For symmetric information complete positive operator value measurement, calculate the required compilation parameter U S and c, and U S Substitute into the designed fixed circuit structure to complete the compilation;

[0011] S4: For other types of positive operator-valued measurements, the matrix form U is optimized by an iterative algorithm that adjusts the redundant parameters P , until the optimized matrix form is obtained Then Perform regular quantum circuit compilation;

[0012] S5: Construct and perform quantum measurement, obtain raw measurement data, and adjust the raw measurement results according to the compilation parameter c.

[0013] Further: the step S1 specifically comprises the following steps:

[0014] S1.1: Legal single-qubit 4-element rank-1 positive operator value measurement scheme Decompose into

[0015]

[0016] in Need to meet

[0017]

[0018] S1.2: Measurement plan to be compiled Construct the matrix V:

[0019]

[0020] in is a row vector with 2 elements, which is The conjugate transpose of ; V is a 4×2 matrix;

[0021] S1.3: Construct a 4×2 matrix W and merge it with the matrix V to obtain the unoptimized quantum circuit matrix representation U P ,

[0022] U P =[VW]

[0023] AndU P is a 4×4 unitary matrix.

[0024] Further: the step S2 specifically comprises the following steps:

[0025] S2.1: Calculate all possible Tr(Π i Π j ), where i, j∈{1, 2, 3, 4};

[0026] S2.2: Execute the judgment, if it satisfies:

[0027]

[0028] Then the measurement type is symmetric information complete positive operator value measurement, otherwise it is other types of positive operator value measurement, where d is the sub-bit dimension to be measured.

[0029] Further: the step S3 specifically comprises the following steps:

[0030] S3.1: Prepare a quantum circuit with a fixed structure. The components of the quantum circuit include auxiliary quantum bits, the auxiliary quantum bits and the single-bit gate U on the quantum bit to be measured. A and The auxiliary qubit controls the CNOT gate of the qubit to be measured and the H gate located on the auxiliary qubit;

[0031] S3.2: The unoptimized quantum circuit matrix obtained in S1.3 is recorded as Calculation of reference U based on fixed line structure P , denoted as

[0032] S3.3: Based on and Calculate the required parameters and c;

[0033] S3.4: Use new Replace the original S3.1 Obtain the compiled quantum circuit and retain c for subsequent measurement result processing.

[0034] Further: U A |0> can be prepared as any of the following |φ>:

[0035]

[0036] where σ x , σ y , σ z are the Pauli matrices, and are chosen as

[0037]

[0038] Where R z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door.

[0039] Further: Initial You can choose any one, usually choose At this time, the optimized line can be directly obtained Where, represents the identity matrix.

[0040] Furthermore: the CNOT gate of the sub-bit to be measured controlled by the auxiliary quantum bit in the fixed circuit and the H gate located on the auxiliary quantum bit are equivalent to any implementation form of Bell measurement.

[0041] Further: S3.3 comprises the following steps:

[0042] S3.3.1 Extraction V (1) and V (2) , and normalize it:

[0043]

[0044] S3.3.2 Calculate the respective angle alignment matrix U (i) :

[0045]

[0046] in For any Orthogonal pure state;

[0047] S3.3.3 Calculation And perform phase calculation to obtain the phase factor α i1 and α i2 :

[0048]

[0049] where a and is a real number;

[0050] S3.3.4 Calculate the value described in S3.3 Among them U r is the phase alignment matrix:

[0051]

[0052] S3.3.5 Calculate the discriminant matrix U pr , if U pr is a diagonal matrix, then c = 1, otherwise c = 0, where U pr The calculation formula is:

[0053]

[0054] in V (i) The 3rd and 4th rows of the matrix:

[0055]

[0056] Further: the step S4 specifically comprises the following steps:

[0057] S4.1: Use C Q Matrix Adjustment U P Redundant parameters, U after the tth iteration P for:

[0058]

[0059] The initial value is Among them U Q (Θ) is defined as:

[0060]

[0061] where Q(Θ) is the value of the parameter Θ = [γ 0 γ 1 γ 2 γ 3 ] is a 2×2 unitary matrix:

[0062]

[0063] The update of Θ after the t-th iteration is:

[0064] Θ [t] =Θ [t-1] +ΔΘ [t]

[0065] The initial value is Θ[0] =[0 0 0 0], where R Z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door;

[0066] S4.2: Use numerical optimization algorithms to Iterate to find the optimal solution The optimized When performing the following KAK decomposition, there are k 3 =0:

[0067]

[0068] Among them U A , U B , V A , V B is a single-qubit gate,

[0069] S4.3: Call the optimal two-qubit gate decomposition algorithm to decompose Get the quantum circuit and remember c=1 to ensure the consistency of subsequent processing flow.

[0070] Further: After constructing the circuit and performing n measurements, the statistical data obtained from a single quantum bit in the system to be measured is in the form of {00:C 1 , 01: C 2 , 10: C 3 , 11: C 4};

[0071] Among them, 00, 01, 10, and 11 are possible measurement results. 1 , C 2 , C 3 , C 4 is the number of occurrences of each result, satisfying n = C 1 +C 2 +C 3 +C 4 ;

[0072] If c = 0, the data is adjusted to {00:C 1 , 01: C 2 , 10: C 4 , 11: C 3}.

[0073] As described above, the optimization method of the single quantum bit 4-element rank 1 positive operator value measurement circuit of the present invention has the following beneficial effects:

[0074] 1. Reduce the use of CNOT gates: By optimizing the redundant parameter strategy, the present invention significantly reduces the use of CNOT gates. CNOT gates are easily affected by noise in short-range quantum devices and have a high error rate. Reducing the use of CNOT gates not only reduces the impact of noise, but also improves the stability of quantum circuits and the accuracy of measurements.

[0075] 2. Optimize circuit design: The present invention simplifies the design and implementation process of quantum circuits through fixed circuit structure and standard revolving door operation.

[0076] 3. Improve measurement accuracy: By optimizing the redundant parameter strategy, the present invention can significantly reduce the noise and error in quantum measurement and improve the accuracy of the measurement results. In particular, for asymmetric information complete positive operator value measurement, the reliability of the measurement is further improved by optimizing the matrix form through iterative algorithms.

[0077] 4. Enhanced experimental repeatability: Through multiple measurements and data statistics, the present invention can obtain a more complete and reliable data set.

[0078] 5. Improve the flexibility of data processing: The present invention allows the initial state to be freely selected, can adapt to different needs and scenarios, and has strong flexibility. In particular, when processing different types of positive operator value measurements, the parameter settings can be flexibly adjusted to adapt to various complex and diverse needs.

[0079] 6. Improve the robustness of measurement: By introducing auxiliary quantum bits and CNOT gates, the present invention can avoid the errors caused by directly measuring the quantum bits to be measured. The high-precision measurement capability of the auxiliary quantum bits improves the robustness of the entire measurement process, making the measurement results more reliable.

[0080] 7. Improve the reliability of data statistics: The present invention ensures the integrity and reliability of data through multiple measurements and data statistics. The data adjustment mechanism can correct potential measurement errors under certain conditions, further improving the reliability of data statistics. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] Figure 1 Shown is a flow chart of the optimization method of the present invention;

[0082] Figure 2 A method for constructing an initial non-optimized U is provided in an example of the present invention. P Detailed flow chart of

[0083] Figure 3 A preset fixed structure quantum circuit diagram for a SIC-POVM measurement scheme provided by an example of the present invention;

[0084] Figure 4A specific iterative flow chart for other POVM measurement schemes provided for the examples of the present invention;

[0085] Figure 5 A measurement data processing map for c provided for an example of the present invention. DETAILED DESCRIPTION

[0086] The following specific embodiments illustrate the implementation of the present invention, and those familiar with the technology can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0087] See also Figure 1 The present invention provides a method for optimizing a single-qubit 4-element rank 1 positive operator value measurement circuit, comprising the following steps: S1: Compile to the initial, unoptimized quantum circuit matrix denoted as U P ; S2: Determine the type of the measurement scheme and classify it into symmetric information complete positive operator value measurement or other type of positive operator value measurement; S3: For symmetric information complete positive operator value measurement, calculate the required compilation parameter U s and c, and U s Substitute into the designed fixed circuit structure to complete the compilation; S4: For other types of positive operator value measurements, optimize the matrix form U by adjusting the iterative algorithm of redundant parameters P , until the optimized matrix form is obtained Then Execute conventional quantum circuit compilation; S5: construct and execute quantum measurement, obtain original measurement data, and adjust the original measurement result according to the compilation parameter c.

[0088] S1 converts the abstract measurement scheme into an executable specific quantum circuit and encodes it into a matrix form U P ; In S2, the type of the measurement scheme needs to be determined and classified into symmetric information complete positive operator value measurement (SIC-POVM) or other types of positive operator value measurement. If yes, proceed to the next step; if not, adopt another strategy to continue optimization; in S3, if the measurement scheme belongs to the symmetric information complete category, then we will calculate a specific set of parameters U s and c, these parameters will be used to construct a fixed quantum circuit template to achieve efficient measurement compilation; in S4, when faced with asymmetric information complete measurement schemes, we will use an iterative algorithm to continuously adjust U P until the optimal solution is found. Afterwards, the final quantum circuit will be generated based on this optimized matrix form; S5 will construct the quantum circuit and perform measurements, collect the resulting data, and then use the previously determined parameters c to perform necessary calibration and corrections on the raw data to obtain the most accurate results.

[0089] The present invention can significantly improve the accuracy and efficiency of quantum measurement. Traditional quantum measurement methods are often affected by noise and errors, resulting in inaccurate measurement results. By adopting this new optimization method, not only can these influencing factors be effectively reduced, but the consistency and stability of the entire process can also be guaranteed. In addition, this method is also highly flexible and can flexibly adjust parameter settings according to different application scenarios to meet various complex and diverse needs.

[0090] like Figure 2 As shown, the step S1 specifically includes the following steps:

[0091] S1.1: Legal single-qubit 4-element rank-1 positive operator value measurement scheme Decompose into

[0092]

[0093] in Need to meet

[0094]

[0095] S1.2: Measurement plan to be compiled Construct the matrix V:

[0096]

[0097] in is a row vector with 2 elements, which is The conjugate transpose of ; V is a 4×2 matrix;

[0098] S1.3: Construct a 4×2 matrix W and merge it with the matrix V to obtain the unoptimized quantum circuit matrix representation U P ,

[0099] U P =[VW]

[0100] AndU P is a 4×4 unitary matrix.

[0101] The present invention provides an example of inputting a measurement to be compiled Get the initial, unoptimized quantum circuit matrix representation U P First, construct matrix and a random 4×4 complex matrix R = [AB]. Here A, B, V are all 4×2 matrices. Then, replace the A matrix with V to obtain R′ = [VB]. Finally, perform Schmidt orthogonalization on the columns and output U p =[VW].

[0102] S1.1 Through transformation, we can visualize the originally more abstract concepts, making them easier to understand and operate; S1.2 organizes the measurement operators into a matrix V. The specific method is to splice the row vectors of each measurement operator together to form a large matrix. By constructing such a matrix, we can better manage the relationship between these measurement operators, especially when it comes to large amounts of data or complex situations. This matrix processing method is particularly necessary; S1.3 After completing the previous two steps, another matrix W of the same size but unknown content will be created, and it will be put together with the previously obtained matrix V to form a new matrix U P , this new matrix U P This is what we call the "unoptimized quantum circuit matrix". After this step, we have successfully integrated the originally scattered parts together.

[0103] The step S2 specifically comprises the following steps: S2.1: Calculate all possible Tr(Π i Π j ), where i, j∈{1, 2, 3, 4};

[0104] S2.2: Execute the judgment, if it satisfies:

[0105]

[0106] Then the measurement type is symmetric information complete positive operator value measurement, otherwise it is other types of positive operator value measurement, where d is the sub-bit dimension to be measured.

[0107] S2.1 We need to calculate all possible trace values, namely Tr(Π i Π j ), i and j are taken from the set {1, 2, 3, 4}, which means that we need to calculate a total of 16 different combinations, and each calculation involves the product of two measurement operators and their trace values; S2.2 When i = j, the trace is 1 / 4, which means that the inner product of each measurement operator with itself is the same. i ≠ j, the trace is 1 / 12, which means that the inner products of different measurement operators are the same. These two conditions serve the symmetry together.

[0108] like Figure 3As shown, the present invention provides a preset fixed structure quantum circuit diagram for the SIC-POVM measurement scheme. The circuit components include auxiliary quantum bits, the auxiliary quantum bits and the single-bit gate U on the quantum bit to be measured. A and The auxiliary bit controls the CNOT gate of the sub-bit to be measured and the H gate located on the auxiliary bit.

[0109] The step S3 specifically comprises the following steps: S3.1: preparing a quantum circuit with a fixed structure, the quantum circuit components including auxiliary quantum bits, the auxiliary quantum bits and the single-bit gate U on the quantum bit to be measured. A and The auxiliary quantum bit controls the CNOT gate of the quantum bit to be measured, and the H gate located on the auxiliary quantum bit; S3.2: The unoptimized quantum circuit matrix obtained in S1.3 is recorded as Calculation of reference U based on fixed line structure P , denoted as S3.3: Based on and Calculate the required parameters and c; S3.4: Use new Replace the original S3.1 Obtain the compiled quantum circuit and retain c for subsequent measurement result processing.

[0110] The fixed quantum circuit in S3.1 provides a standardized measurement platform. Different components work together to promote the effective execution of measurement tasks. The existence of auxiliary quantum bits increases the flexibility and accuracy of measurement. S3.2 We use the previously obtained unoptimized quantum circuit matrix Mark it out, then recalculate a reference matrix based on the fixed line structure By comparison and We can find the difference between the two; S3.3 uses and As input, we can calculate new parameters through certain algorithms and c; the newly calculated parameters in S3.4 are Apply to the original Generate a new U S Parameters, at the same time, we also need to save the parameter c for future use in processing the measurement results.

[0111] U A |0> can be prepared as any of the following |φ>:

[0112]

[0113] where σ x , σ y , σ z are the Pauli matrices, and are chosen as

[0114]

[0115] Where R z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door.

[0116] The advantage of this method is that it can effectively reduce the complexity of quantum circuits and improve the operating efficiency of quantum circuits. At the same time, due to the use of standard revolving gate operations, this method also has good versatility and scalability and is suitable for a variety of different quantum computing tasks.

[0117] initial You can choose any one, usually choose At this time, the optimized line can be directly obtained Where I represents the identity matrix.

[0118] This method provides a simple and effective way to realize complex quantum operations, which is very useful for the design and application of quantum computers. Secondly, since it allows the initial state to be freely selected, it can be adapted to different needs and scenarios and has strong flexibility.

[0119] In the fixed circuit, the CNOT gate of the subbit to be measured controlled by the auxiliary quantum bit and the H gate located on the auxiliary quantum bit are equivalent to any Bell measurement implementation form.

[0120] S3.3 contains the following steps: S3.3.1 Extraction V(1) and V(2) of , and normalize it:

[0121]

[0122] S3.3.2 Calculate the respective angle alignment matrix U (i) :

[0123]

[0124] in For any Orthogonal pure state;

[0125] S3.3.3 Calculation And perform phase calculation to obtain the phase factor α i1 and αi2 :

[0126]

[0127] where a and is a real number;

[0128] S3.3.4 Calculate the value described in S3.3 Among them U r is the phase alignment matrix:

[0129]

[0130] S3.3.5 Calculate the discriminant matrix U pr , if U pr is a diagonal matrix, then c = 1, otherwise c = 0, where U pr The calculation formula is:

[0131]

[0132] in V (i) The 3rd and 4th rows of the matrix:

[0133]

[0134] S3.3.1 The normalization process makes the modulus of the matrix become 1, which ensures the standardization of the matrix and is conducive to the subsequent phase factor calculation; S3.3.2 By calculating the angle alignment matrix, the relative position relationship between the components can be determined, thus paving the way for the next phase factor calculation; The acquisition of the phase factor in S3.3.3 is crucial for adjusting the phase of the quantum state and helps to achieve accurate quantum operations; S3.3.4 By calculating The optimized quantum circuit can be obtained; S3.3.5 uses the discriminant matrix to give the c value to determine whether classical post-processing is needed to re-label the data.

[0135] like Figure 4 As shown, the present invention provides an example of inputting the initial After that, the specific iterative methods for other POVM measurement schemes are presented. First, construct remember Θ=[γ 0 γ 1 γ 2 γ 3 ],Θ [0] =[0 0 0 0] is the initial value. Use C Q Matrix Adjustment U P Redundant parameters, U after the tth iteration P for After the tth iteration, Θ is updated to Θ [t] =Θ [t-1] +ΔΘ [t] Then, KAK decomposition is used to calculate the standard class vector of step t, and we get Use brute force search algorithm to find and Make and The ones greater than zero are denoted as Θ + , those less than zero are denoted as Θ - . Then, using the Brent algorithm in [Θ - , Θ + ] range, and obtain the k 3 =0 * Finally, return

[0136] The step S4 specifically comprises the following steps:

[0137] S4.1: Use C Q Matrix Adjustment U P Redundant parameters, U after the tth iteration P for:

[0138]

[0139] The initial value is Among them U P (Θ) is defined as:

[0140]

[0141] where Q(Θ) is the value of the parameter Θ = [γ 0 γ 1 γ 2 γ 3 ] is a 2×2 unitary matrix:

[0142]

[0143] The update of Θ after the t-th iteration is:

[0144] Θ [t] =Θ [t-1] +ΔΘ [t]

[0145] The initial value is Θ [0] =[0 0 0 0], where R z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door;

[0146] S4.2: Use a numerical optimization algorithm to iterate Θ to find the optimal solution Θ * , so that the optimized When performing the following KAK decomposition, there are k 3 =0:

[0147]

[0148] Among them U A , U B , V A , V B is a single-qubit gate,

[0149] S4.3: Call the optimal two-qubit gate decomposition algorithm to decompose , obtain the quantum circuit, and record c = 1 to ensure the consistency of subsequent processing procedures.

[0150] S4.1 Use C Q Matrix Adjustment U P By iteratively updating the parameter Θ, we can gradually approach the optimal solution and improve the measurement accuracy. Q The use of the (Θ) matrix effectively eliminates the P The redundant parameters in the simplifies the quantum circuit design; S4.2 verifies through KAK decomposition to ensure that the optimized quantum circuit meets specific constraints and enhances the reliability of the solution; S4.3 decomposes the complex It is expressed as a combination of basic quantum gates, which is convenient for actual hardware implementation.

[0151] like Figure 5 As shown, the present invention provides a measurement data processing map for c. After constructing the circuit and performing n measurements, the data obtained from a single quantum bit in the system to be measured is statistically represented in the form of {00:C 1 , 01: C 2 , 10: C 3 , 11: C 4}; 00, 01, 10, 11 are possible measurement results, C 1 , C 2 , C 3 , C 4 is the number of occurrences of each result, satisfying n = C 1 +C 2 +C 3 +C 4 ; If c = 0, adjust the data to {00: C 1 , 01: C 2 , 10: C 4 , 11: C 3}.

[0152] Through multiple measurements and data statistics, a more complete and reliable data set can be obtained. When c=0, the data adjustment mechanism can correct potential measurement errors or deviations and improve data accuracy. The data format is unified and easy to understand, which facilitates subsequent data analysis and processing. Multiple measurements ensure the repeatability of experimental results and enhance the credibility of research conclusions.

[0153] The technical solution of the present invention is not limited to a specific physical platform (such as a superconducting platform, an ion trap platform or an optical platform), a measurement type (such as SIC-POVM, minimal information complete positive operator value measurement (minimal IC-POVM)), an input method (such as directly inputting the measurement to be compiled or the unoptimized circuit) or an implementation programming language (such as Python, C++). At the same time, the present invention is not limited to the expression form of the quantum circuit (such as using CZ, ECR gates plus a small number of single-bit gates to replace CNOT gates, reversing the order of quantum bits, or using equations instead of quantum circuit forms). All variants of the measurement circuit optimization implemented according to the technical solution of the present invention fall within the protection scope of the present invention.

[0154] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. All equivalent modifications or changes made by those skilled in the art without departing from the spirit and technical ideas disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. An optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit, characterized in that: The following steps are involved: S1: The single-qubit 4-element rank-1 positive operator value measurement scheme to be implemented Compile to the initial, unoptimized quantum circuit matrix denoted as U P ; S2: Determine the type of the measurement scheme and classify it as symmetric information complete positive operator value measurement or other type of positive operator value measurement; S3: For symmetric information complete positive operator value measurement, calculate the required compilation parameter U S and c, and U S Substitute into the designed fixed circuit structure to complete the compilation; S4: For other types of positive operator-valued measurements, the matrix form U is optimized by an iterative algorithm that adjusts the redundant parameters P , until the optimized matrix form is obtained Then Perform regular quantum circuit compilation; S5: Construct and perform quantum measurement, obtain raw measurement data, and adjust the raw measurement results according to the compilation parameter c.

2. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit according to claim 1, characterized in that: The step S1 specifically comprises the following steps: S1.1: Legal single-qubit 4-element rank-1 positive operator value measurement scheme Decompose into in Need to meet S1.2: Measurement plan to be compiled Construct the matrix V: in is a row vector with 2 elements, which is The conjugate transpose of ; V is a 4×2 matrix; S1.3: Construct a 4×2 matrix W and merge it with the matrix V to obtain the unoptimized quantum circuit matrix representation U P , U P =[VW] AndU P is a 4×4 unitary matrix.

3. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit according to claim 1, characterized in that: The step S2 specifically comprises the following steps: S2.1: Calculate all possible Tr(Π i Π j ), where i, j∈{1, 2, 3, 4}; S2.2: Execute the judgment, if it satisfies: Then the measurement type is symmetric information complete positive operator value measurement, otherwise it is other types of positive operator value measurement, where d is the sub-bit dimension to be measured.

4. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit as claimed in claim 2, characterized in that: The step S3 specifically comprises the following steps: S3.1: Prepare a quantum circuit with a fixed structure. The components of the quantum circuit include auxiliary quantum bits, the auxiliary quantum bits and the single-bit gate U on the quantum bit to be measured. A and The auxiliary qubit controls the CNOT gate of the qubit to be measured and the H gate located on the auxiliary qubit; S3.2: The unoptimized quantum circuit matrix obtained in S1.3 is recorded as Calculation of reference U based on fixed line structure P , denoted as S3.3: Based on and Calculate the required parameters and c; S3.4: Use new Replace the original S3.1 Obtain the compiled quantum circuit and retain c for subsequent measurement result processing.

5. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit as claimed in claim 4, characterized in that: U A |0> can be prepared as any of the following |φ>: where σ x , σ y , σ z are the Pauli matrices, and are chosen as Where R Z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door.

6. The optimization method for the single-qubit 4-element rank-1 positive operator value measurement circuit according to claim 4, characterized in that: initial You can choose any one, usually choose At this time, the optimized line can be directly obtained Where I represents the identity matrix.

7. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit as claimed in claim 4, characterized in that: In the fixed circuit, the CNOT gate of the subbit to be measured controlled by the auxiliary quantum bit and the H gate located on the auxiliary quantum bit are equivalent to any Bell measurement implementation form.

8. The method for optimizing a single-qubit 4-element rank-1 positive operator value measurement circuit as claimed in claim 4, characterized in that: S3.3 contains the following steps: S3.3.1 Extraction V (1) and V (2) , and normalize it: S3.3.2 Calculate the respective angle alignment matrix U (i) : in For any Orthogonal pure state; S3.3.3 Calculation And perform phase calculation to obtain the phase factor α i1 and α i2 : where a and is a real number; S3.3.4 Calculate the value described in S3.3 Among them U r is the phase alignment matrix: S3.3.5 Calculate the discriminant matrix U pr , if U pr is a diagonal matrix, then c = 1, otherwise c = 0, where U pr The calculation formula is: in V (i) The 3rd and 4th rows of the matrix:

9. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit as claimed in claim 1, characterized in that: The step S4 specifically comprises the following steps: S4.1: Use C Q Matrix Adjustment U P Redundant parameters, U after the tth iteration P for: The initial value is Among them C Q (Θ) is defined as: where Q(Θ) is a 2×2 unitary matrix with parameters Θ = [γ0 γ1 γ2 γ3]: The update of Θ after the t-th iteration is: I [t] =Θ [t-1] +DTH [t] The initial value is Θ [0] =[0 0 0 0], where R Z Represents the operation of rotating around the z-axis, called a z-revolving door; R x The operation represented as a rotation around the x-axis is called an x-revolving door; S4.2: Use a numerical optimization algorithm to iterate Θ to find the optimal solution Θ * , so that the optimized When performing the following KAK decomposition, k3=0: Among them U A , U B , V A , V B is a single-qubit gate, S4.3: Call the optimal two-qubit gate decomposition algorithm to decompose Get the quantum circuit and remember c=1 to ensure the consistency of subsequent processing flow.

10. The optimization method for a single quantum bit 4-element rank 1 positive operator value measurement circuit according to claim 1, characterized in that: After constructing the circuit and performing n measurements, the statistical form of the data obtained from a single quantum bit in the system under test is {00: C1, 01: C2, 10: C3, 11: C4}; Among them, 00, 01, 10, 11 are possible measurement results, C1, C2, C3, C4 are the number of times each result appears, satisfying n = C1 + C2 + C3 + C4; If c=0, the data is adjusted to {00:C1, 01:C2, 10:C4, 11:C3}.

Images