A method and apparatus for quantum gate optimization of a continuous variable quantum system

Abstract

The application provides a quantum gate optimization method and device for a continuous variable quantum system, comprising: sampling a plurality of quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; preparing an initial state of the continuous variable quantum system; applying each sampled quantum circuit at each circuit depth to the initial state and performing a final state measurement on each sampled quantum circuit at each circuit depth; determining a survival probability of each sampled quantum circuit at each circuit depth based on the final state; determining a fidelity of the set of wave color Gaussian quantum gates based on the survival probability of each sampled quantum circuit at each circuit depth; and optimizing the set of wave color Gaussian quantum gates based on the fidelity. The application designs a simple quantum gate fidelity characterization method which decouples the number of quantum circuits and the mode number of the continuous variable quantum system, reduces the resource overhead and implementation difficulty of quantum gate fidelity characterization in the quantum gate optimization process, and improves the quantum gate optimization efficiency.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of quantum computing, and in particular to a quantum gate optimization method and device for a continuous variable quantum system. BACKGROUND

[0002] According to different information encoding methods, current quantum systems can be divided into two categories: discrete variable quantum systems and continuous variable quantum systems. Both of them can realize universal quantum computing and complete various quantum information processing tasks. In a continuous variable quantum system, a high-fidelity quantum gate is the key to improving the performance of quantum information processing tasks. The fidelity calibration of a quantum gate can provide feedback for the hardware design and waveform control of the quantum gate. Therefore, quickly and effectively calibrating the fidelity of a quantum gate is crucial for quantum gate optimization.

[0003] Currently, there are two methods for calibrating the fidelity of a quantum gate in a continuous variable quantum system: quantum process tomography and polarization channel verification. Quantum process tomography reconstructs the actual result of the output quantum state by tomographic methods, and then compares the actual result of the output quantum state with the theoretical result to obtain the fidelity. Specifically, for a quantum channel to be calibrated composed of a sequence of continuous variable quantum logic gates, a set of bases of the density operator of the quantum state is first input into the quantum channel, and then the density matrix matrix elements of the output quantum state are measured and used to reconstruct the output quantum state. Finally, the distance between the output quantum state and its ideal result is calculated to obtain the fidelity of the sequence of continuous variable quantum logic gates. This technique requires an exponential increase in the number of quantum circuits to be executed with the number of modes, and quantum process tomography essentially approximates a continuous variable system as a high-dimensional discrete variable system and then performs quantum process tomography. In order to accurately characterize the fidelity, the approximate dimension must be taken to be very large. However, if a high dimension approximation is not used, the final estimated fidelity will not be accurate. These two factors together result in a huge amount of resources consumed for quantum gate fidelity characterization. In addition, this technique also requires a number state measurement, which is difficult to implement. Polarization channel verification provides a lower bound for the fidelity of the quantum channel to be calibrated by constructing a fidelity witness. Specifically, Figure 1 The principle diagram of the polarization channel verification method is shown in the figure, where |k> TMSVrepresents a pair of entangled states. Given a quantum noise channel ε on one mode of m, and set the noise channel ε acts on one mode of m independent and identical two-mode squeezed vacuum states, constantly change the preparation mode of the two-mode squeezed vacuum state so that the input state is in the quantum noise channel ε in various modes, and then make a corresponding mode homodyne measurement on the output state. Calculate the distance between the measured value of the output state in various modes and the ideal value, and take the average distance as the fidelity lower bound of the noise channel ε. This technique can only depict the lower bound of quantum gate fidelity and cannot depict the fidelity, which is slightly insufficient in accuracy. Moreover, the number of quantum circuits that need to be executed by this technique increases polynomially with the number of modes, and the resources consumed for quantum gate fidelity depiction are huge.

[0004] Therefore, it is not realistic to use the existing quantum gate fidelity calibration technology in quantum gate optimization. SUMMARY

[0005] To solve the above problems, the present application provides a quantum gate optimization method and device for continuous variable quantum systems, which designs a simple quantum gate fidelity depiction method with decoupled quantum circuit number and mode number of continuous variable quantum systems, to reduce the resource consumption and implementation difficulty of quantum gate fidelity depiction in the quantum gate optimization process, and improve the efficiency of quantum gate optimization.

[0006] In the first aspect, the present application provides a quantum gate optimization method for continuous variable quantum systems, which comprises:

[0007] Based on the set of wave color Gaussian quantum gates, sample multiple quantum circuits for each circuit depth;

[0008] Prepare the initial state of the continuous variable quantum system;

[0009] Act each sampled quantum circuit at each circuit depth on the initial state, and perform a final state measurement on each sampled quantum circuit at each circuit depth;

[0010] Based on the final state, determine the survival probability of each sampled quantum circuit at each circuit depth;

[0011] Based on the survival probability of each sampled quantum circuit at each circuit depth, determine the fidelity of the set of wave color Gaussian quantum gates.

[0012] Based on the fidelity, optimize the set of wave color Gaussian quantum gates;

[0013] Wherein, the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and the inverse gate of the product of the d quantum gates; d is the circuit depth corresponding to the quantum circuit.

[0014] According to the quantum gate optimization method for continuous variable quantum systems provided by the present invention, the preparation of the initial state of the continuous variable quantum system includes:

[0015] The initial state of the continuous variable quantum system is prepared as |0><0|. m ;

[0016] Among them, |0><0| m Let m be the vacuum states in m modes, where m is the number of modes in the continuous variable quantum system.

[0017] According to the quantum gate optimization method for continuous variable quantum systems provided by the present invention, the d quantum gates are randomly selected from the set of Bose-Gaussian quantum gates according to a preset probability distribution.

[0018] According to the quantum gate optimization method for continuous variable quantum systems provided by the present invention, determining the fidelity of the Bose-Gaussian quantum gate set based on the survival probability of each quantum circuit sampled at each circuit depth includes:

[0019] The average survival probability of all quantum circuits sampled at each circuit depth is used to obtain the fidelity level for each circuit depth.

[0020] Obtain the fidelity level of the line depth relative to the fitting formula of the line depth;

[0021] Based on the aforementioned fitting formula, data fitting is performed on each line depth and its fidelity level to obtain the fidelity.

[0022] The fidelity is used as the fidelity of the set of Bose-Gaussian quantum gates.

[0023] According to the quantum gate optimization method for continuous variable quantum systems provided by the present invention, the fitting formula is as follows:

[0024] y(d)=Ap d +B

[0025] or

[0026] y(d)=Ap d

[0027] Where y(d) is the fidelity level of the line depth, p is the fidelity, A is the first fitting coefficient, and B is the second fitting coefficient.

[0028] Secondly, this invention provides a quantum gate optimization method for continuous variable quantum systems, the method comprising:

[0029] Based on the set of Bose-Gaussian quantum gates, multiple interleaved quantum circuits are sampled for each type of circuit.

[0030] Preparation of an initial state of a continuous variable quantum system;

[0031] Applying each interleaved quantum circuit with each circuit depth down-sampling to the initial state and performing a final state measurement on each interleaved quantum circuit with each circuit depth down-sampling;

[0032] Determining a survival probability of each interleaved quantum circuit with each circuit depth down-sampling based on the final state;

[0033] Determining a composite fidelity of the set of parity Gaussian quantum gates and the target Gaussian quantum gate based on the survival probability of each interleaved quantum circuit with each circuit depth down-sampling;

[0034] Taking a ratio of the composite fidelity and a fidelity of the set of parity Gaussian quantum gates as the fidelity of the target Gaussian quantum gate;

[0035] Optimizing the target Gaussian quantum gate by using the fidelity of the target Gaussian quantum gate;

[0036] The interleaved quantum circuit is composed of quantum gates in a first sequence and inverse gates of products of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of parity Gaussian quantum gates and d target Gaussian quantum gates respectively inserted after the d quantum gates.

[0037] In a third aspect, the present application provides a quantum gate optimization device for a continuous variable quantum system, the device comprising:

[0038] A first sampling module for sampling a plurality of quantum circuits based on a set of parity Gaussian quantum gates with each circuit depth;

[0039] A first preparation module for preparing an initial state of a continuous variable quantum system;

[0040] A first measurement module for applying each quantum circuit with each circuit depth down-sampling to the initial state and performing a final state measurement on each quantum circuit with each circuit depth down-sampling;

[0041] A quantum circuit survival probability determination module for determining a survival probability of each quantum circuit with each circuit depth down-sampling based on the final state;

[0042] A set of parity Gaussian quantum gate fidelity determination module for determining a fidelity of the set of parity Gaussian quantum gates based on the survival probability of each quantum circuit with each circuit depth down-sampling;

[0043] A first optimization module for optimizing the set of parity Gaussian quantum gates based on the fidelity;

[0044] The quantum circuit is composed of d quantum gates in the set of wave-color Gaussian quantum gates and inverse gates of the product of the d quantum gates; d is a circuit depth corresponding to the quantum circuit.

[0045] In a fourth aspect, the present application provides a quantum gate optimization device for a continuous variable quantum system, the device comprising:

[0046] A second sampling module is configured to sample a plurality of interleaved quantum circuits for each circuit depth based on the set of wave-color Gaussian quantum gates.

[0047] A second preparation module is configured to prepare a primary state of the continuous variable quantum system.

[0048] A second measurement module is configured to apply each sampled interleaved quantum circuit for each circuit depth to the primary state and perform a final state measurement on each sampled interleaved quantum circuit for each circuit depth.

[0049] An interleaved quantum circuit survival probability determination module is configured to determine a survival probability of each sampled interleaved quantum circuit for each circuit depth based on the final state.

[0050] A composite fidelity determination module is configured to determine a composite fidelity of the set of wave-color Gaussian quantum gates and a target Gaussian quantum gate based on the survival probability of each sampled interleaved quantum circuit for each circuit depth.

[0051] A target Gaussian quantum gate fidelity determination module is configured to determine a fidelity of the target Gaussian quantum gate as a ratio of the composite fidelity to a fidelity of the set of wave-color Gaussian quantum gates.

[0052] A second optimization module is configured to optimize the target Gaussian quantum gate using the fidelity of the target Gaussian quantum gate.

[0053] The interleaved quantum circuit is composed of quantum gates in the first sequence and inverse gates of the product of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of wave-color Gaussian quantum gates and d target Gaussian quantum gates inserted after the d quantum gates, respectively.

[0054] In a fifth aspect, the present application provides an electronic device comprising a memory, a quantum processor, and a quantum computer program stored in the memory and executable on the quantum processor, wherein the quantum processor implements the quantum gate optimization method for a continuous variable quantum system according to the first aspect or the second aspect when executing the program.

[0055] In a sixth aspect, the present application provides a non-transitory computer readable storage medium having stored thereon a quantum computer program, which, when executed by a quantum processor, implements the quantum gate optimization method for a continuous variable quantum system according to the first aspect or the second aspect.

[0056] The present application provides a quantum gate optimization method and device for a continuous variable quantum system, which samples a plurality of quantum circuits for each circuit depth based on a set of wave-color Gaussian quantum gates; wherein the quantum circuit is composed of d quantum gates in the set of wave-color Gaussian quantum gates and an inverse gate of the product of the d quantum gates; d is the circuit depth corresponding to the quantum circuit; an initial state of the continuous variable quantum system is prepared; each quantum circuit sampled at each circuit depth is applied to the initial state, and each quantum circuit sampled at each circuit depth is measured for a final state; based on the final state, the survival probability of each quantum circuit sampled at each circuit depth is determined; based on the survival probability of each quantum circuit sampled at each circuit depth, the fidelity of the set of wave-color Gaussian quantum gates is determined; and based on the fidelity, the set of wave-color Gaussian quantum gates is optimized. The present application proposes a fidelity characterization method for the set of wave-color Gaussian quantum gates, which is simple and decouples the number of quantum circuits and the number of modes of the continuous variable quantum system, so that the resource consumption and implementation difficulty of the fidelity characterization of the set of wave-color Gaussian quantum gates in the optimization process are reduced, and the optimization efficiency is improved.

[0057] The application further provides a quantum gate optimization method and device for a continuous variable quantum system, comprising the following steps: sampling a plurality of staggered quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; wherein the staggered quantum circuit is composed of quantum gates in a first sequence and inverse gates of products of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of wave color Gaussian quantum gates and d target Gaussian quantum gates respectively inserted after the d quantum gates; preparing an initial state of the continuous variable quantum system; applying each staggered quantum circuit sampled at each circuit depth to the initial state, and performing a final state measurement on each staggered quantum circuit sampled at each circuit depth; determining a survival probability of each staggered quantum circuit sampled at each circuit depth based on the final state; determining a composite fidelity of the set of wave color Gaussian quantum gates and the target Gaussian quantum gates based on the survival probability of each staggered quantum circuit sampled at each circuit depth; taking a ratio of the composite fidelity and a fidelity of the set of wave color Gaussian quantum gates as a fidelity of the target Gaussian quantum gate; and optimizing the target Gaussian quantum gate by using the fidelity of the target Gaussian quantum gate. The application takes any one of the Gaussian quantum gates in the set of wave color Gaussian quantum gates as the target Gaussian quantum gate, and proposes a fidelity description method of the target Gaussian quantum gate, which is simple and decouples the number of quantum circuits and the number of modes of the continuous variable quantum system, so that the resource consumption and implementation difficulty of the fidelity description of the target Gaussian quantum gate in the optimization process are reduced, and the optimization efficiency is improved. BRIEF DESCRIPTION OF DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the present application or the prior art, the following will briefly introduce the drawings needed in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0059] Figure 1 is a schematic diagram of the principle of the wave color channel verification method provided by the prior art;

[0060] Figure 2 is a flowchart of a first quantum gate optimization method for a continuous variable quantum system provided by the present application;

[0061] Figure 3 is a structural diagram of a quantum circuit provided by the present application;

[0062] Figure 4 is a flowchart of a second quantum gate optimization method for a continuous variable quantum system provided by the present application;

[0063] Figure 5is a structural schematic diagram of an interleaved quantum circuit provided by the present application.

[0064] Figure 6 is a structural schematic diagram of a quantum gate device of a first continuous variable quantum system provided by the present application.

[0065] Figure 7 is a structural schematic diagram of a quantum gate optimization device of a second continuous variable quantum system provided by the present application. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described below in conjunction with the accompanying drawings in the present application. Obviously, the described embodiments are only some of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0067] The continuous variable quantum system and the quantum gate optimization method and device of the present application will be described below in conjunction with Figures 1-7 The present application provides a quantum gate optimization method and device for a continuous variable quantum system.

[0068] In a first aspect, the present application provides a quantum gate optimization method for a continuous variable quantum system, as shown in the formula (1). Figure 2 The method comprises the following steps:

[0069] S11, based on a set of wave color Gaussian quantum gates, sampling a plurality of quantum circuits for each circuit depth; wherein the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and the inverse gate of the product of the d quantum gates; d is the circuit depth corresponding to the quantum circuit;

[0070] It should be noted that in the continuous variable quantum system, the Gaussian quantum gate is the most easily implemented and most commonly used quantum gate; and through research, even if a non-Gaussian state is input, the continuous variable universal quantum computation can be realized by using the Gaussian quantum gate and the homodyne measurement. Therefore, the present application describes the quantum gate fidelity in the continuous variable quantum system, and is developed for the Gaussian quantum gate.

[0071] In addition, the circuit depth is used to limit the number of quantum gates belonging to the set of wave color Gaussian quantum gates on the quantum circuit, so the value range of the circuit depth is [1, M], and M is the total number of quantum gates contained in the set of wave color Gaussian quantum gates. The quantum circuit constructed by the present application is ideally normalized, that is, the input state and the output state of the quantum circuit are consistent in the ideal case. In fact, there is noise in the quantum gate on the quantum circuit, which is also the reason for describing the quantum gate fidelity.

[0072] S12, preparing an initial state of the continuous variable quantum system;

[0073] S13, apply each quantum circuit with each circuit depth down-sampling to the initial state, and perform final state measurement on each quantum circuit with each circuit depth down-sampling;

[0074] S14, determine the survival probability of each quantum circuit with each circuit depth down-sampling based on the final state;

[0075] Here, the survival probability refers to the probability of the initial state and the final state being consistent.

[0076] S15, determine the fidelity of the set of wave color Gaussian quantum gates based on the survival probability of each quantum circuit with each circuit depth down-sampling;

[0077] S16, optimize the set of wave color Gaussian quantum gates based on the fidelity.

[0078] An example of continuous variable quantum gate fidelity optimization is provided below: given a continuous variable quantum gate e -iθP , i is the imaginary unit, P is the generalized momentum operator (also known as the orthogonal component under continuous variable), and θ is a real parameter. Due to the influence of noise, the actual implementation is e -i(θ+η)P , where η is also a real parameter. Then, by characterizing the fidelity f(e -i(θ+η)P , e -iθP ) between the actual quantum gate e -i(θ+η)P and the ideal quantum gate e -iθP , the difference between the two can be measured. By maximizing the fidelity f(e -i(θ+η)P , e -i ) through a suitable optimization algorithm, the actual quantum gate and the ideal quantum gate can be made closest. It is worth noting that the fidelity f(e -i(θ+η)P , e -iθP ) here is not unique, as long as it can measure the difference between the actual quantum gate and the ideal quantum gate.

[0079] For the general case, the ideal quantum gate can be a simple form such as However, due to the form of the achievable Hamiltonian, in order to implement this quantum gate, the ideal Hamiltonian evolution input is where H(c1, c2, c3) = c1X + c2P + c3(XP + PX), t is time. c1, c2, c3, t are real numbers, X, P are coordinate and momentum operators respectively. In practice, due to noise, the actual implementation is where H'(c1+η'1, c2+η'2, c3+η'3) = (c1+η'1)X + (c2+η'2)P + (c3+η'3)(XP + PX). Where η'1, η'2, η'3, t' are real numbers. Estimate the fidelity After that, we can choose the appropriate optimization algorithm to adjust the selection of c1, c2, c3, t to maximize the fidelity, and finally achieve the evolution of .

[0080] The application provides a quantum gate optimization method for a continuous variable quantum system, based on a set of wave color Gaussian quantum gates, a plurality of quantum circuits are sampled for each circuit depth, wherein the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and an inverse gate of the product of the d quantum gates, d is the circuit depth corresponding to the quantum circuit, a initial state of the continuous variable quantum system is prepared, each quantum circuit sampled under each circuit depth is applied to the initial state, and a final state measurement is performed on each quantum circuit sampled under each circuit depth, based on the final state, the survival probability of each quantum circuit sampled under each circuit depth is determined, based on the survival probability of each quantum circuit sampled under each circuit depth, the fidelity of the set of wave color Gaussian quantum gates is determined, and the set of wave color Gaussian quantum gates is optimized based on the fidelity. The quantum gate fidelity characterization method provided by the application is simple, and the number of quantum circuits and the number of modes of the continuous variable quantum system are decoupled, so that the resource overhead and implementation difficulty of quantum gate fidelity characterization in the quantum gate optimization process are reduced, and the quantum gate optimization efficiency is improved.

[0081] In addition, the application has wide application range, low cost, and important practical value for quantum gate calibration in a continuous variable quantum system.

[0082] Specifically, the d quantum gates in the S11 are randomly selected from the set of wave color Gaussian quantum gates according to a preset probability distribution.

[0083] The set of wave color Gaussian quantum gates is a group formed by multiplication of quantum gates, and can be regarded as a semi-direct product of a Heisenberg-Weyl group and a symplectic group in the sense of isomorphism. Mathematically, the group formed by Gaussian quantum gates on m modes W(m) is a Heisenberg-Weyl group on m modes, is a real symplectic matrix with a dimension of 2m*2m. Defining a probability distribution on G(m) is equivalent to defining a probability distribution on , and group elements on G(m) can be selected independently from W(m) and . Therefore, the preset probability distribution refers to any probability distribution of independently selecting group elements from W(m) and .

[0084] Correspondingly, it is assumed that the d gates selected from the set of wave color Gaussian quantum gates are G1, G2, …, G dThe inverse gate of the d gate products is G inv = (G d …G2G1) -1 The quantum circuit is connected to G1, G2, …, G d , G inv The d+1 gates are quantum circuits.

[0085] Figure 3 The structure diagram of the corresponding quantum circuit, wherein p is the initial state, and M is the final state of measurement.

[0086] Specifically, the S12 comprises: the initial state of the prepared continuous variable quantum system, comprising:

[0087] The initial state of the continuous variable quantum system is prepared as |0><0| m ;

[0088] Wherein, |0><0| m is the vacuum state on m modes, and m is the mode number of the continuous variable quantum system. |0><0| m is the abbreviation of m |0><0|, and |0><0| is the tensor product of right vector |0> and left vector <0|.

[0089] The initial state is prepared as |0><0| m , which makes the quantum state preparation and final state measurement relatively simple and easy to operate, but this is not a limitation on the initial state. In fact, the initial state can be prepared in any suitable form.

[0090] Specifically, the S15 comprises:

[0091] S15.1: average the survival probability of all quantum circuits under each circuit depth to obtain the fidelity level of each circuit depth;

[0092] S15.2: obtain a fitting formula of the fidelity level of the circuit depth with respect to the circuit depth;

[0093] Preferably, the fitting formula is

[0094] y(d)=Ap d +B

[0095] or

[0096] y(d)=Ap d

[0097] Wherein, y(d) is the fidelity level of the circuit depth, p is the fidelity, A is the first fitting coefficient, and B is the second fitting coefficient.

[0098] S15.3: Based on the fitting formula, data fitting is performed on each circuit depth and its fidelity level to obtain the fidelity by fitting;

[0099] S15.4: The fidelity is taken as the fidelity of the set of wave color Gaussian quantum gates.

[0100] In addition, the fidelity can also be subjected to a fixed bijective transformation, and the bijective transformation result is taken as the fidelity of the set of wave color Gaussian quantum gates. The two methods are essentially equivalent.

[0101] The quantum process tomography method and the wave color channel verification method depend on the accuracy of state preparation and measurement for the characterization of quantum gates, and are not robust to state preparation and measurement errors. In the present application, state preparation and measurement errors are fitted into the first fitting coefficient A in the fitting process, and do not affect the result of the fidelity p, so the present application is robust to state preparation and measurement errors, and the fidelity of the quantum gate is more accurate.

[0102] In a second aspect, the present application provides a quantum gate optimization method for a continuous variable quantum system, as shown in Figure 4 The method comprises:

[0103] S21: Based on the set of wave color Gaussian quantum gates, a plurality of interleaved quantum circuits are sampled for each circuit depth;

[0104] S21: Prepare an initial state of a continuous variable quantum system;

[0105] S22: Apply each interleaved quantum circuit sampled at each circuit depth to the initial state, and perform final state measurement on each interleaved quantum circuit sampled at each circuit depth;

[0106] S23: Based on the final state, determine the survival probability of each interleaved quantum circuit sampled at each circuit depth;

[0107] S24: Based on the survival probability of each interleaved quantum circuit sampled at each circuit depth, determine the composite fidelity of the set of wave color Gaussian quantum gates and the target Gaussian quantum gate;

[0108] S25: Take the ratio of the composite fidelity to the fidelity of the set of wave color Gaussian quantum gates as the fidelity of the target Gaussian quantum gate;

[0109] S26: Use the fidelity of the target Gaussian quantum gate to optimize the target Gaussian quantum gate;

[0110] The staggered quantum circuit is composed of quantum gates in the first sequence and inverse gates of all quantum gate products in the first sequence.

[0111] The application further provides a quantum gate optimization method of a continuous variable quantum system, which comprises the following steps: sampling a plurality of staggered quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; wherein the staggered quantum circuit is composed of quantum gates in the first sequence and inverse gates of all quantum gate products in the first sequence; the first sequence is composed of d quantum gates in the set of wave color Gaussian quantum gates and d target Gaussian quantum gates inserted after the d quantum gates respectively; preparing an initial state of the continuous variable quantum system; applying each staggered quantum circuit sampled at each circuit depth to the initial state, and performing a final state measurement on each staggered quantum circuit sampled at each circuit depth; determining a survival probability of each staggered quantum circuit sampled at each circuit depth based on the final state; determining a composite fidelity of the set of wave color Gaussian quantum gates and the target Gaussian quantum gate based on the survival probability of each staggered quantum circuit sampled at each circuit depth; taking a ratio of the composite fidelity to a fidelity of the set of wave color Gaussian quantum gates as the fidelity of the target Gaussian quantum gate; and optimizing the target Gaussian quantum gate by using the fidelity of the target Gaussian quantum gate. The quantum gate fidelity characterization method provided by the application is simple, decouples the number of quantum circuits and the number of modes of the continuous variable quantum system, reduces resource consumption and implementation difficulty of quantum gate fidelity characterization in the quantum gate optimization process, and improves quantum gate optimization efficiency.

[0112] Specifically, the d quantum gates in the first sequence in the S21 are randomly selected from the set of wave color Gaussian quantum gates according to a preset probability distribution.

[0113] Correspondingly, assuming that the d gates randomly selected from the set of wave color Gaussian quantum gates are G1, G2, …, Gd respectively. d The target Gaussian quantum gate is G, and the first sequence is G1, G, G2, G…, Gd, G, G′, G′2, G′d, G′d+1, G′d+2, …, G′2d+1. d The inverse gates of the product of the 2d gates are G′ unv = (GG d …GG2GG1) -1 The staggered quantum circuit is a quantum circuit in which G1, G, G2, G…, Gd, G, G′, G′2, G′d, G′d+1, G′d+2, …, G′2d+1 are sequentially connected. d inv

[0114] Figure 5 ​​is a structural schematic diagram of a corresponding interleaved quantum circuit, wherein p is an initial state, and M is a final state of measurement.

[0115] Specifically, the S22 comprises: preparing an initial state of the continuous variable quantum system as |0><0| m ;

[0116] wherein |0><0| m is a vacuum state on m modes, and m is a mode number of the continuous variable quantum system.

[0117] Specifically, the S25 comprises:

[0118] S25.1: averaging survival probabilities of all interleaved quantum circuits under each circuit depth to obtain a fidelity level of each circuit depth;

[0119] S25.2: obtaining a fitting formula of the fidelity level of the circuit depth with respect to the circuit depth;

[0120] Preferably, the fitting formula is

[0121] y(d)=Ap d +B

[0122] or

[0123] y(d)=Ap d

[0124] wherein y(d) is the fidelity level of the circuit depth, p is the fidelity, A is a first fitting coefficient, and B is a second fitting coefficient.

[0125] S25.3: based on the fitting formula, performing data fitting on each circuit depth and the fidelity level thereof to obtain a fidelity.

[0126] The fidelity is taken as a composite fidelity of the set of Pauli Gaussian quantum gates and the target Gaussian quantum gate.

[0127] The quantum process tomography method and the Pauli channel verification method depend on the accuracy of state preparation and measurement for the characterization of quantum gates, and are not robust to state preparation and measurement errors. However, in the present application, the state preparation and measurement errors are fitted into the first fitting coefficient A in the fitting process, and thus do not affect the result of the fidelity p. Therefore, the present application is robust to state preparation and measurement errors, and is more accurate in calibrating the fidelity of quantum gates.

[0128] Specifically, the S26 comprises:

[0129] taking as the fidelity of the target Gaussian quantum gate, wherein p* is the composite fidelity, is a fidelity of a set of Weyl-Gaussian quantum gates.

[0130] or a fixed bijective transformation is performed on the values, and the bijective transformation result is taken as the fidelity of the target Gaussian quantum gate. The two ways are essentially equivalent.

[0131] In a third aspect, a quantum gate optimization device for a continuous variable quantum system is described below, which can be correspondingly referred to the quantum gate optimization method for a continuous variable quantum system described above. Figure 6 An example of a quantum gate optimization device for a continuous variable quantum system is shown in FIG. 1. Figure 6 As shown in FIG. 1, the device includes:

[0132] A first sampling module 31 is configured to sample a plurality of quantum circuits for each circuit depth based on a set of Weyl-Gaussian quantum gates.

[0133] A first preparation module 32 is configured to prepare an initial state of a continuous variable quantum system.

[0134] A first measurement module 33 is configured to apply each sampled quantum circuit at each circuit depth to the initial state and perform a final state measurement on each sampled quantum circuit at each circuit depth.

[0135] A quantum circuit survival probability determination module 34 is configured to determine a survival probability of each sampled quantum circuit at each circuit depth based on the final state.

[0136] A set of Weyl-Gaussian quantum gate fidelity determination module 35 is configured to determine a fidelity of the set of Weyl-Gaussian quantum gates based on the survival probability of each sampled quantum circuit at each circuit depth.

[0137] A first optimization module 35 is configured to optimize the set of Weyl-Gaussian quantum gates based on the fidelity.

[0138] The quantum circuit is composed of d quantum gates in the set of Weyl-Gaussian quantum gates and an inverse gate of the product of the d quantum gates; d is a circuit depth corresponding to the quantum circuit.

[0139] ​The application provides a quantum gate optimization device for a continuous variable quantum system, based on a set of wave color Gaussian quantum gates, a plurality of quantum circuits are sampled for each circuit depth; wherein the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and the inverse gate of the product of the d quantum gates; d is the circuit depth corresponding to the quantum circuit; a initial state of the continuous variable quantum system is prepared; each quantum circuit sampled under each circuit depth is applied to the initial state, and a final state measurement is performed on each quantum circuit sampled under each circuit depth; based on the final state, the survival probability of each quantum circuit sampled under each circuit depth is determined; based on the survival probability of each quantum circuit sampled under each circuit depth, the fidelity of the set of wave color Gaussian quantum gates is determined; and based on the fidelity, the set of wave color Gaussian quantum gates is optimized. The quantum gate fidelity characterization method provided by the application is simple, decouples the number of quantum circuits and the mode number of the continuous variable quantum system, reduces the resource overhead and implementation difficulty of quantum gate fidelity characterization in the quantum gate optimization process, and improves the quantum gate optimization efficiency.

[0140] On the basis of each of the above embodiments, as an optional embodiment, the first preparation module 32 is specifically used for:

[0141] The initial state of the continuous variable quantum system is prepared as |0><0| m ;

[0142] Wherein, |0><0| m is a vacuum state on m modes, and m is the mode number of the continuous variable quantum system.

[0143] On the basis of each of the above embodiments, as an optional embodiment, the d quantum gates are randomly selected from the set of wave color Gaussian quantum gates according to a preset probability distribution.

[0144] On the basis of each of the above embodiments, as an optional embodiment, the set of wave color Gaussian quantum gate fidelity determination module comprises:

[0145] A first setting unit is configured to average the survival probabilities of all quantum circuits under each circuit depth to obtain the fidelity level of each circuit depth;

[0146] A first acquisition unit is configured to acquire a fitting formula of the fidelity level of the circuit depth with respect to the circuit depth;

[0147] A first fitting unit is configured to perform data fitting on each circuit depth and its fidelity level based on the fitting formula, and fit the fidelity;

[0148] A second setting unit is configured to take the fidelity as the fidelity of the set of wave color Gaussian quantum gates.

[0149] As an optional embodiment based on the above embodiments, the fitting formula is

[0150] y(d)=Ap d +B

[0151] or

[0152] y(d)=Ap d

[0153] wherein y(d) is the fidelity level of the circuit depth, p is the fidelity, A is a first fitting coefficient, and B is a second fitting coefficient.

[0154] In a fourth aspect, a quantum gate optimization apparatus for a continuous variable quantum system is described as follows, which can be correspondingly referred to the quantum gate optimization method for a continuous variable quantum system described above. Figure 7 An example of a quantum gate optimization apparatus for a continuous variable quantum system is shown in FIG. 4, which includes: Figure 7

[0155] A second sampling module 41 is configured to sample a plurality of interleaved quantum circuits for each circuit depth based on the set of wave-color Gaussian quantum gates.

[0156] A second preparation module 42 is configured to prepare an initial state of the continuous variable quantum system.

[0157] A second measurement module 43 is configured to apply each of the sampled interleaved quantum circuits for each circuit depth to the initial state and perform a final state measurement on each of the sampled interleaved quantum circuits for each circuit depth.

[0158] An interleaved quantum circuit survival probability determination module 44 is configured to determine a survival probability of each of the sampled interleaved quantum circuits for each circuit depth based on the final state.

[0159] A composite fidelity determination module 45 is configured to determine a composite fidelity of the set of wave-color Gaussian quantum gates and the target Gaussian quantum gate based on the survival probability of each of the sampled interleaved quantum circuits for each circuit depth.

[0160] A target Gaussian quantum gate fidelity determination module 46 is configured to determine a fidelity of the target Gaussian quantum gate as a ratio of the composite fidelity to a fidelity of the set of wave-color Gaussian quantum gates.

[0161] A second optimization module 47 is configured to optimize the target Gaussian quantum gate using the fidelity of the target Gaussian quantum gate.

[0162] ​The interleaved quantum circuit is composed of quantum gates in a first sequence and inverse gates of products of all quantum gates in the first sequence.

[0163] The application further provides a quantum gate optimization device for a continuous variable quantum system, which samples a plurality of interleaved quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; wherein the interleaved quantum circuit is composed of quantum gates in a first sequence and inverse gates of products of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of wave color Gaussian quantum gates and d target Gaussian quantum gates inserted after the d quantum gates respectively; a primary state of the continuous variable quantum system is prepared; each interleaved quantum circuit sampled for each circuit depth is applied to the primary state, and a final state measurement is performed on each interleaved quantum circuit sampled for each circuit depth; based on the final state, a survival probability of each interleaved quantum circuit sampled for each circuit depth is determined; based on the survival probability of each interleaved quantum circuit sampled for each circuit depth, a composite fidelity of the set of wave color Gaussian quantum gates and the target Gaussian quantum gate is determined; a ratio of the composite fidelity to a fidelity of the set of wave color Gaussian quantum gates is taken as a fidelity of the target Gaussian quantum gate; and the target Gaussian quantum gate is optimized by using the fidelity of the target Gaussian quantum gate. The quantum gate fidelity characterization method provided by the application is simple, decouples the number of quantum circuits and the number of modes of the continuous variable quantum system, reduces resource consumption and implementation difficulty of quantum gate fidelity characterization in the quantum gate optimization process, and improves quantum gate optimization efficiency.

[0164] On the basis of each of the above embodiments, as an optional embodiment, the second preparation module is specifically used for:

[0165] The primary state of the continuous variable quantum system is prepared as |0><0| m ;

[0166] wherein |0><0| m is a vacuum state on m modes, and m is the number of modes of the continuous variable quantum system.

[0167] On the basis of each of the above embodiments, as an optional embodiment, the d quantum gates in the first sequence are randomly selected from the set of wave color Gaussian quantum gates according to a preset probability distribution.

[0168] On the basis of each of the above embodiments, as an optional embodiment, the composite fidelity determination module comprises:

[0169] The third setting unit is configured to average the survival probabilities of all the interleaved quantum circuits at each circuit depth to obtain a fidelity level of each circuit depth.

[0170] The second obtaining unit is configured to obtain a fitting formula of the fidelity level of the circuit depth with respect to the circuit depth.

[0171] Preferably, the fitting formula is

[0172] y(d)=Ap d +B

[0173] or

[0174] y(d)=Ap d

[0175] wherein y(d) is the fidelity level of the circuit depth, p is the fidelity, A is a first fitting coefficient, and B is a second fitting coefficient.

[0176] The second fitting unit is configured to perform data fitting on each circuit depth and the fidelity level thereof based on the fitting formula to obtain the fidelity.

[0177] The fourth setting unit is configured to take the fidelity as a composite fidelity of the set of the Pauli-Gaussian quantum gates and the target Gaussian quantum gate.

[0178] On the basis of the above embodiments, as an optional embodiment, the fitting formula is

[0179] y(d)=Ap d +B

[0180] or

[0181] y(d)=Ap d

[0182] wherein y(d) is the fidelity level of the circuit depth, p is the fidelity, A is a first fitting coefficient, and B is a second fitting coefficient.

[0183] In a fifth aspect, the present application provides an electronic device, comprising a memory, a quantum processor, and a quantum computer program stored in the memory and capable of running on the quantum processor, wherein the quantum processor implements the quantum gate optimization method of the continuous variable quantum system according to the first aspect or the second aspect when executing the program.

[0184] The quantum processor mentioned above refers to a processor that can be implemented on various main quantum computing systems such as superconducting, ion trap, and optical systems.

[0185] In addition, operations other than the preparation-state measurement, such as survival probability calculation, data fitting calculation fidelity, etc., can also be completed on a classical computer.

[0186] In a sixth aspect, the present application further provides a quantum computer program product, which comprises a quantum computer program, the quantum computer program can be stored on a non-transitory computer readable storage medium, and the quantum computer program can be executed by a quantum processor, and the computer can execute the quantum gate optimization method of the continuous variable quantum system according to the first aspect or the second aspect.

[0187] In a seventh aspect, the present application further provides a non-transitory computer readable storage medium, which stores a quantum computer program, and the quantum computer program can be executed by a quantum processor to implement the quantum gate optimization method of the continuous variable quantum system according to the first aspect or the second aspect.

[0188] The device embodiments described above are only schematic, and the units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one place, or distributed on multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the embodiment. Those skilled in the art can understand and implement without creative labor.

[0189] From the above description of the embodiments, those skilled in the art can clearly understand that the embodiments can be realized by means of software plus necessary universal hardware platforms, and of course, can also be realized by hardware. Based on such understanding, the above technical solutions, essentially or in other words, the part that contributes to the prior art, can be embodied in the form of a software product, which can be stored in a computer readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes a number of instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute the methods described in each embodiment or some parts of the embodiments.

[0190] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacements to some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A quantum gate optimization method for continuous variable quantum systems, characterized in that, The method comprises: sampling a plurality of quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; preparing an initial state of a continuous variable quantum system; applying each sampled quantum circuit at each circuit depth to the initial state and performing a final state measurement on each sampled quantum circuit at each circuit depth; determining a survival probability of each sampled quantum circuit at each circuit depth based on the final state; determining a fidelity of the set of wave color Gaussian quantum gates based on the survival probability of each sampled quantum circuit at each circuit depth; optimizing the set of wave color Gaussian quantum gates based on the fidelity; wherein the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and inverse gates of the product of the d quantum gates; d is the circuit depth corresponding to the quantum circuit.

2. The method of claim 1, wherein, The preparing an initial state of a continuous variable quantum system comprises: preparing an initial state of the continuous variable quantum system as |0>0 m ; Among them, |0><0| m Let m be the vacuum states in m modes, where m is the number of modes in the continuous variable quantum system.

3. The method of Claim 1, wherein The d quantum gates are randomly selected from the set of wave color Gaussian quantum gates according to a preset probability distribution.

4. The method of Claim 1-3, wherein, The determining a fidelity of the set of wave color Gaussian quantum gates based on the survival probability of each sampled quantum circuit at each circuit depth comprises: averaging the survival probabilities of all quantum circuits sampled at each circuit depth to obtain a fidelity level of each circuit depth; obtaining a fitting formula of the fidelity level of the circuit depth with respect to the circuit depth; performing data fitting on each circuit depth and its fidelity level based on the fitting formula to obtain a fidelity by fitting; taking the fidelity as the fidelity of the set of wave color Gaussian quantum gates.

5. The method for quantum gate optimization of a continuous-variable quantum system according to claim 4, wherein, The fitting formula is y(d) = Ap d + B or y(d) = Ap d wherein y(d) is the fidelity level of the circuit depth, p is the fidelity, A is a first fitting coefficient, and B is a second fitting coefficient.

6. A method for quantum gate optimization of a continuous-variable quantum system, characterized in that, The method comprises: sampling a plurality of interleaved quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; preparing an initial state of a continuous variable quantum system; applying each sampled interleaved quantum circuit at each circuit depth to the initial state and performing a final state measurement on each sampled interleaved quantum circuit at each circuit depth; determining a survival probability of each sampled interleaved quantum circuit at each circuit depth based on the final state; determining a composite fidelity of the set of wave color Gaussian quantum gates and a target Gaussian quantum gate based on the survival probability of each sampled interleaved quantum circuit at each circuit depth; taking a ratio of the composite fidelity to the fidelity of the set of wave color Gaussian quantum gates as the fidelity of the target Gaussian quantum gate; optimizing the target Gaussian quantum gate using the fidelity of the target Gaussian quantum gate; wherein the interleaved quantum circuit is composed of quantum gates in a first sequence and inverse gates of the product of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of wave color Gaussian quantum gates and d target Gaussian quantum gates respectively inserted after the d quantum gates.

7. A quantum gate optimization device for a continuous variable quantum system, characterized in that, The device comprises: a first sampling module configured to sample a plurality of quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; a first preparation module configured to prepare an initial state of a continuous variable quantum system; a first sampling module configured to sample a plurality of quantum circuits for each circuit depth based on a set of wave color Gaussian quantum gates; a first measurement module, configured to apply each sampled quantum circuit at each circuit depth to the initial state, and perform a final state measurement on each sampled quantum circuit at each circuit depth; a quantum circuit survival probability determination module, configured to determine a survival probability of each sampled quantum circuit at each circuit depth based on the final state; a set of wave color Gaussian quantum gate fidelity determination module, configured to determine a fidelity of the set of wave color Gaussian quantum gates based on the survival probability of each sampled quantum circuit at each circuit depth; a first optimization module, configured to optimize the set of wave color Gaussian quantum gates based on the fidelity; wherein the quantum circuit is composed of d quantum gates in the set of wave color Gaussian quantum gates and inverse gates of the product of the d quantum gates; d is a circuit depth corresponding to the quantum circuit.

8. A quantum gate optimization device for a continuous variable quantum system, characterized in that, The device comprises: a second sampling module, configured to sample a plurality of interleaved quantum circuits at each circuit depth based on a set of wave color Gaussian quantum gates; a second preparation module, configured to prepare an initial state of a continuous variable quantum system; a second measurement module, configured to apply each sampled interleaved quantum circuit at each circuit depth to the initial state, and perform a final state measurement on each sampled interleaved quantum circuit at each circuit depth; an interleaved quantum circuit survival probability determination module, configured to determine a survival probability of each sampled interleaved quantum circuit at each circuit depth based on the final state; a composite fidelity determination module, configured to determine a composite fidelity of the set of wave color Gaussian quantum gates and a target Gaussian quantum gate based on the survival probability of each sampled interleaved quantum circuit at each circuit depth; a target Gaussian quantum gate fidelity determination module, configured to take a ratio of the composite fidelity and a fidelity of the set of wave color Gaussian quantum gates as the fidelity of the target Gaussian quantum gate; a second optimization module, configured to optimize the target Gaussian quantum gate by using the fidelity of the target Gaussian quantum gate; wherein the interleaved quantum circuit is composed of quantum gates in a first sequence and inverse gates of the product of all quantum gates in the first sequence; the first sequence is composed of d quantum gates in the set of wave color Gaussian quantum gates and d target Gaussian quantum gates respectively inserted after the d quantum gates.

9. An electronic device comprising a memory, a quantum processor, and a quantum computer program stored on the memory and executable on the quantum processor, wherein, The quantum processor implements the continuous variable quantum system quantum gate optimization method in any one of claims 1 to 5 or claim 6 when executing the program.

10. A non-transitory computer readable storage medium having stored thereon a quantum computer program, the program comprising: The quantum computer program implements the continuous variable quantum system quantum gate optimization method in any one of claims 1 to 5 or claim 6 when executed by the quantum processor.

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