WO2020228470A1 - 量子噪声过程分析方法、装置、设备及存储介质 - Google Patents

量子噪声过程分析方法、装置、设备及存储介质 Download PDF

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WO2020228470A1
WO2020228470A1 PCT/CN2020/084897 CN2020084897W WO2020228470A1 WO 2020228470 A1 WO2020228470 A1 WO 2020228470A1 CN 2020084897 W CN2020084897 W CN 2020084897W WO 2020228470 A1 WO2020228470 A1 WO 2020228470A1
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quantum
noise process
quantum noise
tensor
mapping
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PCT/CN2020/084897
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French (fr)
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谢昌谕
陈玉琴
郑一聪
马凯丽
张胜誉
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腾讯科技（深圳）有限公司
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Priority to JP2021531175A priority Critical patent/JP7098840B2/ja
Priority to KR1020217011244A priority patent/KR102496415B1/ko
Priority to EP20805042.7A priority patent/EP3968187A4/en
Publication of WO2020228470A1 publication Critical patent/WO2020228470A1/zh
Priority to US17/174,665 priority patent/US11893453B2/en
Priority to US18/538,946 priority patent/US20240169228A1/en

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/30—Circuit design
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/70—Quantum error correction, detection or prevention, e.g. surface codes or magic state distillation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N20/00—Machine learning
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N7/00—Computing arrangements based on specific mathematical models
    • G06N7/01—Probabilistic graphical models, e.g. probabilistic networks
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
    • G06F2119/10—Noise analysis or noise optimisation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N10/00—Quantum computing, i.e. information processing based on quantum-mechanical phenomena
    • G06N10/40—Physical realisations or architectures of quantum processors or components for manipulating qubits, e.g. qubit coupling or qubit control

Definitions

  • the embodiments of this application relate to the field of quantum technology, and in particular to a quantum noise process analysis technology.
  • the quantum noise process is the pollution process of quantum information due to the interaction of quantum systems or quantum devices with the environment, or the imperfection of the control itself.
  • Quantum process tomography In related technologies, quantum process tomography (QPT) is used to extract the relevant information of the dynamic mapping of the quantum noise process.
  • Quantum process tomography refers to the reconstruction of a mathematical description of the quantum noise process through a series of measurement processes by inputting a set of standard quantum states to the noise channel.
  • the pure quantum process tomography has limited information about the quantum noise process, which is not enough to accurately and comprehensively analyze the quantum noise process.
  • the embodiments of the present application provide a quantum noise process analysis method, device, equipment, and storage medium, which can be used to solve the above technical problems in related technologies.
  • the technical solution is as follows:
  • an embodiment of the present application provides a quantum noise process analysis method, the method includes:
  • the quantum noise process is analyzed according to the tensor transfer map.
  • an embodiment of the present application provides a quantum noise process analysis device, the device includes:
  • An obtaining module which is used to perform quantum process tomography on the quantum noise process of the target quantum system to obtain a dynamic mapping of the quantum noise process
  • An extraction module for extracting a tensor transfer map of the quantum noise process from the dynamic map, and the tensor transfer map is used to characterize the dynamic evolution of the quantum noise process;
  • the analysis module is used to analyze the quantum noise process according to the tensor transfer map.
  • an embodiment of the present application provides a computer device, the computer device includes a processor and a memory, and at least one instruction, at least a program, code set, or instruction set is stored in the memory, and the at least one instruction, The at least one program, the code set or the instruction set is loaded and executed by the processor to realize the quantum noise process analysis method described above.
  • an embodiment of the present application provides a computer-readable storage medium that stores at least one instruction, at least one program, code set, or instruction set, the at least one instruction, the at least one program, The code set or instruction set is loaded and executed by the processor to realize the quantum noise process analysis method described above.
  • an embodiment of the present application provides a computer program product, which is used to execute the foregoing quantum noise process analysis method when the computer program product is executed.
  • the quantum noise process is subjected to quantum process tomography to obtain the dynamic map of the quantum noise process, and the tensor transfer map of the quantum noise process is further extracted from the dynamic map of the quantum noise process.
  • the tensor transfer map is used to characterize the dynamic evolution of the quantum noise process, that is, it reflects the evolution law of the dynamic map of the quantum noise process over time. Compared with pure quantum process tomography, it can obtain richer and more comprehensive information about the quantum noise process. Therefore, when analyzing the quantum noise process based on the tensor transfer mapping of the quantum noise process, it is based on more abundant, Comprehensive information can achieve a more accurate and comprehensive analysis of the quantum noise process.
  • Figure 1 is an overall flow chart of the technical solution of this application.
  • Figures 3 to 8 exemplarily show schematic diagrams of several sets of experimental results in a simulated environment
  • Figures 9 to 14 exemplarily show schematic diagrams of several sets of experimental results in a real environment
  • 15 is a block diagram of a quantum noise process analysis device provided by an embodiment of the present application.
  • FIG. 16 is a block diagram of a quantum noise process analysis device provided by another embodiment of the present application.
  • Figure 17 is a schematic structural diagram of a computer device provided by an embodiment of the present application.
  • Quantum system A part of the entire universe whose motion law follows quantum mechanics.
  • Quantum state All information of a quantum system is represented by a quantum state ⁇ .
  • ⁇ is a d ⁇ d complex matrix, where d is the dimension of the quantum system.
  • Quantum noise process due to the interaction of quantum systems or quantum devices with the environment, or the imperfection of the control itself, the pollution process of quantum information. Mathematically, this process is a channel represented by a super operator, and it can be represented by a matrix when extended to higher dimensions.
  • Memory core It is an operator that acts on a quantum state and contains all the information about the decoherence of the system caused by the environment.
  • Second-order memory core the second-order number expansion of the memory core for the coupling strength of the quantum system and the environment.
  • the second-order correlation function of noise The correlation function of system noise at two different time points is used to calculate the noise frequency spectrum.
  • TTM Tensor transfer mapping
  • Quantum process tomography Input a set of standard quantum states to the noise channel, and reconstruct the mathematical description of the quantum noise process through a series of measurement processes.
  • quantum information processing all the information of a quantum system is characterized by the evolution ⁇ (t) of a quantum state with time t.
  • ⁇ (t) is a complex matrix of d ⁇ d.
  • Ak is also a d ⁇ d matrix and satisfies Represents the k-th component of the effect of the environment on the quantum system, and I is the identity matrix.
  • Represents the Hermitian conjugate of Ak that is, the complex conjugate is taken after transposition. Due to the completeness of the finite-dimensional complex matrix space, we now define a set of orthogonal basis matrices ⁇ E i ⁇ in the d ⁇ d matrix space, then we can get:
  • a quantum noise process analysis method based on quantum process tomography is provided.
  • each input state ⁇ j is transferred to the quantum noise process to obtain an output state ⁇ ( ⁇ j ). Due to the completeness of the input state, the output state can be expressed as a linear combination of input states:
  • ⁇ ( ⁇ j ) is the output quantum state of the quantum state ⁇ j after the dynamics mapping. In this way, by inputting the same quantum state ⁇ j multiple times and performing quantum state tomography on the output state, the solution can be solved experimentally And the coefficient c jk .
  • the specific process is as follows:
  • B m,n,j,k is a complex number
  • B m,n,j,k is regarded as a complex number matrix composed of ⁇ m,n ⁇ and ⁇ j,k ⁇ indicators
  • m, n, j, k is a positive integer.
  • c jk ⁇ m,n ⁇ m,n B m,n,j,k ;
  • ⁇ m,n contains all the information of the dynamics mapping of the quantum noise process
  • the ⁇ m,n is obtained through the quantum process tomography, and all the information of the dynamics mapping of the quantum noise process is obtained.
  • the pure quantum process tomography has limited information about the quantum noise process, which is not enough to accurately and comprehensively analyze the quantum noise process. For example, no judgment is made on whether the quantum noise process is a Markov process or a non-Markov process, the spectrum of the quantum noise process is not obtained, and the correlation noise between different quantum devices in the quantum system is not analyzed. .
  • the embodiment of the present application provides a quantum noise process analysis method.
  • Figure 1 shows the overall flow chart of the technical solution of the present application.
  • the quantum noise process is subjected to quantum process tomography to obtain the dynamic map of the quantum noise process.
  • the tensor transfer map of the quantum noise process is further extracted, Then analyze the quantum noise process according to the tensor transfer map.
  • the tensor transfer mapping is used to characterize the dynamic evolution of the quantum noise process, that is, it reflects the evolution law of the dynamic mapping of the quantum noise process over time. Therefore, the tensor transfer mapping based on the quantum noise process analyzes the quantum noise process. Compared with the pure quantum process tomography, it can obtain more abundant and comprehensive information about the quantum noise process, so as to realize the quantum noise process. More accurate and comprehensive analysis.
  • the technical solution provided in this application is suitable for analyzing the quantum noise process of any quantum system, such as quantum computer, quantum secure communication, quantum internet or other quantum systems. Because the quantum system is disturbed by quantum noise, the impact on the performance of the quantum system is very serious, and it is the biggest obstacle hindering the practical application of the quantum system. Therefore, analyzing the quantum noise process and understanding the nature of the noise are crucial to the development of quantum systems.
  • the technical solution provided by this application analyzes the quantum noise process based on the tensor transfer mapping of the quantum noise process, and may include the following analysis content: As shown in Figure 1, for example, the Markov process judgment, that is, the quantum noise process is Markov Whether the Koff process or the non-Markov process is judged, unique noise suppression schemes can be designed for non-Markov noise, such as dynamic decoupling to suppress the occurrence of noise; state evolution prediction, that is, the quantum noise process State evolution prediction; correlation function and spectrum extraction, that is, the correlation function and frequency spectrum of the quantum noise process can be obtained, so as to help integrate the filter of the corresponding frequency band when manufacturing quantum devices; correlation noise analysis, that is, the different quantum devices in the quantum system Analyze the correlation noise between them, understand the source of the correlation noise, and design a corresponding plan to suppress the correlation noise. Therefore, the technical solution provided by the present application can obtain more abundant and comprehensive information about the quantum noise process, thereby providing more information support for the performance improvement of the quantum system.
  • FIG. 2 shows a flowchart of a quantum noise process analysis method provided by an embodiment of the present application.
  • This method can be applied to a computer device, which can be any electronic device with data processing and storage capabilities, such as a PC (personal computer, personal computer), a server, a computer host, and other electronic devices.
  • the method may include the following steps (step 201 to step 203):
  • Step 201 Perform quantum process tomography on the quantum noise process of the target quantum system to obtain a dynamic map of the quantum noise process.
  • this embodiment can perform quantum process tomography on discrete time points in the quantum noise process. For example, if quantum process tomography is performed at K different time points, the dynamics of the quantum noise process at K time points can be obtained. Learn mapping, K is an integer greater than or equal to 1.
  • the interval between two adjacent time points is equal. Of course, the interval between two adjacent time points may not be equal, which is not limited in this embodiment. .
  • Step 202 Extract the tensor transfer map of the quantum noise process according to the dynamic map.
  • the tensor transfer map of the quantum noise process is used to characterize the dynamic evolution of the quantum noise process, that is, it reflects the evolution law of the dynamic map of the quantum noise process over time.
  • step 201 may be to calculate the quantum noise process according to the dynamic mapping of the quantum noise process at K time points.
  • the tensor transfer mapping of the noise process at K time points is extracted in a recursive manner. For example, calculate the tensor transfer map T n of the quantum noise process at the nth time point according to the following formula:
  • T 1 ⁇ 1
  • ⁇ n the dynamic mapping of the quantum noise process at the nth time point
  • ⁇ m the dynamic mapping of the quantum noise process at the mth time point
  • T nm the quantum The tensor transfer mapping of the noise process at the nmth time point, n and m are both positive integers.
  • Step 203 Analyze the quantum noise process according to the tensor transfer map.
  • the quantum noise process After extracting the tensor transfer mapping of the quantum noise process at K time points, the quantum noise process can be analyzed accordingly.
  • the quantum noise process is a Markov process.
  • the quantum noise process can be regarded as a non-Markov process.
  • the quantum noise process is determined to be a Markov process
  • the first time point is the K time points divided by the first one Other time points other than the time point
  • the quantum noise process is determined to be a non-Markov process
  • the second time point is K times At least one point in time except the first point in point.
  • the tensor transfer mapping based on the quantum noise process can determine whether the quantum noise process is a Markov process or a non-Markov process.
  • a unique noise suppression scheme can be designed for non-Markov noise, such as by Dynamic decoupling to suppress the occurrence of noise.
  • the general equation describing the evolution of a quantum system in an open environment is the non-time localized quantum master equation, which can better reveal the mathematical structure of the quantum noise process.
  • This equation is a differential integral equation:
  • ⁇ (t) represents the quantum state of the quantum system at time t, represented by a d ⁇ d complex number matrix.
  • L s is the Liuville operator, which represents the coherent part in the evolution of the quantum system.
  • s is the integral parameter.
  • ⁇ (t) is the memory core, which contains all the information about system decoherence caused by the environment. If L s and ⁇ (t) of a quantum noise process are obtained, then the noise mechanism can be fully understood.
  • the basic idea of the technical solution of the present application is to calculate the tensor transfer map through experiments and quantum process tomography, so as to extract relevant information of L s and ⁇ (t).
  • the joint Hamiltonian can be expressed as:
  • H s is the Hamiltonian of the quantum system
  • H sb is the interaction Hamiltonian between the quantum system and the environment
  • g i is the coupling strength between system and bath.
  • ⁇ (t) represents the quantum state of the quantum system at time t
  • ⁇ (0) represents the initial quantum state of the quantum system
  • ⁇ B is the quantum state of the environment
  • Tr B represents the deviation calculation of the degree of freedom of the environment
  • exp + , exp - are the clockwise and inverse and time-chronological exponential operators, respectively
  • ⁇ (t) represents the dynamic evolution of the quantum system at time t
  • i is the unit pure imaginary number
  • s is the integral parameter.
  • ⁇ (t n ) represents the quantum state at the nth time point t n
  • ⁇ (t nm ) represents the quantum state at the n - m time point t nm
  • T m represents the tensor transition at the mth time point Mapping.
  • the tensor transfer mapping of this period of time can be obtained through the quantum process tomography of a short period of time dynamics mapping.
  • this short period of tensor transfer mapping can be used to predict the evolution of a long-term open system.
  • the quantum state ⁇ (t n ) at the nth time point t n can be calculated by the above formula.
  • the predicted quantum state can be directly compared with experiments to verify the effectiveness of describing the dynamics of the open system through tensor transfer mapping. That is to say, this provides a preliminary criterion for the effectiveness of the technical solution of this application.
  • the quantum noise process is subjected to quantum process tomography to obtain the dynamic map of the quantum noise process, and the dynamic map of the quantum noise process is further extracted from the dynamic map of the quantum noise process.
  • Tensor transfer mapping is used to characterize the dynamic evolution of the quantum noise process, that is, it reflects the evolution law of the dynamic map of the quantum noise process over time. Compared with pure quantum process tomography, it can obtain richer and more comprehensive information about the quantum noise process. Therefore, when analyzing the quantum noise process based on the tensor transfer mapping of the quantum noise process, it is based on more abundant, Comprehensive information can achieve a more accurate and comprehensive analysis of the quantum noise process.
  • the tensor transfer mapping based on the quantum noise process is also implemented to determine whether the quantum noise process is a Markov process or a non-Markov process; it is also implemented based on the quantum noise process
  • the tensor transfer mapping in a period of time predicts the state evolution of the quantum noise process in the subsequent period.
  • the correlation function and frequency spectrum of the quantum noise process can also be obtained accordingly.
  • the process can include the following steps:
  • the quantum noise process is steady-state noise, extract the second-order memory core of the quantum noise process according to the tensor transfer mapping of the quantum noise process;
  • the correlation function of the noise process determines the nature of the noise.
  • the correlation function of the noise process can be calculated according to the second-order memory core of the noise process.
  • the second-order memory core of the quantum noise process is extracted according to the tensor transfer map of the quantum noise process.
  • T n (1+L s ⁇ t) ⁇ n,1 + ⁇ (t n ) ⁇ t 2 ;
  • ⁇ t is a time step
  • ⁇ n 1 is a Kronecker function
  • n is a positive integer
  • ⁇ (t n ) is the value of the memory core at time t n .
  • I a mapping operator
  • L the effect on the system operator and the environment joint Liouville
  • ⁇ SB joint environment and ecosystems joint state of system and bath
  • ⁇ 2 (t) is the value of the second-order memory core at time t, Is the complex conjugate of C ⁇ ' (t). Note that the above expression is under Schrödinger's representation, and it is also assumed that the Hamiltonian of the joint system does not change with time. Among them, the second order correlation function C ⁇ ′ (t) is defined as
  • the dynamic map can be extracted in the experiment, and the tensor transfer map can be obtained through quantum process tomography, which approximates the memory core ⁇ exp . That is, ⁇ exp is an approximate second-order memory core obtained through experiments.
  • the second-order perturbation is no longer a good approximation. More high-order terms are needed to get a better approximation, but it is still possible to extract tensors from experimental data Transfer the mapping to extract the second-order memory core.
  • the specific steps are as follows: select N different parameters, perform experiments on the quantum noise process, extract the memory cores corresponding to the N different parameters from the experiment; according to the memory cores corresponding to the N different parameters, calculate the second part of the quantum noise process Order memory core.
  • A is the normalized parameter matrix of order N, and the memory core on the right side of the equation can be directly extracted from the experiment through quantum process tomography and data processing. Because A is a full-rank matrix, by solving linear equations to obtain memory cores with no physical units of order 2 to N, naturally second order memory cores are obtained.
  • ⁇ 2 represents the second-order memory core of the quantum noise process
  • t n represents the nth time point
  • C ⁇ ′ (t n ) is the second-order correlation function at the nth time point t n
  • ⁇ exp represents the experiment
  • Is the Kronecker function (when n 0, its value is 1, and in other cases its value is 0)
  • ⁇ n is an adjustable parameter
  • C aa' (t n-1 ) is at the n-1th time
  • the second-order correlation function at point t n-1 is used to ensure that the correlation function can still be continuous after the objective function is minimized.
  • the choice of ⁇ n can be achieved by first selecting an initial value, observing the size of the objective function, and then adjusting it iteratively. Its value selection has certain robustness.
  • the Fourier transform of the correlation function can be performed to obtain the frequency spectrum J ⁇ ′ ( ⁇ ) of the quantum noise process:
  • This method of obtaining the frequency spectrum of the quantum noise process is not limited to quantum noise (the system has feedback to the noise source) or classical noise, and is not limited to a specific type of noise.
  • the correlation function and frequency spectrum of the quantum noise process can also be obtained accordingly, thereby helping to integrate the corresponding frequency bands when manufacturing quantum devices. Filter.
  • the correlation noise between different quantum devices in the target quantum system can also be analyzed accordingly to understand the source of the correlation noise.
  • the process can include the following steps:
  • a quantum system can contain multiple quantum devices.
  • a qubit is the simplest type of quantum device that contains only two quantum states.
  • the noise correlation between multiple quantum devices in the same quantum system can be completed. The following is mainly the case of two quantum devices. Other cases can be similarly promoted.
  • any three or more quantum devices Correlation of noise between devices can be determined.
  • ⁇ n,1 represents the dynamics mapping of the first quantum device
  • ⁇ n,2 represents the dynamics mapping of the second quantum device
  • ⁇ n is the unseparated part, which represents the influence of correlated noise.
  • the above dynamic mapping decomposition can use the form of Choi matrix to express the dynamic mapping ⁇ n ⁇ n , that is, ⁇ n is the Choi matrix, which is an equivalent representation of the dynamic mapping, and the Choi matrix is taken The trace:
  • the dynamics mapping ⁇ n of the two quantum devices can be obtained by the combined quantum process tomography of the two quantum devices.
  • ⁇ n can be used to analyze correlated noise.
  • the mode of ⁇ n will be more than It's much smaller.
  • ⁇ n and The modulus value of may be equivalent, even
  • it is difficult to analyze the source of correlated noise because all the data are mixed together.
  • the sources of correlated noise between two quantum devices include: (1) Correlated noise generated by direct coupling between two quantum devices; (2) Correlated noise induced by two quantum devices through a shared environment ; (3) Both of the above.
  • the embodiment of the present application provides a correlation noise analysis method based on tensor transfer mapping, which can obtain more information about correlation noise. First, pass To calculate the separable tensor transition map
  • ⁇ T n is the noise correlation in transfer tensor map (noise correlation in transfer tensor map).
  • ⁇ T n can be broken down into:
  • ⁇ T n ⁇ L ⁇ t ⁇ n,1 + ⁇ n ⁇ t 2 ;
  • the Liuweier super-operator ⁇ L reveals whether there is correlated noise generated by the direct coupling between two quantum devices, and ⁇ n represents the correlated noise induced by the shared environment. It can be found that the coupling increment caused by ⁇ L and ⁇ t have a linear relationship, while the coupling increment caused by ⁇ n and ⁇ t 2 are linear. Two different time steps ⁇ t and ⁇ t' can be selected, so that two different dynamic mappings ⁇ 1 and ⁇ 1 ′ will be generated to determine the source of the correlation noise. In view of the significant impact of correlated noise on fault-tolerant quantum computing, the technical solution of this application can better understand correlated noise and provide guidance on how to control it, and design different noise suppression solutions for ⁇ L and ⁇ n .
  • the joint dynamics map ⁇ n of the two quantum devices in the target quantum system can be obtained, and the tensor transfer map T n can be further obtained, and then the two quantum devices can be traced separately through ⁇ n .
  • the correlation noise between different quantum devices in the target quantum system can also be analyzed accordingly to understand Correlate the source of the noise, and design a corresponding plan to suppress the correlated noise.
  • Line 32, line 33, and line 34 respectively show the prediction effects of different tensor transfer mapping lengths (that is, when K is 1, 3, and 5) on the density matrix. It can be seen that when K is set to 5, the evolution obtained by the tensor transfer mapping overlaps the exact solution well, which can perfectly predict the long-term experimental evolution.
  • Figure 4 shows the change of Bloch volume over time.
  • the growth of Bloch volume V(t) in a certain period of time (t 4 , t 5 , t 6 ) clearly shows the dynamic process
  • Part (a) of Fig. 7 shows that two qubits coupled to each other in the z-direction are in their own independent environmental noise, and the tensor transfer mapping results of the free evolution of the two qubits.
  • the system Hamiltonian is:
  • the environmental Hamiltonian is:
  • the correlation function is:
  • Line 71, line 72, and line 73 respectively represent the full tensor transfer map T n , which can separate the tensor transfer map And the associated tensor transition map ⁇ T n .
  • ⁇ T 1 is non-trivial. That is to say, the result shows that the correlation part of the tensor transfer mapping under independent noise environment is almost Markovian. Further analysis shows that the entanglement of two qubits caused by ⁇ L s will lead to associated decoherence effects, even if the noise sources are spatially separated or independent of each other.
  • Part (b) of Fig. 7 shows the tensor transfer mapping result of the free evolution of the two qubits that are not directly coupled in the associated environmental noise.
  • the system Hamiltonian is:
  • the environmental Hamiltonian is:
  • Line 74, line 75, and line 76 respectively represent the full tensor transfer map T n , which can separate the tensor transfer map And the associated tensor transition map ⁇ T n . In this case, multiple ⁇ T n are non-trivial.
  • ⁇ K(t 1 ) is the main contributor to ⁇ T 1 . Therefore, the relative importance of different physical mechanisms that lead to collective decoherence can be estimated directly based on the distribution of the norm of the tensor transfer mapping over time.
  • Figure 8 shows the dynamic evolution of the off-diagonal matrix elements of the two-qubit density matrix.
  • the prediction result of the physical state of the tensor transfer map of length (that is, K is 1, 8, and 16 respectively) is compared with the real dynamic simulation result.
  • the two parts (a) and (b) of Figure 8 respectively show the pair based on the full tensor transfer map and the separable tensor transfer map under the first model. Forecast results.
  • the two parts (c) and (d) of Figure 8 respectively show the pair based on the full tensor transfer map and the separable tensor transfer map under the second model. Forecast results.
  • the effect of collective withdrawal cannot be determined by Describe separately. From Fig. 7, ⁇ T n is small overall and does not cause any influence. But this shows that ⁇ T n still plays an important role in the prediction of the state of matter. This further validates the complex characteristics of highly non-Markov systems.
  • IBM Quantum Experience is a superconducting quantum computing cloud platform provided by IBM. All calculations run on real superconducting quantum computers. For superconducting qubits, on the one hand, because the time to operate the quantum gate is too long relative to the environment ( ⁇ 100ns), on the other hand, because the noise process is not pure phase decoherence, dynamic decoupling extraction based on CPMG The spectrum method is not applicable.
  • Part (a) of Fig. 9 shows the distribution of the specification of the tensor transfer map over time.
  • Part (b) in Figure 9 shows the dynamic evolution of state
  • Line 92, line 93, and line 94 are the prediction results of the evolution of
  • Figure 10 shows the distribution of the single-qubit Bloch volume V(t) over time.
  • the short-term growth demonstrated the non-Markovian properties of quantum systems.
  • DD single-qubit dynamic decoupling
  • DD single-qubit dynamic decoupling
  • ⁇ t 2.64 ⁇ s.
  • XY4DD protocol the distribution of the specification of tensor transfer mapping over time.
  • the internal mechanism of the extension of quantum coherence can be reflected by this tensor transfer mapping: the effective noise under the XY4DD protocol has more Markov characteristics than the result of free evolution.
  • the black line represented by the black dot is the experimental result of the density matrix evolution, and the three lines represented by the circle, triangle and square are the effects of selecting (1, 2, 4) tensor transition maps to predict the evolution of the density matrix.
  • Figure 14 (a) and (b) respectively show that the initial state is a non-entangled state The following is based on the prediction results of the complete tensor transition map and the separable tensor transition map pair.
  • FIG. 15 shows a block diagram of a quantum noise process analysis device provided by an embodiment of the present application.
  • the device has the function of realizing the above method example, and the function can be realized by hardware, or by hardware executing corresponding software.
  • the device can be a computer device, or it can be set in a computer device.
  • the device 1500 may include: an acquisition module 1510, an extraction module 1520, and an analysis module 1530.
  • the obtaining module 1510 is configured to perform quantum process tomography on the quantum noise process of the target quantum system to obtain a dynamic mapping of the quantum noise process.
  • the extraction module 1520 is configured to extract a tensor transfer map of the quantum noise process according to the dynamic map, and the tensor transfer map is used to characterize the dynamic evolution of the quantum noise process.
  • the analysis module 1530 is configured to analyze the quantum noise process according to the tensor transfer mapping.
  • the quantum noise process is subjected to quantum process tomography to obtain the dynamic map of the quantum noise process, and the dynamic map of the quantum noise process is further extracted from the dynamic map of the quantum noise process.
  • Tensor transfer mapping is used to characterize the dynamic evolution of the quantum noise process, that is, it reflects the evolution law of the dynamic map of the quantum noise process over time. Compared with pure quantum process tomography, it can obtain richer and more comprehensive information about the quantum noise process. Therefore, when analyzing the quantum noise process based on the tensor transfer mapping of the quantum noise process, it is based on more abundant, Comprehensive information can achieve a more accurate and comprehensive analysis of the quantum noise process.
  • the dynamic mapping includes: dynamic mapping of the quantum noise process at K time points, where K is a positive integer;
  • the extraction module 1520 is configured to calculate a tensor transfer map of the quantum noise process at the K time points according to the dynamic mapping of the quantum noise process at the K time points.
  • the extraction module 1520 is configured to calculate the tensor transfer map T n of the quantum noise process at the nth time point according to the following formula:
  • T 1 ⁇ 1
  • ⁇ n represents the dynamic mapping of the quantum noise process at the nth time point
  • ⁇ m represents the dynamic mapping of the quantum noise process at the mth time point
  • T nm Represents the tensor transfer mapping of the quantum noise process at the nmth time point
  • n and m are both positive integers.
  • the analysis module 1530 includes a Markov discrimination sub-module 1531.
  • the Markov discrimination sub-module 1531 is used for:
  • the modulus of the tensor transfer map of the quantum noise process at the first time point is all less than the preset threshold, it is determined that the quantum noise process is a Markov process; the first time point is the K time points In addition to the first time point in other time points;
  • the modulus of the tensor transfer map of the quantum noise process at the second time point is greater than the preset threshold, it is determined that the quantum noise process is a non-Markov process; the second time point is the K At least one point in time except the first point in time.
  • the analysis module 1530 includes a state evolution prediction sub-module 1532.
  • the state evolution prediction sub-module 1532 is configured to predict the state evolution of the quantum noise process in a subsequent time according to the tensor transfer mapping at the K time points.
  • the evolution of the state prediction submodule 1532 configured to: calculate the quantum noise process in the n-th time point T n according to the formula of the quantum states ⁇ (t n):
  • T m represents the tensor transfer mapping at the m-th time point
  • ⁇ (t nm ) represents the quantum state at the nm-th time point t nm
  • n and m are both positive integers.
  • the analysis module 1530 includes:
  • the memory core extraction sub-module 1533 is configured to extract the second-order memory core of the quantum noise process according to the tensor transfer map if the quantum noise process is steady-state noise;
  • the correlation function calculation submodule 1534 is configured to calculate the correlation function of the quantum noise process according to the second-order memory core of the quantum noise process
  • the frequency spectrum acquisition sub-module 1535 is configured to perform Fourier transform on the correlation function of the quantum noise process to obtain the frequency spectrum of the quantum noise process.
  • the memory core extraction submodule 1533 is configured to: select N different parameters, perform experiments on the quantum noise process, and extract memory cores corresponding to the N different parameters from the experiment; According to the memory cores corresponding to the N different parameters, the second-order memory core of the quantum noise process is calculated.
  • the correlation function calculation submodule 1534 is used to numerically extract the correlation function C ⁇ ′ of the quantum noise process according to the following formula:
  • ⁇ 2 represents the second-order memory core of the quantum noise process
  • t n represents the n-th time point
  • ⁇ exp represents the approximate second-order memory core obtained by the experiment
  • ⁇ n is an adjustable parameter
  • C aa' (t n-1 ) is the second-order correlation at the n-1th time point t n-1 function.
  • the analysis module 1530 includes a correlated noise analysis sub-module 1536.
  • the correlated noise analysis sub-module 1536 is configured to: for the s quantum devices included in the target quantum system, calculate the tensor transfer mapping corresponding to each of the s quantum devices.
  • the device provided in the above embodiment when implementing its functions, only uses the division of the above functional modules for illustration. In practical applications, the above functions can be allocated by different functional modules as needed, namely The internal structure of the device is divided into different functional modules to complete all or part of the functions described above.
  • the apparatus and method embodiments provided by the above-mentioned embodiments belong to the same concept, and the specific implementation process is detailed in the method embodiments, which will not be repeated here.
  • FIG. 17 shows a schematic structural diagram of a computer device provided by an embodiment of the present application.
  • the computer device is used to implement the quantum noise process analysis method provided in the foregoing embodiment. Specifically:
  • the computer device 1700 includes a central processing unit (CPU) 1701, a system memory 1704 including a random access memory (RAM) 1702 and a read-only memory (ROM) 1703, and a system bus 1705 connecting the system memory 1704 and the central processing unit 1701 .
  • the computer device 1700 also includes a basic input/output system (I/O system) 1706 that helps to transfer information between various devices in the computer, and a large-capacity storage system 1713, application programs 1714, and other program modules 1715.
  • the basic input/output system 1706 includes a display 1708 for displaying information and an input device 1709 such as a mouse and a keyboard for the user to input information.
  • the display 1708 and the input device 1709 are both connected to the central processing unit 1701 through the input and output controller 1710 connected to the system bus 1705.
  • the basic input/output system 1706 may also include an input and output controller 1710 for receiving and processing input from multiple other devices such as a keyboard, a mouse, or an electronic stylus.
  • the input and output controller 1710 also provides output to a display screen, a printer, or other types of output devices.
  • the mass storage device 1707 is connected to the central processing unit 1701 through a mass storage controller (not shown) connected to the system bus 1705.
  • the mass storage device 1707 and its associated computer readable medium provide non-volatile storage for the computer device 1700. That is, the mass storage device 1707 may include a computer-readable medium (not shown) such as a hard disk or a CD-ROM drive.
  • the computer-readable media may include computer storage media and communication media.
  • Computer storage media includes volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storing information such as computer readable instructions, data structures, program modules or other data.
  • Computer storage media include RAM, ROM, EPROM, EEPROM, flash memory or other solid-state storage technologies, CD-ROM, DVD or other optical storage, tape cartridges, magnetic tape, disk storage or other magnetic storage devices.
  • RAM random access memory
  • ROM read-only memory
  • EPROM Erasable programmable read-only memory
  • EEPROM electrically erasable programmable read-only memory
  • the computer device 1700 may also be connected to a remote computer on the network through a network such as the Internet to operate. That is, the computer device 1700 can be connected to the network 1712 through the network interface unit 1711 connected to the system bus 1705, or in other words, the network interface unit 1711 can also be used to connect to other types of networks or remote computer systems (not shown) ).
  • the memory stores at least one instruction, at least one section of program, code set or instruction set, and the at least one instruction, at least one section of program, code set or instruction set is configured to be executed by one or more processors to realize the foregoing The quantum noise process analysis method provided by the embodiment.
  • a computer-readable storage medium stores at least one instruction, at least one program, a code set, or an instruction set, the at least one instruction, the at least one program
  • the aforementioned computer-readable storage medium may be ROM, RAM, CD-ROM, magnetic tape, floppy disk, optical data storage device, and the like.
  • a computer program product is also provided.
  • the computer program product When executed, it is used to implement the quantum noise process analysis method provided in the foregoing embodiment.
  • the "plurality” mentioned herein refers to two or more.
  • “And/or” describes the association relationship of the associated objects, indicating that there can be three types of relationships, for example, A and/or B, which can mean: A alone exists, A and B exist at the same time, and B exists alone.
  • the character "/” generally indicates that the associated objects are in an "or” relationship.
  • the numbering of the steps described in this article only exemplarily shows a possible order of execution among the steps. In some other embodiments, the above steps may also be executed out of the order of numbers, such as two different numbers. The steps are executed at the same time, or the two steps with different numbers are executed in the reverse order of the figure, which is not limited in the embodiment of the present application.

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Abstract

一种量子噪声过程分析方法、装置、设备及存储介质，属于量子技术领域。所述方法包括：对目标量子系统的量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射（201）；从动力学映射中提取量子噪声过程的张量转移映射（202）；根据张量转移映射对量子噪声过程进行分析（203）。其中，张量转移映射用于表征量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。因此，基于量子噪声过程的张量转移映射对量子噪声过程进行分析，相比于单纯的量子过程层析，能够得到有关量子噪声过程的更为丰富、全面的信息，从而实现对量子噪声过程进行更为准确全面地分析。

Description

量子噪声过程分析方法、装置、设备及存储介质
本申请要求于2019年5月10日提交中国专利局、申请号201910390722.5、申请名称为“量子噪声过程分析方法、装置、设备及存储介质”的中国专利申请的优先权，其全部内容通过引用结合在本申请中。
技术领域
本申请实施例涉及量子技术领域，特别涉及一种量子噪声过程分析技术。
背景技术
量子噪声过程是由于量子系统或量子器件与环境相互作用，或者控制本身的不完美导致量子信息的污染过程。
在相关技术中，采用量子过程层析(quantum process tomography，QPT)提取量子噪声过程的动力学映射的相关信息。量子过程层析是指通过对噪声通道输入一组标准量子态，通过一系列测量过程来重构量子噪声过程的数学描述。
单纯的量子过程层析，所获得的关于量子噪声过程的信息有限，不足以对量子噪声过程进行准确全面地分析。
发明内容
本申请实施例提供了一种量子噪声过程分析方法、装置、设备及存储介质，可用于解决相关技术所存在的上述技术问题。所述技术方案如下：
一方面，本申请实施例提供一种量子噪声过程分析方法，所述方法包括：
对目标量子系统的量子噪声过程进行量子过程层析，得到所述量子噪声过程的动力学映射；
从所述动力学映射中提取所述量子噪声过程的张量转移映射，所述张量转移映射用于表征所述量子噪声过程的动力学演化；
根据所述张量转移映射对所述量子噪声过程进行分析。
另一方面，本申请实施例提供一种量子噪声过程分析装置，所述装置包括：
获取模块，用于对目标量子系统的量子噪声过程进行量子过程层析，得到所述量子噪声过程的动力学映射；
提取模块，用于从所述动力学映射中提取所述量子噪声过程的张量转移映射，所述张量转移映射用于表征所述量子噪声过程的动力学演化；
分析模块，用于根据所述张量转移映射对所述量子噪声过程进行分析。
再一方面，本申请实施例提供一种计算机设备，所述计算机设备包括处理器和存储器，所述存储器中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现上述量子噪声过程分析方法。
又一方面，本申请实施例提供一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由处理器加载并执行以实现上述量子噪声过程分析方法。
又一方面，本申请实施例提供一种计算机程序产品，当该计算机程序产品被执行时，其用于执行上述量子噪声过程分析方法。
本申请实施例提供的技术方案至少包括如下有益效果：
在本申请提供的技术方案中，通过对量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射，从量子噪声过程的动力学映射中，进一步提取量子噪声过程的张量转移映射。张量转移映射用于表征量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。其相比于单纯的量子过程层析，能够得到有关量子噪声过程的更为丰富、全面的信息，因此，基于量子噪声过程的张量转移映射对量子噪声过程进行分析时，基于更为丰富、全面的信息可以实现对量子噪声过程进行更为准确全面地分析。
附图说明
为了更清楚地说明本申请实施例中的技术方案，下面将对实施例描述中所需要使用的附图作简单地介绍，显而易见地，下面描述中的附图仅仅是本申请的一些实施例，对于本领域普通技术人员来讲，在不付出创造性劳动的前提下，还可以根据这些附图获得其他的附图。
图1是本申请技术方案的整体流程图；
图2是本申请一个实施例提供的量子噪声过程分析方法的流程图；
图3至图8示例性示出了在模拟环境下的几组实验结果的示意图；
图9至图14示例性示出了在真实环境下的几组实验结果的示意图；
图15是本申请一个实施例提供的量子噪声过程分析装置的框图；
图16是本申请另一个实施例提供的量子噪声过程分析装置的框图；
图17是本申请一个实施例提供的计算机设备的结构示意图。
具体实施方式
为使本申请的目的、技术方案和优点更加清楚，下面将结合附图对本申请实施方式作进一步地详细描述。
在对本申请实施例进行介绍说明之前，首先对本申请中涉及的一些名词进行解释说明。
1、量子系统：整个宇宙的一部分，其运动规律遵循量子力学。
2、量子态：量子系统的所有信息由一个量子态ρ来表征。ρ是一个d×d复数矩阵，其中d是量子系统的维数。
3、量子噪声过程：由于量子系统或量子器件与环境相互作用，或者控制本身的不完美导致量子信息的污染过程。数学上这个过程是一个用超算符表示的信道，拓展到更高维度，则可以用矩阵表示。
4、记忆核：是一个作用在量子态上的算子，包含了所有由环境引发的系统退相干的信息。
5、二阶记忆核：记忆核针对量子系统和环境的耦合强度的二阶级数展开。
6、噪声的二阶关联函数：系统噪声在两个不同时间点的关联函数，用以计算噪声的频谱。
7、张量转移映射(tensorial transfer mapping，TTM)：从量子噪声过程的动力学映射中递归提取的一组映射，该组映射编码了量子系统的记忆核，可以用来预言量子系统的动力学演化，并判断噪声的性质。
8、量子过程层析：通过对噪声通道输入一组标准量子态，通过一系列测量过程来重构量子噪声过程的数学描述。
在量子信息处理中，量子系统的所有信息都由一个量子态随时间t的演化ρ(t)来表征。ρ(t)是d×d的复矩阵。任意量子过程，包括量子信息处理过程和量子噪声过程，若初始时系统和环境是可分离态，则可以用一个动力学映射来表征：
Figure PCTCN2020084897-appb-000001
其中，A k也是d×d矩阵并满足
Figure PCTCN2020084897-appb-000002
表示环境对量子系统的影响的作用的第k个分量，I为单位矩阵。这里，
Figure PCTCN2020084897-appb-000003
代表由A k的厄米共轭，即转置后取复数共轭。由于有限维复矩阵空间的完备性，现定义一组在d×d矩阵空间的正交基矩阵集合{E i}，那么可以得到：
A i＝∑ ma imE m；
其中，
Figure PCTCN2020084897-appb-000004
代表复数集，E m是{E i}中的一个元素，i、m均为正整数。
这样，可以得到：
Figure PCTCN2020084897-appb-000005
其中，
Figure PCTCN2020084897-appb-000006
是复数转换矩阵χ指标为m,n的元素，
Figure PCTCN2020084897-appb-000007
代表由E n的厄米共轭，E n是{E i}中的一个元素，ρ表示输入态。
在相关技术中，提供了一种基于量子过程层析的量子噪声过程分析方法。使用d 2×d 2个线性无关的输入态ρ j，把每个输入态ρ j传递到量子噪声过程中得到输出态ε(ρ j)。由于输入态的完备性，输出态可以表示成输入态的线性组合：
ε(ρ j)＝∑ kc jkρ k；其中，
Figure PCTCN2020084897-appb-000008
ε(ρ j)是量子态ρ j经过动力学映射后的输出量子态，这样，通过多次输入同一个量子态ρ j并对输出态做量子态层析，就可以在实验上解得求和系数c jk。具体过程如下：
Figure PCTCN2020084897-appb-000009
其中，B m,n,j,k是一个复数，B m,n,j,k看成是一个由{m,n}和{j,k}指标组成的复数矩阵，m、n、j、k均为正整数。那么，
∑ kc jkρ k＝ε(ρ j )＝∑ m,n,kχ m,nB m,n,j,kρ k；
由于{ρ i}是线性无关的，可以得到：
c jk＝∑ m,nχ m,nB m,n,j,k；
通过转置B m,n,j,k，可以得到：
Figure PCTCN2020084897-appb-000010
因为χ m,n包含了量子噪声过程的动力学映射的所有信息，因此通过量子过程层析得到χ m,n，也就得到了量子噪声过程的动力学映射的所有信息。
但是，单纯的量子过程层析，所获得的关于量子噪声过程的信息有限，不足以对量子噪声过程进行准确全面地分析。例如，并没有对量子噪声过程是马尔科夫过程还是非马尔科夫过程做出判定，也没有获得量子噪声过程的频谱，也没有对量子系统中的不同量子器件之间的关联噪声做出分析。
为了解决上述技术问题，本申请实施例提供一种量子噪声过程分析方法。如图1所示，其示出了本申请技术方案的整体流程图。在本申请提供的技术方案中，通过对量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射，从量子噪声过程的动力学映射中，进一步提取量子噪声过程的张量转移映射，然后根据该张量转移映射对量子噪声过程进行分析。其中，张量转移映射用于表征量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。因此，基于量子噪声过程的张量转移映射对量子噪声过程进行分析，相比于单纯的量子过程层析，能够得到有关量子噪声过程的更为丰富、全面的信息，从而实现对量子噪声过程进行更为准确全面地分析。
本申请提供的技术方案，适用于对任何量子系统的量子噪声过程进行分析，如量子计算机、量子保密通信、量子互联网或者其它量子系统。由于量子系统受到量子噪声的干扰，对量子系统的性能的影响非常严重，是阻碍量子系统实用化的最大障碍。因此，对量子噪声过程进行分析，了解噪声的性质，对于量子系统的发展至关重要。本申请提供的技术方案，基于量子噪声过程的张量转移映射对量子噪声过程进行分析，可以包括以下分析内容：如图1所示，例如马尔科夫过程判定，即能够对量子噪声过程是马尔科夫过程还是非马尔科夫过程做出判定，针对非马尔科夫噪声可以设计独特的噪声抑制方案，比如通过动力学解耦来抑制噪声的发生；态演化预测，即能够对量子噪声过程的态演化进行预测；关联函数和频谱提取，即能够获得量子噪声过程的关联函数和频谱，从而帮助制造量子器件时集成相应频段的滤波器；关联噪声分析，即能够对量子系统中的不同量子器件之间的关联噪声做出分析，了解关联噪声的来源，从而设计相应的方案对关联噪声进行抑制。因此，本申请提供的技术方案，能够得到有关量子噪声过程的更为丰富、全面的信息，从而为量子系统的性能提升提供更多的信息支持。
请参考图2，其示出了本申请一个实施例提供的量子噪声过程分析方法的流程图。该方法可应用于计算机设备中，所述计算机设备可以是任何具备数据处理和存储能力的电子设备，如PC(personal computer，个人计算机)、服务器、计算主机等电子设备。该方法可以包括如下几个步骤(步骤201～步骤203)：
步骤201，对目标量子系统的量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射。
有关对量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射的介绍说明，在上文已经介绍说明，此处不再赘述。
可选地，本实施例可以对量子噪声过程中离散的时间点进行量子过程层析，例如在K个不同的时间点进行量子过程层析，则可以得到量子噪声过程在K个时间点的动力学映射，K为大于等于1的整数。可选地，上述K个时间点中，相邻两个时间点之间的间隔时长相等，当然，相邻两个时间点之间的间隔时长也可以不相等，本实施例对此不做限定。
步骤202，根据动力学映射提取量子噪声过程的张量转移映射。
在本申请实施例中，量子噪声过程的张量转移映射用于表征该量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。
可选地，若步骤201中得到量子噪声过程在K个时间点的动力学映射，则步骤201的一种可能的实现方式可以是根据量子噪声过程在K个时间点的动力学映射，计算量子噪声过程在K个时间点的张量转移映射。在示例性实施例中，通过递归方式提取K个时间点的张量转移映射。例如，按照下述公式计算量子噪声过程在第n个时间点的张量转移映射T n：
Figure PCTCN2020084897-appb-000011
其中，T 1＝ε 1，ε n表示量子噪声过程在第n个时间点的动力学映射，ε m表示所述量子噪声过程在第m个时间点的动力学映射，T n-m表示所述量子噪声过程在第n-m个时间点的张量转移映射，n、m均为正整数。
步骤203，根据张量转移映射对量子噪声过程进行分析。
在提取到量子噪声过程在K个时间点的张量转移映射之后，可以据此对量子噪声过程进行分析。
在示例性实施例中，确定出T n之后，根据定义，如果对n＞1，|T n|的值小到可以忽略，可以认为量子噪声过程是马尔科夫过程。反之，则可以认为该量子噪声过程是非马尔科夫过程。也即，若量子噪声过程在第一时间点的张量转移映射的模均小于预设阈值，则确定量子噪声过程为马尔科夫过程，第一时间点为K个时间点中除第一个时间点之外的其它时间点；若量子噪声过程在第二时间点的张量转移映射的模大于预设阈值，则确定量子噪声过程为非马尔科夫过程，第二时间点为K个时间点中除第一个时间点之外的至少一个时间点。
通过上述方式，基于量子噪声过程的张量转移映射，能够对量子噪声过程是马尔科夫过程还是非马尔科夫过程做出判定，针对非马尔科夫噪声可以设计独特的噪声抑制方案，比如通过动力学解耦来抑制噪声的发生。
另外，相比于动力学映射，通用的描述量子系统在开放环境下演化的方程是非时间定域量子主方程，能更好地揭示量子噪声过程的数学结构。这个方程是一个微分积分方程：
Figure PCTCN2020084897-appb-000012
其中，ρ(t)代表量子系统在时间t的量子态，用d×d的复数矩阵来表示。L s是刘维尔算子，代表量子系统演化过程中相干的部分。s为积分参量。κ(t)是记忆核，包含了所有由环境引发的系统退相干的信息。如果获得一个量子噪声过程的L s和κ(t)，那么就可 以完全了解该噪声机制。本申请技术方案的基本思路即是通过实验和量子过程层析来计算张量转移映射，从而提取L s和κ(t)的相关信息。
另一方面，量子系统和环境的联合演化由联合哈密顿量来决定。联合哈密顿量可以表示为：
Figure PCTCN2020084897-appb-000013
其中，H s是量子系统的哈密顿量，H sb是量子系统和环境耦合的相互作用哈密顿量，
Figure PCTCN2020084897-appb-000014
是作用在系统第i个量子比特(qubit)上的第α类泡利算子(Pauli Operator)，这里i,α都是正整数指标，
Figure PCTCN2020084897-appb-000015
是与第i个量子比特耦合的第α类环境算子(bath operator)。这里α＝x,y,z代表时空的三个方向。g i是系统和环境的耦合强度(coupling strength between system and bath)。
量子系统的态函数演化遵循：
Figure PCTCN2020084897-appb-000016
其中，ρ(t)代表量子系统在时间t的量子态，ρ(0)代表量子系统初始的量子态，ρ B是环境的量子态，Tr B代表对环境的自由度求偏迹运算，exp +,exp -分别是顺时逆、时编时指数算子，ε(t)代表量子系统在时间t的动力学演化，i是单位纯虚数，s为积分参量。
如果将时间离散化t k+1-t k＝δt(k为正整数)，可以定义一组随时间演化的动力学映射{ε k≡ε(t k)}。实验上，这些动力学映射可以通过在不同的时间点进行量子过程层析获得。
结合上述关于张量转移映射的公式定义，通过将ε n用T n表示出来，代入到上述态函数的公式，可以得到：
Figure PCTCN2020084897-appb-000017
其中，ρ(t n)表示第n个时间点t n的量子态，ρ(t n-m)表示第n -m个时间点t n-m的量子态，T m表示第m个时间点的张量转移映射。这个公式清楚地表示了在有噪声的情况下，量子系统的态演化取决于量子系统本身的历史演化。一般来说，动力学演化对历史的依赖不会超过一定的时间跨度。这意味着可以通过对上式的卷积进行截断，保留K(K为正整 数)个时间点来很精确地预估噪声对态的影响——也即丢弃所有t＞t K的项。这样，可以通过一小段时间动力学映射的量子过程层析来获得这段时间的张量转移映射。之后，可以利用这一小段时间的张量转移映射来预言长时间的开放系统演化。其中，在第n个时间点t n的量子态ρ(t n)可通过上述公式计算得到。并且，预测出的量子态可以与实验直接比较来验证通过张量转移映射描述开放系统动力学的有效性。也就是说这提供了本申请技术方案有效性的一个初步判据。
综上所述，在本申请提供的技术方案中，通过对量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射，从量子噪声过程的动力学映射中，进一步提取量子噪声过程的张量转移映射。张量转移映射用于表征量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。其相比于单纯的量子过程层析，能够得到有关量子噪声过程的更为丰富、全面的信息，因此，基于量子噪声过程的张量转移映射对量子噪声过程进行分析时，基于更为丰富、全面的信息可以实现对量子噪声过程进行更为准确全面地分析。
另外，在本申请提供的技术方案中，还实现了根据量子噪声过程的张量转移映射，对量子噪声过程是马尔科夫过程还是非马尔科夫过程做出判定；还实现了根据量子噪声过程在一段时间内的张量转移映射，预测该量子噪声过程在后续时间内的态演化。
在示例性实施例中，在提取得到量子噪声过程的张量转移映射之后，还可据此获得量子噪声过程的关联函数和频谱。该过程可以包括如下几个步骤：
1、若量子噪声过程为稳态噪声，则根据量子噪声过程的张量转移映射，提取量子噪声过程的二阶记忆核；
对于稳态噪声(如高斯稳态噪声)来说，噪声过程的关联函数决定了噪声的性质。而噪声过程的关联函数可以根据该噪声过程的二阶记忆核计算得到。
在本申请实施例中，对于量子噪声过程，如果该量子噪声过程为稳态噪声，则根据该量子噪声过程的张量转移映射，提取该量子噪声过程的二阶记忆核。
考虑到时间已经被离散化，近似到时间步长δt的二阶，可以得到张量转移映射的近似：
T n＝(1+L sδt)δ n,1+κ(t n)δt 2；
其中，δt是时间间隔(time step)，δ n,1是克罗内克函数(Kronecker function)，当n＝1时值为1，其余情况下值为0，n为正整数。κ(t n)是在时间t n时记忆核的值。
同时，从开放系统理论中，动力学记忆核κ的精确表达式是：
Figure PCTCN2020084897-appb-000018
这里，
Figure PCTCN2020084897-appb-000019
是一个映射算子，
Figure PCTCN2020084897-appb-000020
L是作用在系统和环境上的联合刘维尔算子，ρ SB是系统和环境的联合态(joint state of system and bath)，Q＝I-P是P与单位算符I(identity operator)的差。
由于在一般的量子系统中，噪声会在工程上被初步控制，所以量子系统和环境的耦合强度相对会比较弱。在目标量子系统和环境为弱耦合关系时，二阶微扰近似可以成立，因此可以得到：
Figure PCTCN2020084897-appb-000021
κ 2(t)是二阶记忆核在t时间的值，
Figure PCTCN2020084897-appb-000022
为C αα′(t)的复数共轭。注意上述表达式是在薛定谔表象下，并同时假设联合系统的哈密顿量是不随时间改变的。其中，二阶关联函数C αα′(t)定义为：
Figure PCTCN2020084897-appb-000023
是一组环境关联函数。基于二阶微扰，可以在实验中提取动力学映射，并通过量子过程层析得到张量转移映射，从而近似出记忆核κ exp。也即，κ exp是通过实验获得的近似的二阶记忆核。
在目标量子系统和环境为强耦合关系时，二阶微扰不再是一个较好的近似，需要更多的高阶项才能得到更好的近似，但是仍然可以通过从实验数据中提取张量转移映射来提取二阶记忆核。具体步骤如下：选择N个不同参数，对量子噪声过程进行实验，从实验中提取N个不同参数分别对应的记忆核；根据该N个不同参数分别对应的记忆核，计算得到量子噪声过程的二阶记忆核。
先定义N阶截断近似记忆核：
Figure PCTCN2020084897-appb-000024
并假设系统的记忆核可以被它近似。然后假设有一个可调参数的系统，每次实验可以调节系统参数ω s,i，其哈密顿量为：
H s＝ω s,iσ z；
其中i表示选择第i个参数所进行的实验，σ z是泡利z算子
Figure PCTCN2020084897-appb-000025
对选定的参数ω s,i(ω s,i属于实验可以达到的一个区间)，对哈密顿量做归一化处理，可以得到：
Figure PCTCN2020084897-appb-000026
其中，
Figure PCTCN2020084897-appb-000027
是归一化哈密顿量，g∝1/ω s,i。通过对N个不同ω s,i进行实验，可以构建一组无物理单位的记忆核，其关系是：
Figure PCTCN2020084897-appb-000028
其中γ i＝ω s,0/ω s,i为归一化参数，
Figure PCTCN2020084897-appb-000029
表示在ω s,i情况下的2n阶记忆核。这样就可以定义以下矩阵；
Figure PCTCN2020084897-appb-000030
并有以下方程：
Figure PCTCN2020084897-appb-000031
其中，A是N阶的归一化参数矩阵，方程右边的记忆核可以通过量子过程层析和数据处理从实验中直接提取。因为A是满秩矩阵，所以通过解线性方程得到2至N阶的无物理单位记忆核，自然也就得到了二阶记忆核。
2、根据量子噪声过程的二阶记忆核，计算量子噪声过程的关联函数；
可选地，按照下述公式在数值上提取量子噪声过程的关联函数C αα′：
Figure PCTCN2020084897-appb-000032
其中，κ 2表示量子噪声过程的二阶记忆核，t n表示第n个时间点，C αα′(t n)是在上述第n个时间点t n的二阶关联函数，κ exp表示实验获取的近似的二阶记忆核，
Figure PCTCN2020084897-appb-000033
是克罗内克函数(当n＝0，其值为1，其余情况下其值为0)，λ n为可调参数，C aa‘(t n-1)是在第n-1个时间点t n-1的二阶关联函数。需要说明的是，λ n用于保证对目标函数取最小后，关联函 数仍然可以是连续的。λ n的选择可以通过先选定一个初始值，观察目标函数的大小，然后迭代进行调整，它的值选取具有一定的鲁棒性。
可选地，对于非高斯型的稳态噪声来说，需要高于2阶的关联函数才能充分表征噪声的统计性质。上文介绍了基于解此线性方程
Figure PCTCN2020084897-appb-000034
以取得噪声的二阶关联函数。处理非高斯型的稳态噪声，可以假设噪声的记忆核写成：
Figure PCTCN2020084897-appb-000035
基于这个更广义的记忆核，可以根据上文介绍的方案得到：
Figure PCTCN2020084897-appb-000036
解此线性方程，可以得到二阶和更高阶的关联函数。
3、对量子噪声过程的关联函数做傅里叶变换，得到量子噪声过程的频谱。
一旦得到了量子噪声过程的关联函数，就可以通过对该关联函数做傅里叶变换，得到该量子噪声过程的频谱J αα′(ω)：
Figure PCTCN2020084897-appb-000037
这种得到量子噪声过程的频谱的方法不受限于量子噪声(系统对噪声源有反馈)还是经典噪声，不受限于某个特定的噪声种类。
综上所述，在本申请提供的技术方案中，在提取得到量子噪声过程的张量转移映射之后，还可据此获得量子噪声过程的关联函数和频谱，从而帮助制造量子器件时集成相应频段的滤波器。
在示例性实施例中，在提取得到量子噪声过程的张量转移映射之后，还可据此对目标量子系统中的不同量子器件之间的关联噪声做出分析，了解关联噪声的来源。该过程可以包括如下几个步骤：
1、对于目标量子系统中包含的s个量子器件，根据该s个量子器件各自对应的张量转移映射，计算该s个量子器件之间的关联张量转移映射，s为大于1的整数；
2、根据关联张量转移映射，分析该s个量子器件之间的关联噪声的来源。
一个量子系统可以包含多个量子器件，量子比特是一种最简单的量子器件，只包含两个量子态。使用张量转移映射，能够完成同一量子系统中的多个量子器件之间噪声的关联。下文主要以两个量子器件的情况进行介绍说明，其它情况可做类似推广，如按照本申请实 施例提供的方法判定任意两个量子器件之间噪声的关联，任意三个或更多数量的量子器件之间噪声的关联。
任意两个量子系统(或量子器件)的动力学映射可以做如下分解：
Figure PCTCN2020084897-appb-000038
其中，ε n,1表示第一量子器件的动力学映射，ε n,2表示第二量子器件的动力学映射，δε n是不可分离部分(unseparated part)，代表关联噪声(correlated noise)的影响。以上的动力学映射分解，可以使用Choi矩阵的形式来表达动力学映射ε n→χ n，即χ n是Choi矩阵(Choi matrix)，是动力学映射的一种等价表示，并取Choi矩阵的迹：
Figure PCTCN2020084897-appb-000039
或者
Figure PCTCN2020084897-appb-000040
然后，再把单个量子器件的Choi矩阵χ n,i表达回动力学映射ε n,i。两个量子器件的动力学映射ε n都可以通过对这两个量子器件做联合的量子过程层析来获得。δε n可以被用来分析关联噪声。在二阶微扰的情况下，通常δε n的模会比
Figure PCTCN2020084897-appb-000041
要小很多。在非微扰的区域内，δε n和
Figure PCTCN2020084897-appb-000042
的模值则可能相当，甚至|δε n|比
Figure PCTCN2020084897-appb-000043
要大很多。所以，单纯的量子过程层析能够对关联噪声的强弱做一个初步的判定。但是，很难对关联噪声的来源做出分析，因为所有数据都混杂在一起。通常来说，两个量子器件之间的关联噪声的来源包括：(1)两个量子器件之间直接的耦合所产生的关联噪声；(2)两个量子器件通过共享环境所诱导的关联噪声；(3)以上两者皆有。
本申请实施例提供了一种基于张量转移映射的关联噪声分析方法，这种方法可以得到关于关联噪声的更多信息。首先，通过
Figure PCTCN2020084897-appb-000044
来计算可分离张量转移映射
Figure PCTCN2020084897-appb-000045
Figure PCTCN2020084897-appb-000046
Figure PCTCN2020084897-appb-000047
其中，
Figure PCTCN2020084897-appb-000048
δT n是张量转移映射的噪声关联部分(noise correlation in transfer tensor map)。同样地，可以将δT n拆解成：
δT n＝δLδtδ n,1+δκ nδt 2；
其中刘维尔超算子δL揭示是否有两个量子器件之间直接的耦合所产生的关联噪声，而δκ n代表由共享环境所诱导的关联噪声。可以发现，由δL引起的耦合增量和δt是线性关系，而由δκ n引起的耦合增量和δt 2是线性关系。可以通过选择两个不同的时间步长δt和δt′，这样就会产生两个不同的动力学映射ε 1和ε 1′，进而来判断关联噪声的来源。鉴于关联噪声对容错量子计算的影响重大，本申请技术方案可以更好地了解关联噪声并对如何进行控制做出指导，针对δL和δκ n设计不同的噪声抑制方案。
例如，通过量子过程层析，可以得到目标量子系统中的两个量子器件的联合动力学映射ε n，并进一步得到张量转移映射T n，然后通过ε n对两个量子器件分别求迹，可以得到ε n,1和ε n,2，以及
Figure PCTCN2020084897-appb-000049
然后通过
Figure PCTCN2020084897-appb-000050
得到
Figure PCTCN2020084897-appb-000051
最后，
Figure PCTCN2020084897-appb-000052
然后考虑两组不同的时间步长δt和δt′：
Figure PCTCN2020084897-appb-000053
进而分别求出δL和δκ n。
综上所述，在本申请提供的技术方案中，在提取得到量子噪声过程的张量转移映射之后，还可据此对目标量子系统中的不同量子器件之间的关联噪声做出分析，了解关联噪声的来源，从而设计相应的方案对关联噪声进行抑制。
为了进一步证实本申请技术方案的有效性，针对典型的模型进行数值分析。在这之后，在IBM的Quantum Experience(Quantum Experience是IBM提供的一种量子计算云平台)上尝试使用本申请技术方案对真实超导量子比特进行实验观测并从中提取有关噪声过程的信息。
针对典型的模型进行数值分析的结果如下：
案例一，单个量子比特在纯相位退相干下的数值模拟
取H s＝0.1σ z,H sb＝B z(t)σ z,C zz(0)＝λ＝4,δt＝0.2，单量子比特自由演化的张量转移映射结果如图3所示。图3中(a)部分示出了张量转移映射的Frobenious模随着时间的变化，由图中可以看出，t 1→t 6范围内的张量转移映射有非平庸的贡献，也即噪声过程呈现出非马尔科夫性质。图3中(b)部分的线条31表示初始态
Figure PCTCN2020084897-appb-000054
对应的密度矩阵非对角元实部随着时间的演化。线条32、线条33和线条34分别展示了不同张量转移映射长度(即K分别取1、3、5时)对密度矩阵的预测效果。可以看出，当K取5时，通过张量转移映射得到的演化与精确解较好地重合，可以完美的预测长时间实验演化。
另外，图4示出了布洛赫体积随时间的变化情况，布洛赫体积V(t)在某一时段(t 4,t 5,t 6)的增长，清楚地展示了该动力学过程的非马尔科夫特性，从侧面印证了图3的结论。
案例二，单个量子比特在纯相位退相干下的噪声关联函数提取
取H s＝0.02σ z,C zz(0)＝<B z(t)B z(0)>＝0.01,δt＝0.04，单量子比特自由演化的张量转移映射方法获得量子噪声过程的频谱(相当于环境噪声谱)。图5中(a)部分示出了在量子系统和环境弱耦合的情况下，噪声关联函数C zz(t)随着时间的变化。线条51展示了噪声关联函数的准确理论结果，各个圆圈展示了在K(t)≈K 2(t)的假设下从记忆核得到的数值结果。可见在弱耦合情况下，张量转移映射所得二阶近似下的记忆核可以很好地刻画量子噪声过程。
在图5(b)部分中，取H s＝0.02σ z,C zz(0)∈(0,2.56),δt＝0.04。量子系统和环境强耦合的情况。特殊时间点C ZZ(t＝15δt)的噪声关联函数随着噪声系统耦合强度C ZZ(0)＝λ变化的结果。线条42是准确的理论结果。线条53展示的第一种数值结果：即直接假设K(t)≈K 2(t),可见在强耦合的情况下与真实噪声谱有很大差距。线条54展示的第二种数值结果：即直接假K(t)≈K 2(t)+K 4(t)，即使在所研究的强耦合的情况下，张量转移映射所得的记忆核考虑到更高阶也可以很好的反应真实噪声谱。
案例三，单个量子比特在比特翻转噪声下关联函数的提取
取H s＝0.02δ z,C xx(0)＝0.01,δt＝0.04，单量子比特自由演化的张量转移映射方法获得量子噪声过程的频谱(相当于环境噪声谱)。注意在这种情况，噪声不再是纯相位退相干噪声。如图6所示，圆圈展示的从张量转移映射记忆核得到的关联函数 C xx(t)＝<B x(t)B x(0)>与线条61展示的真实噪声谱非常吻合。这组模拟显示了，当环境噪声产生的影响超出纯退相位,例如B x(t),B y(t)时，张量转移映射记忆核推及噪声谱的方法仍然适用。
案例四，双量子比特下两种纯退相位模型下两个量子比特自由演化的张量转移映射结果
图7中(a)部分示出了两个在z方向相互耦合的量子比特处于各自独立的环境噪声中，这两个量子比特自由演化的张量转移映射结果。
系统哈密顿量为：
Figure PCTCN2020084897-appb-000055
环境哈密顿量为：
Figure PCTCN2020084897-appb-000056
关联函数为：
Figure PCTCN2020084897-appb-000057
线条71、线条72和线条73分别表示全张量转移映射T n，可分离张量转移映射
Figure PCTCN2020084897-appb-000058
和关联张量转移映射δT n。如图所示关联张量转移映射中只有第一项即δT 1是非平庸的。也即结果表明独立噪声环境下张量转移映射的关联部分几乎是马尔科夫性质的。进一步我们分析得到δL s产生两量子比特的纠缠会导致关联的退相干效应，即使噪声源空间分离或相互独立。
图7中(b)部分示出了两个没有直接耦合的量子比特处于有关联的环境噪声中，这两个量子比特自由演化的张量转移映射结果。
系统哈密顿量为：
Figure PCTCN2020084897-appb-000059
环境哈密顿量为：
Figure PCTCN2020084897-appb-000060
线条74、线条75和线条76分别表示全张量转移映射T n，可分离张量转移映射
Figure PCTCN2020084897-appb-000061
和关联张量转移映射δT n。这种情况下，多个δT n是非平庸的。经过分析可以发现δK(t 1)是δT 1的主要贡献因素。从而直接根据张量转移映射的规范随时间的分布就可以估计出导致集体退相干的不同物理机制的相对重要性。
案例五，双量子比特下张量转移映射的开放系统动力学预言有效性。
为了考察δT n的重要性，图8展示了两量子比特密度矩阵的非对角矩阵元的动力学演化。将长度为(即K分别取1，8，16时)的张量转移映射对于物理态的预测结果与真实动力学模拟结果进行对比。图8的(a)、(b)两部分分别展示了第一种模型下基于全张 量转移映射和可分离张量转移映射对
Figure PCTCN2020084897-appb-000062
的预测结果。图8的(c)、(d)两部分分别展示了第二种模型下基于全张量转移映射和可分离张量转移映射对
Figure PCTCN2020084897-appb-000063
的预测结果。对于两种情况，集体退相关的效果都不能由
Figure PCTCN2020084897-appb-000064
单独描述。从图7看来，δT n总体很小，不造成影响。但这里表明δT n对物态的预测还是扮演重要的角色。这更加验证了高度非马尔科夫系统的复杂特性。
另外，为了验证本申请技术方案的实用性，在IBM的Quantum Experience上进行测试。IBM Quantum Experience是IBM提供的超导量子计算云平台，所有计算运行在真实的超导量子计算机上。对超导量子比特来说，一方面由于操作量子门的时间相对于环境的关联时间过长(～100ns)，另一方面由于噪声过程并非纯粹的相位退相干，基于CPMG的动力学解耦提取频谱的方法并不适用。
图9示出了IBM量子计算云平台“ibmq 16 Melourne”上的单量子比特自由演化的张量转移映射研究。其中δt＝2.2μs。图9中(a)部分示出了张量转移映射的规范随着时间的分布。图9中(b)部分示出了态|1>的动力学演化，线条91是实验结果。线条92、线条93和线条94是分别取(1、3、5)个张量转移映射对于|1>演化的预测结果。可以看出记忆核的时间尺度是μs量级的，与100ns的量子门时间相比并不短。
图10示出了单量子比特布洛赫体积V(t)随着时间的分布。短暂的增长展示了量子体系的非马尔科夫特性。
图11示出了IBM量子计算云平台“ibmq 16 Melourne”上的单量子比特动态解耦(DD)演化，其中δt＝2.64μs。在XY4DD协议下四个初始态(a)|ψ(0)>＝|0>(b)|ψ(0)>＝|1>(c)
Figure PCTCN2020084897-appb-000065
的三个自旋方向的测量结果。可以观察到量子相干性的延长。
图12示出了IBM量子计算云平台“ibmq 16 Melourne”上的单量子比特动态解耦(DD)演化，其中δt＝2.64μs。在XY4DD协议下，张量转移映射的规范随时间的分布。其中量子相干性的延长内在机制可以由此张量转移映射反应出来：XY4DD协议下的有效噪声与自由演化的结果相比更具有马尔科夫特性。
图13示出了IBM量子计算云平台“ibmq 16 Melourne”上的两个量子比特自由演化的张量转移映射研究。其中δt＝2.2μs。完全张量转移映射|T n|，可分离张量转移映射
Figure PCTCN2020084897-appb-000066
关联张量转移映射|δT n|的规范随时间的分布。可以看出在这一组实验中，张量转移映射在较长的时间尺度下都是非平庸的，有较强的非马尔科夫特性。结合数值模拟的结果，可以初 步认为IBM量子云平台上近邻两比特有比特间的耦合，也有环境噪声的关联。
图14示出了IBM量子计算云平台“ibmq 16 Melourne”上的两个量子比特自由演化的张量转移映射研究。其中δt＝2.2μs。黑色圆点所代表的黑色线条是密度矩阵演化的实验结果，圆圈、三角形和方形所代表的三条线条分别是选取(1，2，4)个张量转移映射的预测密度矩阵演化的效果。图14中(a)、(b)分别展示了初始态为非纠缠态
Figure PCTCN2020084897-appb-000067
下基于完全张量转移映射和可分离张量转移映射对的预测结果。图14中(c)、(d)分别展示了初始态为纠缠态
Figure PCTCN2020084897-appb-000068
下基于完全张量转移映射和可分离张量转移映射对的预测结果。可见不包含关联张量转移映射无论是纠缠态或者非纠缠态都无法准确的预测其演化。进一步分析δT 1，可以看出δL s有重要贡献，说明两个量子比特之间本身存在耦合。
下述为本申请装置实施例，可以用于执行本申请方法实施例。对于本申请装置实施例中未披露的细节，请参照本申请方法实施例。
请参考图15，其示出了本申请一个实施例提供的量子噪声过程分析装置的框图。该装置具有实现上述方法示例的功能，所述功能可以由硬件实现，也可以由硬件执行相应的软件实现。该装置可以是计算机设备，也可以设置在计算机设备中。该装置1500可以包括：获取模块1510、提取模块1520和分析模块1530。
获取模块1510，用于对目标量子系统的量子噪声过程进行量子过程层析，得到所述量子噪声过程的动力学映射。
提取模块1520，用于根据所述动力学映射提取所述量子噪声过程的张量转移映射，所述张量转移映射用于表征所述量子噪声过程的动力学演化。
分析模块1530，用于根据所述张量转移映射对所述量子噪声过程进行分析。
综上所述，在本申请提供的技术方案中，通过对量子噪声过程进行量子过程层析，得到量子噪声过程的动力学映射，从量子噪声过程的动力学映射中，进一步提取量子噪声过程的张量转移映射。张量转移映射用于表征量子噪声过程的动力学演化，也即体现了量子噪声过程的动力学映射随时间的演化规律。其相比于单纯的量子过程层析，能够得到有关量子噪声过程的更为丰富、全面的信息，因此，基于量子噪声过程的张量转移映射对量子噪声过程进行分析时，基于更为丰富、全面的信息可以实现对量子噪声过程进行更为准确全面地分析。
在一些可能的设计中，所述动力学映射包括：所述量子噪声过程在K个时间点的动力学映射，所述K为正整数；
所述提取模块1520，用于根据所述量子噪声过程在所述K个时间点的动力学映射，计算所述量子噪声过程在所述K个时间点的张量转移映射。
在一些可能的设计中，所述提取模块1520，用于按照下述公式计算所述量子噪声过程在第n个时间点的张量转移映射T n：
Figure PCTCN2020084897-appb-000069
其中，T 1＝ε 1，ε n表示所述量子噪声过程在所述第n个时间点的动力学映射，ε m表示所述量子噪声过程在第m个时间点的动力学映射，T n-m表示所述量子噪声过程在第n-m个时间点的张量转移映射，n、m均为正整数。
在一些可能的设计中，如图16所示，所述分析模块1530，包括：马尔科夫判别子模块1531。
所述马尔科夫判别子模块1531，用于：
若所述量子噪声过程在第一时间点的张量转移映射的模均小于预设阈值，则确定所述量子噪声过程为马尔科夫过程；所述第一时间点为所述K个时间点中除第一个时间点之外的其它时间点；
若所述量子噪声过程在第二时间点的张量转移映射的模大于所述预设阈值，则确定所述量子噪声过程为非马尔科夫过程；所述第二时间点为所述K个时间点中除第一个时间点之外的至少一个时间点。
在一些可能的设计中，如图16所示，所述分析模块1530，包括：态演化预测子模块1532。
所述态演化预测子模块1532，用于根据所述K个时间点的张量转移映射，预测所述量子噪声过程在后续时间内的态演化。
在一些可能的设计中，所述态演化预测子模块1532，用于：按照下述公式计算所述量子噪声过程在第n个时间点t n的量 子态ρ(t n)：
Figure PCTCN2020084897-appb-000070
其中，T m表示第m个时间点的张量转移映射，ρ(t n-m)表示第n-m个时间点t n-m的量子态，n、m均为正整数。
在一些可能的设计中，如图16所示，所述分析模块1530，包括：
记忆核提取子模块1533，用于若所述量子噪声过程为稳态噪声，则根据所述张量转移映射，提取所述量子噪声过程的二阶记忆核；
关联函数计算子模块1534，用于根据所述量子噪声过程的二阶记忆核，计算所述量子噪声过程的关联函数；
频谱获取子模块1535，用于对所述量子噪声过程的关联函数做傅里叶变换，得到所述量子噪声过程的频谱。
在一些可能的设计中，所述记忆核提取子模块1533，用于：选择N个不同参数，对所述量子噪声过程进行实验，从实验中提取所述N个不同参数分别对应的记忆核；根据所述N个不同参数分别对应的记忆核，计算得到所述量子噪声过程的二阶记忆核。
在一些可能的设计中，所述关联函数计算子模块1534，用于按照下述公式在数值上提取所述量子噪声过程的关联函数C αα′：
Figure PCTCN2020084897-appb-000071
其中，κ 2表示所述量子噪声过程的二阶记忆核，t n表示第n个时间点，κ exp表示实验获取的近似的二阶记忆核，
Figure PCTCN2020084897-appb-000072
表示所述第n个时间点与初始时刻之间的间隔时长，λ n为可调参数，C aa‘(t n-1)是在第n-1个时间点t n-1的二阶关联函数。
在一些可能的设计中，如图16所示，所述分析模块1530，包括：关联噪声分析子模块1536。
所述关联噪声分析子模块1536，用于：对于所述目标量子系统中包含的s个量子器件，根据所述s个量子器件各自对应的张量转移映射，计算所述s个量子器件之间的关联张量转移映射，所述s为大于1的整数；根据所述关联张量转移映射，分析所述s个量子器件之间的关联噪声的来源。
需要说明的是，上述实施例提供的装置，在实现其功能时，仅以上述各功能模块的划分进行举例说明，实际应用中，可以根据需要而将上述功能分配由不同的功能模块完成，即将设备的内部结构划分成不同的功能模块，以完成以上描述的全部或者部分功能。另外，上述实施例提供的装置与方法实施例属于同一构思，其具体实现过程详见方法实施例，这里不再赘述。
请参考图17，其示出了本申请一个实施例提供的计算机设备的结构示意图。该计算机设备用于实施上述实施例中提供的量子噪声过程分析方法。具体来讲：
所述计算机设备1700包括中央处理单元(CPU)1701、包括随机存取存储器(RAM)1702和只读存储器(ROM)1703的系统存储器1704，以及连接系统存储器1704和中央处理单元1701的系统总线1705。所述计算机设备1700还包括帮助计算机内的各个器件之间传输信息的基本输入/输出系统(I/O系统)1706，和用于存储操作系统1713、应用程序1714和其他程序模块1715的大容量存储设备1707。
所述基本输入/输出系统1706包括有用于显示信息的显示器1708和用于用户输入信息的诸如鼠标、键盘之类的输入设备1709。其中所述显示器1708和输入设备1709都通过连接到系统总线1705的输入输出控制器1710连接到中央处理单元1701。所述基本输入/输出系统1706还可以包括输入输出控制器1710以用于接收和处理来自键盘、鼠标、或电子触控笔等多个其他设备的输入。类似地，输入输出控制器1710还提供输出到显示屏、打印机或其他类型的输出设备。
所述大容量存储设备1707通过连接到系统总线1705的大容量存储控制器(未示出)连接到中央处理单元1701。所述大容量存储设备1707及其相关联的计算机可读介质为计算机设备1700提供非易失性存储。也就是说，所述大容量存储设备1707可以包括诸如硬盘或者CD-ROM驱动器之类的计算机可读介质(未示出)。
不失一般性，所述计算机可读介质可以包括计算机存储介质和通信介质。计算机存储介质包括以用于存储诸如计算机可读指令、数据结构、程序模块或其他数据等信息的任何方法或技术实现的易失性和非易失性、可移动和不可移动介质。计算机存储介质包括RAM、ROM、EPROM、EEPROM、闪存或其他固态存储其技术，CD-ROM、DVD或其他光学存储、磁带盒、磁带、磁盘存储或其他磁性存储设备。当然，本领域技术人员可知所述计算机存储介质不局限于上述几种。上述的系统存储器1704和大容量存储设备1707可以统称为存储器。
根据本申请的各种实施例，所述计算机设备1700还可以通过诸如因特网等网络连接到网络上的远程计算机运行。也即计算机设备1700可以通过连接在所述系统总线1705上的网络接口单元1711连接到网络1712，或者说，也可以使用网络接口单元1711来连接到其他类型的网络或远程计算机系统(未示出)。
所述存储器中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、至少一段程序、代码集或指令集经配置以由一个或者一个以上处理器执行，以实现上述实施例提供的量子噪声过程分析方法。
在示例性实施例中，还提供了一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或所述指令集在被计算机设备的处理器执行时实现上述实施例提供的量子噪声过程分析方法。在示例性实施例中，上述计算机可读存储介质可以是ROM、RAM、CD-ROM、磁带、软盘和光数据存储设备等。
在示例性实施例中，还提供了一种计算机程序产品，当该计算机程序产品被执行时，其用于实现上述实施例提供的量子噪声过程分析方法。
应当理解的是，在本文中提及的“多个”是指两个或两个以上。“和/或”，描述关联对象的关联关系，表示可以存在三种关系，例如，A和/或B，可以表示：单独存在A，同时存在A和B，单独存在B这三种情况。字符“/”一般表示前后关联对象是一种“或”的关系。另外，本文中描述的步骤编号，仅示例性示出了步骤间的一种可能的执行先后顺序，在一些其它实施例中，上述步骤也可以不按照编号顺序来执行，如两个不同编号的步骤同时执行，或者两个不同编号的步骤按照与图示相反的顺序执行，本申请实施例对此不作限定。
以上所述仅为本申请的示例性实施例，并不用以限制本申请，凡在本申请的精神和原则之内，所作的任何修改、等同替换、改进等，均应包含在本申请的保护范围之内。

Claims (14)

  1. 一种量子噪声过程分析方法，所述方法应用于计算机设备，所述方法包括：
    对目标量子系统的量子噪声过程进行量子过程层析，得到所述量子噪声过程的动力学映射；
    根据所述动力学映射提取所述量子噪声过程的张量转移映射，所述张量转移映射用于表征所述量子噪声过程的动力学演化；
    根据所述张量转移映射对所述量子噪声过程进行分析。
  2. 根据权利要求1所述的方法，所述动力学映射包括：所述量子噪声过程在K个时间点的动力学映射，所述K为正整数；
    所述根据所述动力学映射提取所述量子噪声过程的张量转移映射，包括：
    根据所述量子噪声过程在所述K个时间点的动力学映射，计算所述量子噪声过程在所述K个时间点的张量转移映射。
  3. 根据权利要求2所述的方法，所述根据所述量子噪声过程在所述K个时间点的动力学映射，计算所述量子噪声过程在所述K个时间点的张量转移映射，包括：
    按照下述公式计算所述量子噪声过程在第n个时间点的张量转移映射T n：
    Figure PCTCN2020084897-appb-100001
    其中，T 1＝ε 1，ε n表示所述量子噪声过程在所述第n个时间点的动力学映射，ε m表示所述量子噪声过程在第m个时间点的动力学映射，T n-m表示所述量子噪声过程在第n-m个时间点的张量转移映射，n、m均为正整数。
  4. 根据权利要求2所述的方法，所述根据所述张量转移映射对所述量子噪声过程进行分析，包括：
    若所述量子噪声过程在第一时间点的张量转移映射的模均小于预设阈值，则确定所述量子噪声过程为马尔科夫过程；所述第一时间点为所述K个时间点中除第一个时间点之外的其它时间点；
    若所述量子噪声过程在第二时间点的张量转移映射的模大于所述预设阈值，则确定所述量子噪声过程为非马尔科夫过程；所述第二时间点为所述K个时间点中除第一个时间点之外的至少一个时间点。
  5. 根据权利要求2所述的方法，所述根据所述张量转移映射对所述量子噪声过程进行分析，包括：
    根据所述K个时间点的张量转移映射，预测所述量子噪声过程在后续时间内的态演化。
  6. 根据权利要求5所述的方法，所述根据所述K个时间点的张量转移映射，预测所述量子噪声过程在后续时间内的态演化，包括：
    按照下述公式计算所述量子噪声过程在第n个时间点t n的量子态ρ(t n)：
    Figure PCTCN2020084897-appb-100002
    其中，T m表示第m个时间点的张量转移映射，ρ(t n-m)表示第n-m个时间点t n-m的量子态，n、m均为正整数。
  7. 根据权利要求1至6任一项所述的方法，所述根据所述张量转移映射对所述量子噪声过程进行分析，包括：
    若所述量子噪声过程为稳态噪声，则根据所述张量转移映射，提取所述量子噪声过程的二阶记忆核；
    根据所述量子噪声过程的二阶记忆核，计算所述量子噪声过程的关联函数；
    对所述量子噪声过程的关联函数做傅里叶变换，得到所述量子噪声过程的频谱。
  8. 根据权利要求7所述的方法，所述根据所述K个时间点的张量转移映射，提取所述量子噪声过程的二阶记忆核，包括：
    选择N个不同参数，对所述量子噪声过程进行实验，从实验中提取所述N个不同参数分别对应的记忆核；
    根据所述N个不同参数分别对应的记忆核，计算得到所述量子噪声过程的二阶记忆核。
  9. 根据权利要求7所述的方法，所述根据所述量子噪声过程的二阶记忆核，计算所述量子噪声过程的关联函数，包括：
    按照下述公式在数值上提取所述量子噪声过程的关联函数C αα′：
    Figure PCTCN2020084897-appb-100003
    其中，κ 2表示所述量子噪声过程的二阶记忆核，t n表示第n个时间点，C αα′(t n)是在所述第n个时间点t n的二阶关联函数，κ exp表示实验获取的近似的二阶记忆核，
    Figure PCTCN2020084897-appb-100004
    是克罗内克函数，λ n为可调参数，C αα′(t n-1)是在第n-1个时间点t n-1的二阶关联函数。
  10. 根据权利要求1至6任一项所述的方法，所述根据所述张量转移映射对所述量子噪声过程进行分析，包括：
    对于所述目标量子系统中包含的s个量子器件，根据所述s个量子器件各自对应的张量转移映射，计算所述s个量子器件之间的关联张量转移映射，所述s为大于1的整数；
    根据所述关联张量转移映射，分析所述s个量子器件之间的关联噪声的来源。
  11. 一种量子噪声过程分析装置，所述装置包括：
    获取模块，用于对目标量子系统的量子噪声过程进行量子过程层析，得到所述量子噪声过程的动力学映射；
    提取模块，用于从所述动力学映射中提取所述量子噪声过程的张量转移映射，所述张量转移映射用于表征所述量子噪声过程的动力学演化；
    分析模块，用于根据所述张量转移映射对所述量子噪声过程进行分析。
  12. 一种计算机设备，所述计算机设备包括处理器和存储器，所述存储器中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由所述处理器加载并执行以实现如权利要求1至10任一项所述的方法。
  13. 一种计算机可读存储介质，所述存储介质中存储有至少一条指令、至少一段程序、代码集或指令集，所述至少一条指令、所述至少一段程序、所述代码集或指令集由处理器加载并执行以实现如权利要求1至10任一项所述的方法。
  14. 一种计算机程序产品，当所述计算机程序产品被执行时，用于执行如权利要求1至10任一项所述的方法。
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