WO2022160528A1 - 循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法 - Google Patents

循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法 Download PDF

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WO2022160528A1
WO2022160528A1 PCT/CN2021/095988 CN2021095988W WO2022160528A1 WO 2022160528 A1 WO2022160528 A1 WO 2022160528A1 CN 2021095988 W CN2021095988 W CN 2021095988W WO 2022160528 A1 WO2022160528 A1 WO 2022160528A1
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quantum
equation
master equation
neural network
simulating
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李晓瑜
朱钦圣
胡勇
杨庆
卢俊邑
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电子科技大学
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Definitions

  • the invention relates to a method for simulating the quantum condition master equation in the process of simulating quantum transport by a circulating neural network.
  • quantum transport As an important physical phenomenon in mesoscopic systems, quantum transport has been widely studied in recent years. For conventional devices, the signal-to-noise ratio can be improved by suppressing shot noise, but in systems composed of quantum dots, the shot noise cannot be reduced indefinitely. In fact, quantum transport noise in quantum devices is not necessarily harmful. These fine time-dependent shot noises can be sensitive to the fine dynamics of reaction transport processes, rich in quantum transport properties, and fine energy scales within them. Therefore, in the process of studying the transport characteristics of low-dimensional mesoscopic nanodevices, the test and analysis of the quantum shot noise system will become an important theoretical tool and method.
  • quantum conditional master equation can describe the transport process of electric charge in detail, it is very difficult to further study the physical quantities related to this process because it is an infinite recursive differential equation system. Therefore, it is extremely important to solve the quantum conditional master equation in the transport process.
  • the recurrent neural network that simulates the master equation of quantum conditions can be used to guide the design of micro-nano quantum devices.
  • the purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a simulation method of the quantum condition master equation in the process of simulating quantum transport by the cyclic neural network.
  • a first aspect of the present invention provides a method for simulating the master equation of quantum conditions in the process of simulating quantum transport by a recurrent neural network, comprising the following steps:
  • the long-short-term memory network includes T LSTM cells arranged in time sequence, each LSTM cell has an input value x t and an output value h t , and outputs The value h t will be passed into the LSTM cell at the next moment, and the LSTM cell has parameters (W, b);
  • the quantum transport process corresponds to an achievable physical actual system.
  • the quantum conditional master equation is derived from a two-level quantum charge bit transport system;
  • the two-level quantum charge bit transport system includes a quantum dot system S and a power supply V, and the left electrode L of the quantum dot system S and The positive pole of the power supply V is connected, and the right electrode R of the quantum dot system S is connected to the negative pole of the power supply V;
  • the total Hamiltonian of the two-level quantum charge bit transport system is:
  • H s represents the Hamiltonian of the quantum dot system S
  • HE represents the Hamiltonian of the left electrode L and the right electrode R
  • H′ represents the interaction between the quantum dot system S and the electrodes. Hamiltonian.
  • ⁇ (n) (t) represents the reduction of the system when n electrons pass through the quantum dot system S in time ⁇ t density matrix, represents the first derivative of ⁇ (n) (t) with respect to time.
  • H s H s , HE and H'
  • s represents the spin of the electron
  • ⁇ and ⁇ represent the spin-up and spin-down, respectively
  • j represents the energy level
  • ⁇ j represents the energy of the jth energy level
  • ⁇ represents the generation/annihilation operators of electrons at the jth energy level and spin s, respectively
  • ⁇ is the Coulomb interaction energy of two electrons occupying the same energy level but with different spins
  • n j ⁇ , n j ⁇ , n js represents the particle number operator when the electron occupies the jth energy level and the spin is ⁇ , ⁇ , s
  • C E is the charge energy related to the number of electrons occupying the energy level
  • ⁇ represents the electrode
  • k represents the electron ⁇ ⁇ ks represents the energy of the electron with momentum k on the electrode.
  • hc represents the generation operator of electrons with spin s and momentum k on the ⁇ electrode
  • c ⁇ ks represents the annihilation operator of electrons with spin s and momentum k on the ⁇ electrode
  • ⁇ ⁇ kj represents the interaction between the system and the environment Strength of action
  • hc denotes Hermitian conjugation.
  • ⁇ (n) is ⁇ (n) (t)
  • ⁇ (n) (t) represents the generation operator of an electron with spin s at the jth energy level
  • ⁇ represents the electron annihilation operator at the jth energy level with spin s
  • ⁇ represents the spectral function independent variable in ;
  • the current flowing through the quantum dot system S is expressed as:
  • P(n,t) represents the probability that n electrons pass through the quantum dot system in ⁇ t time, e is the unit charge, and n is the number of electrons passing through the quantum dot system S per unit time;
  • the shot noise spectrum of the current is expressed as:
  • ⁇ represents the independent variable in the shot noise S( ⁇ ) function.
  • the relationship between the density matrix of the two-level quantum charge bit transport system at different times is represented by the Kraus operator, that is, quantum hidden Markov: where m represents different K, and Km is the mth Kraus operator; this formula is equivalent to the quantum master equation;
  • the data of the shot noise spectrum is used to construct the relationship between the density matrix traces, that is, the time t-1 and the time t, that is, to construct
  • Tr[ ⁇ (n) (t)] to the h t parameter in the long short-term memory network
  • the parameters (W, b) in the long-short-term memory network can be used as effect.
  • the method also includes the following steps:
  • Tr[ ⁇ (n) (t)] contribution to the total current to effectively truncate the value of n, where n represents the number of particles in the rewritten equation of the quantum conditional master equation;
  • M is the maximum particle value that can be obtained in numerical experiments, and P M corresponds to the probability value of M electrons flowing through the quantum dot system;
  • the data of the shot noise spectrum generated in the quantum transport process is divided into training data and test data;
  • the first relation and the second relation are used to determine the simulation effect of the long-short-term memory network to simulate the quantum conditional master equation.
  • the relationship between the long-short-term memory network in the recurrent neural network and the quantum conditional master equation is established, and the equivalent relationship between the two is obtained.
  • the problem of infinite loop closure of the equation when solving the quantum conditional master equation is solved, and the simulation of the quantum conditional master equation by the recurrent neural network is realized.
  • the premise of the derivation of the quantum conditional master equation is disclosed, that is, the specific implementation of the two-level quantum charge bit transport system; at the same time, in another exemplary implementation of the present invention
  • the specific structure of the long and short-term memory network is disclosed.
  • the value of n is effectively truncated by the method of the contribution of Tr[ ⁇ (n) (t)] to the total current, and the equation for solving the quantum condition master equation is further solved.
  • the equation for solving the quantum condition master equation is further solved.
  • FIG. 1 is a flowchart of a method disclosed by an exemplary embodiment of the present invention
  • FIG. 2 is a technology implementation roadmap disclosed by an exemplary embodiment of the present invention.
  • FIG. 3 is a schematic structural diagram of a two-level quantum charge bit transport system disclosed in an exemplary embodiment of the present invention.
  • FIG. 4 is a quantum hidden Markov computation diagram disclosed by an exemplary embodiment of the present invention.
  • FIG. 5 is a long-short-term memory network computation diagram disclosed by an exemplary embodiment of the present invention.
  • FIG. 6 is a schematic diagram of an LSTM cell structure of a long-short-term memory network disclosed in an exemplary embodiment of the present invention.
  • FIG. 8 is a relationship diagram of the error of the training data and the number of iterations disclosed by an exemplary embodiment of the present invention.
  • FIG. 9 is a relationship diagram of the error of the test data with the number of iterations disclosed by an exemplary embodiment of the present invention.
  • first, second, third, etc. may be used in this application to describe various information, such information should not be limited by these terms. These terms are only used to distinguish the same type of information from each other.
  • first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information without departing from the scope of the present application.
  • word "if” as used herein can be interpreted as "at the time of” or "when” or "in response to determining.”
  • the quantum conditional master equation describing the quantum transport process
  • the quantum hidden Markov process and the quantum master equation have a certain relationship
  • the computational graph of found a connection between it and Recurrent Neural Networks.
  • the recurrent neural network is trained with the noise spectrum data generated in the quantum transport process (a realizable physical system) to simulate the quantum conditional master equation. It can be used for the design of micro-nano quantum devices.
  • FIG. 1 shows a method for simulating a quantum condition master equation in a quantum transport process by a recurrent neural network provided by an exemplary embodiment of the present invention, including the following steps:
  • the long-short-term memory network includes T LSTM cells arranged in time sequence, each LSTM cell has an input value x t and an output value h t , and outputs The value h t will be passed into the LSTM cell at the next moment, and the LSTM cell has parameters (W, b);
  • the shot noise spectrum S( ⁇ ) of the current obtained according to the master equation of quantum conditions (wherein, the shot noise spectrum S( ⁇ ) represents the actual calculated value, which can be collected from the quantum transport system under experimental conditions ), replace the input value x t ; use the density matrix trace Tr[ ⁇ (n) (t)] in the quantum condition master equation, replace the output value h t ; use the quantum condition master at time t-1 and time t before and after The relationship between the density matrix traces in the equation Substitute parameters(W,b);
  • the quantum transport process corresponds to an achievable physical actual system.
  • the connection between the long-short-term memory network in the recurrent neural network and the quantum conditional master equation is established, and the equivalent relationship between the two is obtained.
  • the problem of infinite loop closure of the equation when solving the quantum conditional master equation is solved, and the simulation of the quantum conditional master equation by the recurrent neural network is realized.
  • the three parameters correspond to the three parameters of the long and short-term memory network because: the quantum conditional master equation and the recurrent neural network are equivalent in the expansion calculation graph, that is, Figure 4 and Figure 5 ( The following exemplary embodiments will be expanded in detail); at the same time, since the long short-term memory network is related to the quantum transport system, and the shot noise spectrum is used to describe the quantum transport system/transport process, the use of The shot noise spectrum is used as the input parameter x t of the long short-term memory network.
  • the xt parameter is the input parameter of the network, which is a sequence data
  • the shot noise spectrum is also a sequence data.
  • the sequence data of the shot noise spectrum is regarded as xt and input to the network.
  • the change between the previous step of h and the two steps of this step is connected by ⁇ , and then the connection between the previous step and this step of the h parameter is through
  • the network parameters are connected, whether it is the network parameters or ⁇ , they all do the same thing, that is, to connect the previous step and this step of a certain quantity, and then because h corresponds to ⁇ , we correspond ⁇ to the network parameters.
  • the trained recurrent neural network or long short-term memory network can be used to guide the technical field of designing micro-nano quantum devices.
  • the input value x t that is, the data of the shot noise spectrum S( ⁇ ) generated in the quantum transport process
  • the parameter (W, b) is the parameter to be trained
  • the output value h t the density matrix trace Tr[ ⁇ (n) (t)] in the quantum condition master equation
  • the output value h t is unknown and is calculated by the long-short-term memory network. In the calculation process, only an initial value h 0 is required, and the subsequent time steps are calculated by the long-short-term memory network. owned.
  • the following exemplary embodiment first derives the quantum conditional master equation describing the quantum transport process, and then finds that the quantum hidden Markov process and the quantum master equation are related to a certain extent.
  • the computational graph found a connection between it and the recurrent neural network, as shown in Figure 2.
  • the quantum condition master equation is derived from a two-level quantum charge bit transport system; as shown in FIG. 3 , the two-level quantum charge bit transport system includes quantum dots System S and power supply V, the left electrode L of the quantum dot system S is connected to the positive electrode of the power supply V, and the right electrode R of the quantum dot system S is connected to the negative electrode of the power supply V; electrons flow through the quantum dots under the excitation of an external voltage.
  • the total Hamiltonian of the two-level quantum charge bit transport system is:
  • H s represents the Hamiltonian of the quantum dot system S
  • HE represents the Hamiltonian of the left electrode L and the right electrode R
  • H′ represents the interaction between the quantum dot system S and the electrodes. Hamiltonian.
  • H s , HE and H' are:
  • s represents the spin of the electron
  • ⁇ and ⁇ represent the spin-up and spin-down, respectively
  • j represents the energy level
  • ⁇ j represents the energy of the jth energy level
  • ⁇ represents the generation/annihilation operators of electrons at the jth energy level and spin s, respectively
  • ⁇ is the Coulomb interaction energy of two electrons occupying the same energy level but with different spins
  • n j ⁇ , n j ⁇ , n js represents the particle number operator when the electron occupies the jth energy level and the spin is ⁇ , ⁇ , s
  • C E is the charge energy related to the number of electrons occupying the energy level
  • ⁇ represents the electrode
  • k represents the electron ⁇ ⁇ ks represents the energy of the electron with momentum k on the electrode.
  • hc represents the generation operator of electrons with spin s and momentum k on the ⁇ electrode
  • c ⁇ ks represents the annihilation operator of electrons with spin s and momentum k on the ⁇ electrode
  • ⁇ ⁇ kj represents the interaction between the system and the environment Strength of action
  • hc denotes Hermitian conjugation.
  • ⁇ (n) (t) represents the approximate density of the system when n electrons pass through the quantum dot system S in time ⁇ t densification matrix, represents the first derivative of ⁇ (n) (t) with respect to time.
  • Equation (6) is referred to as a rewritten equation of the quantum conditional master equation in the following.
  • the current flowing through the quantum dot system S is expressed as:
  • P(n,t) represents the probability that n electrons pass through the quantum dot system S in ⁇ t time, e is the unit charge, and n is the number of electrons passing through the quantum dot system S per unit time;
  • the shot noise spectrum of the current is expressed as:
  • ⁇ represents the independent variable in the shot noise S( ⁇ ) function, which can be similarly understood as the frequency in the Fourier transform.
  • the above exemplary embodiment deduces the quantum condition master equation describing the quantum transport process.
  • the following content finds that the quantum hidden Markov process and the quantum master equation have a certain connection.
  • the connection between it and the recurrent neural network specifically:
  • the relationship between the density matrix of the two-level quantum charge bit transport system at different times is represented by the Kraus operator, that is, quantum hidden Markov: where m represents different K, and Km is the mth Kraus operator; this formula is equivalent to the quantum master equation, that is, formula (4);
  • the following content compares the computational graph of quantum hidden Markov and the computational graph of recurrent neural network, and finds that there is a high similarity between the two. specifically:
  • Figure 4 is a quantum hidden Markov calculation diagram.
  • the evolution process of the density matrix is actually a process of cyclic calculation of parameters that do not change with time, that is, each transformation uses the ⁇ parameter.
  • Figure 5 shows the calculation diagram of the long-short-term memory network. After the long-short-term memory network is trained, the (W, b) parameters of each calculation remain unchanged. Therefore, it can be seen that the connection between the computational graph of the quantum hidden Markov process and the recurrent neural network (long-short-term memory network computational graph) is found by expanding the computational graph of the quantum hidden Markov process.
  • long short-term memory network is a subclass of recurrent neural network, which has great advantages in processing time series data.
  • Figure 6 shows the specific structure of the LSTM cell of the long-short-term memory network.
  • the relationship between the input value x t and the output value h t of the LSTM cell is given by the following equation:
  • x t is the current input value
  • h t can be output as the current output value and passed into the LSTM cell at the next moment.
  • only the density matrix trace is used in the calculation of the shot noise spectrum due to the current (ie equation (8)). Therefore, only the shot noise spectrum data can be used to construct the relationship between the density matrix traces, that is, the connection between time t-1 and time t, that is, to construct (The constructed relationship does not include time);
  • the evolution process of the density matrix is actually a process of cyclic calculation of parameters that do not change with time, which is consistent with the calculation idea of the cyclic neural network, that is, after the cyclic neural network is trained, the parameters (W, b) remain unchanged;
  • the parameters (W, b) in the long short-term memory network can act as The role of linking the relationship between the previous step and the next step.
  • Our goal is to construct such a relationship using data on the noise spectrum produced by two-level quantum systems.
  • the method further includes the following steps:
  • Tr[ ⁇ (n) (t)] contribution to the total current to effectively truncate the value of n, where n represents the number of particles in the rewritten equation of the quantum conditional master equation;
  • M is the maximum particle value that can be obtained in numerical experiments, and P M corresponds to the probability value of M electrons flowing through the quantum dot system;
  • the data of the shot noise spectrum generated in the quantum transport process is divided into training data and test data;
  • the first relation and the second relation are used to determine the simulation effect of the long-short-term memory network to simulate the quantum conditional master equation.
  • Figure 8 shows the error of the training data as a function of the number of iterations
  • Figure 9 shows the error of the test data as a function of the number of iterations.
  • the error gradually decreases with the number of iterations until it converges, which shows that we have constructed a good long-short-term memory network. That is to say, we use the long-short-term memory network to simulate the quantum conditional master equation very well.

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Abstract

本发明公开了一种循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，包括：建立循环神经网络，循环神经网络为长短时记忆网络；长短时记忆网络包括T个按时间顺序排列的LSTM细胞，每个LSTM细胞具有输入值xt和输出值ht，LSTM细胞内具有参数(W,b)；将根据量子条件主方程得到的电流的散粒噪声谱S(ω)，替代输入值xt；利用量子条件主方程中的密度矩阵迹，替代输出值ht；利用前后时刻的量子条件主方程中的密度矩阵迹之间联系，替代参数(W,b)。本发明建立了循环神经网络中的长短时记忆网络和量子条件主方程的联系，利用量子系统产生的散粒噪声谱的数据，解决求解量子条件主方程时方程无限循环闭合的难题，实现循环神经网络对量子条件主方程的模拟。

Description

循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法 技术领域
本发明涉及一种循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法。
背景技术
量子输运现象作为介观系统中的一种重要的物理现象，近年来被广泛研究。对于传统器件，信噪比可以通过抑制散粒噪声来提高，但是在量子点构成的系统中，散粒噪声不会被无限的减少。事实上，量子器件的量子输运噪声并不是一定有害的。这些和精细时间有关的散粒噪声能敏感的反应输运过程中精细的动力学，丰富的量子输运性质以及在其中的精细的能量尺度。因此，在研究低维介观纳米器件的输运特点的过程中，对量子散粒噪声系统的测试和分析会成为一个重要的理论工具和方法。
对于理论计算，我们需要去面对一个含有噪声和量子点的开放系统并研究其性质。前人提出了很多方法去研究它，包括Buttiker和Beenaker等人提出的散射矩阵方法、非平衡格林函数方法、量子主方程方法。不同于前人的研究，李兴奇等人沿着Gurvitz的方法提出了一个研究电荷比特细致输运过程的条件主方程。
尽管量子条件主方程能够描述细致的描述电荷的输运过程，但是进一步研究此过程相关的物理量却是非常困难的，因为其是一个无限递归的微分方程系统。因此，对输运过程中的量子条件主方程的求解就显得极为重要。
因此，提供循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，属于本领域亟待解决的问题。其中，模拟量子条件主方程的循环神经网络可以用于指导微纳量子器件的设计。
发明内容
本发明的目的在于克服现有技术的不足，提供循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法。
本发明的目的是通过以下技术方案来实现的：
本发明的第一方面，提供循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，包括以下步骤：
建立一个循环神经网络，所述循环神经网络为长短时记忆网络；所述长短时记忆网络包括T个按时间顺序排列的LSTM细胞，每个LSTM细胞具有输入值x t和输出值h t，输出值h t会传入下一时刻的LSTM细胞中，LSTM细胞内具有参数(W,b)；
将根据量子条件主方程得到的电流的散粒噪声谱，替代输入值x t；利用量子条件主方程中的密度矩阵迹，替代输出值h t；利用前后时刻即t-1时刻和t时刻的量子条件主方程中的密 度矩阵迹之间联系，替代参数(W,b)；
利用量子输运过程中产生的散粒噪声谱的数据来训练所述循环神经网络从而达到模拟量子条件主方程的目的；所述量子输运过程对应一个可实现的物理实际系统。
进一步地，所述量子条件主方程由二能级量子电荷比特输运系统推导；所述二能级量子电荷比特输运系统包括量子点系统S和电源V，量子点系统S的左电极L与电源V的正极连接，量子点系统S的右电极R与电源V的负极连接；所述二能级量子电荷比特输运系统的总哈密顿量为：
Figure PCTCN2021095988-appb-000001
式中，H s表示的是量子点系统S的哈密顿量，H E表示的是左电极L和右电极R的哈密顿量，H′表示的是量子点系统S和电极之间相互作用的哈密顿量。
进一步地，假设量子点系统S和环境之间的相互作用不是很强，把H′当作微扰来处理，根据二阶矩累积展开和Lindblad方程，得到描述量子输运过程的量子主方程：
Figure PCTCN2021095988-appb-000002
式中，刘维尔超算符定义为：
Figure PCTCN2021095988-appb-000003
Figure PCTCN2021095988-appb-000004
G(t,τ)是与量子点系统S哈密顿量H s有关的传播子；量子点系统S的约化密度矩阵为ρ(t)＝Tr E[ρ T(t)]，<(…)>＝Tr E[(…)ρ E]，ρ E表示电极的密度矩阵；i表示虚数单位，ρ(t)表示在t时刻的密度矩阵，τ表示小于时间t的任意时刻，
Figure PCTCN2021095988-appb-000005
表示ρ(t)对时间的一阶导数；
对电极所处的希尔伯特空间进行划分，用E (n)表示在Δt时间内有n个电子经过量子点系统S时电极处于的空间，则电极所在的空间就可以表示为
Figure PCTCN2021095988-appb-000006
把所述假设带到量子主方程中，得到量子条件主方程：
Figure PCTCN2021095988-appb-000007
这里
Figure PCTCN2021095988-appb-000008
表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，ρ (n)(t)表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，
Figure PCTCN2021095988-appb-000009
表示ρ (n)(t)对时间的一阶导数。
进一步地，H s、H E和H′的具体形式为：
Figure PCTCN2021095988-appb-000010
Figure PCTCN2021095988-appb-000011
Figure PCTCN2021095988-appb-000012
式中，s表示电子的自旋，↑,↓分别表示自旋向上和自旋向下；j表示能级，∈ j表示第j个能级的能量；
Figure PCTCN2021095988-appb-000013
分别表示电子处于第j个能级上且自旋为s的产生/湮灭算符；ω是两个电子占据同一能级但自旋不相同的库伦作用能，n j↑、n j↓、n js分别表示电子占据第j个能级且自旋为↑,↓,s时的粒子数算符；C E是与占据能级的电子数有关的电荷能；α表示电极；k表示的是电子的动量；∈ αks表示电极上动量为k的电子的能量，考虑到电极上的电子处于热统计平衡状态，其分布函数为：
Figure PCTCN2021095988-appb-000014
μ表示费米能量，考虑外部电压是对成的加在系统上的，这里费米能量等于μ L＝eV/2,μ R＝-eV/2；T表示的是温度，就是量子输运系统处于的温度，k B表示玻尔兹曼常数；
Figure PCTCN2021095988-appb-000015
表示α电极上自旋为s、动量为k的电子的产生算符；c αks表示α电极上自旋为s、动量为k的电子的湮灭算符；τ αkj表示系统和环境之间的相互作用强度，h.c.表示厄米共轭。
进一步地，假设
Figure PCTCN2021095988-appb-000016
并在马尔可夫近似下，所述量子条件主方程改写为：
Figure PCTCN2021095988-appb-000017
式中，
Figure PCTCN2021095988-appb-000018
是电极中电子的谱函数；ρ (n)即ρ (n)(t)，
Figure PCTCN2021095988-appb-000019
表示处于第j个能级上、自旋为s的电子的产生算符，
Figure PCTCN2021095988-appb-000020
表示处于第j个能级上、自旋为s的电子湮灭算符，γ表示谱函数
Figure PCTCN2021095988-appb-000021
中的自变量；
流过量子点系统S中的电流表示为：
Figure PCTCN2021095988-appb-000022
式中，P(n,t)表示在Δt时间内由n个电子穿过量子点系统的概率，e表示单位电荷，n表示单位时间穿过量子点系统S的电子数目；
根据MacDonald公式，电流的散粒噪声谱表示为：
Figure PCTCN2021095988-appb-000023
式中，ω表示散粒噪声S(ω)函数中的自变量。
进一步地，所述二能级量子电荷比特输运系统的密度矩阵在不同时刻之间的联系，利用Kraus算符即量子隐马尔可夫进行表示：即
Figure PCTCN2021095988-appb-000024
式中m表示不同的K,Km是第m个Kraus算符；该公式与所述量子主方程等价；
而在量子条件主方程下，将ρ(t)＝∑ nρ (n)(t)带入上式就有
Figure PCTCN2021095988-appb-000025
根据量子条件主方程的改写方程，ρ (n)(t+Δt)和ρ (n)(t),ρ (n-1)(t),ρ (n+1)(t)相关，因此联合上式可知：
Figure PCTCN2021095988-appb-000026
即该式与量子条件主方程的改写方程有关系，目标就是构建不含时的映射
Figure PCTCN2021095988-appb-000027
进一步地，所述LSTM细胞的输入值x t和输出值h t的关系，由下式方程给出：
f t＝σ(W f·[h t-1,x t]+b f)
i t＝σ(W i·[h t-1,x t]+b i)
Figure PCTCN2021095988-appb-000028
O t＝σ(W O·[h t-1,x t]+b O)
h t＝O t×tanh(C t)
式中，(W f,W i,W c,W o,b f,b i,b c,b o)作为所述参数(W,b)；f t为遗忘门限层的输出，i t和
Figure PCTCN2021095988-appb-000029
为输入门限层的输出，O t和h t为输出门限层的输出。
进一步，利用散粒噪声谱的数据来构建密度矩阵迹之间即t-1时刻和t时刻之间的联系，即构建
Figure PCTCN2021095988-appb-000030
把Tr[ρ (n)(t)]和长短时记忆网络中的h t参数相对应；
将长短时记忆网络中的参数(W,b)就可以充当
Figure PCTCN2021095988-appb-000031
的作用。
进一步地，所述方法还包括以下步骤：
用Tr[ρ (n)(t)]对总电流的贡献度的方法来有效的截断n值，n表示量子条件主方程的改写 方程中的粒子数；定义评估函数：
Figure PCTCN2021095988-appb-000032
式中，M是数值实验上能取到的最大粒子数值，P M对应为有M个电子流过量子点系统的概率值；
通过不断调整M的值，绘制出了E(M)随M的变化图像，根据所述变化图像来确定M的取值。
进一步地，所述量子输运过程中产生的散粒噪声谱的数据分为训练数据和测试数据；
利用训练数据来训练所述循环神经网络，得到训练数据的误差随迭代次数的第一关系；利用所述测试数据来测试所述循环神经网络，得到测试数据的误差随迭代次数的第二关系；
利用第一关系和第二关系确定长短时记忆网络模拟量子条件主方程的模拟效果。
本发明的有益效果是：
(1)在本发明的一示例性实施例中，建立了循环神经网络中的长短时记忆网络和量子条件主方程的联系，得到二者的等价关系。同时利用量子系统产生的散粒噪声谱的数据，解决求解量子条件主方程时方程无限循环闭合的难题，实现循环神经网络对量子条件主方程的模拟。
(2)在本发明的又一示例性实施例中，公开了量子条件主方程的推导前提，即二能级量子电荷比特输运系统的具体实现方式；同时在本发明的又一示例性实施例中，公开了长短时记忆网络的具体结构。
(3)在本发明的又一示例性实施例中，用Tr[ρ (n)(t)]对总电流的贡献度的方法来有效的截断n值，进一步解决求解量子条件主方程时方程无限循环闭合的难题，实现循环神经网络对量子条件主方程的模拟。
附图说明
图1为本发明一示例性实施例公开的方法流程图；
图2为本发明一示例性实施例公开的技术实现路线图；
图3为本发明一示例性实施例公开的二能级量子电荷比特输运系统结构示意图；
图4为本发明一示例性实施例公开的量子隐马尔可夫计算图；
图5为本发明一示例性实施例公开的长短时记忆网络计算图；
图6为本发明一示例性实施例公开的长短时记忆网络的LSTM细胞结构示意图；
图7为本发明一示例性实施例公开的截断判断中E(M)随M的变化图；
图8为本发明一示例性实施例公开的训练数据的误差随迭代次数的关系图；
图9为本发明一示例性实施例公开的测试数据的误差随迭代次数的关系图。
具体实施方式
下面结合附图对本发明的技术方案进行清楚、完整地描述，显然，所描述的实施例是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。
在本申请使用的术语是仅仅出于描述特定实施例的目的，而非旨在限制本申请。在本申请和所附权利要求书中所使用的单数形式的“一种”、“所述”和“该”也旨在包括多数形式，除非上下文清楚地表示其他含义。还应当理解，本文中使用的术语“和/或”是指并包含一个或多个相关联的列出项目的任何或所有可能组合。
应当理解，尽管在本申请可能采用术语第一、第二、第三等来描述各种信息，但这些信息不应限于这些术语。这些术语仅用来将同一类型的信息彼此区分开。例如，在不脱离本申请范围的情况下，第一信息也可以被称为第二信息，类似地，第二信息也可以被称为第一信息。取决于语境，如在此所使用的词语“如果”可以被解释成为“在……时”或“当……时”或“响应于确定”。
此外，下面所描述的本发明不同实施方式中所涉及的技术特征只要彼此之间未构成冲突就可以相互结合。
具体地，在下述示例性实施例中，通过推导出描述量子输运过程的量子条件主方程，然后发现量子隐马尔可夫过程和量子主方程有一定的联系，经过展开量子隐马尔可夫过程的计算图发现了其和循环神经网络之间的联系。然后用量子输运过程(一个可实现的物理实际系统)中产生的噪声谱的数据来训练循环神经网络从而达到模拟量子条件主方程的目的。可以用于微纳量子器件的设计。
参见图1，图1示出了本发明的一示例性实施例提供的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，包括以下步骤：
建立一个循环神经网络，所述循环神经网络为长短时记忆网络；所述长短时记忆网络包括T个按时间顺序排列的LSTM细胞，每个LSTM细胞具有输入值x t和输出值h t，输出值h t会传入下一时刻的LSTM细胞中，LSTM细胞内具有参数(W,b)；
将根据量子条件主方程得到的电流的散粒噪声谱S(ω)(其中，散粒噪声谱S(ω)表示实际计算值，在有实验条件的情况下，可以从量子输运系统中采集)，替代输入值x t；利用量子条件主方程中的密度矩阵迹Tr[ρ (n)(t)]，替代输出值h t；利用前后时刻即t-1时刻和t时刻的 量子条件主方程中的密度矩阵迹之间联系
Figure PCTCN2021095988-appb-000033
替代参数(W,b)；
利用量子输运过程中产生的散粒噪声谱的数据来训练所述循环神经网络从而达到模拟量子条件主方程的目的；所述量子输运过程对应一个可实现的物理实际系统。
具体地，在该示例性实施例中，建立了循环神经网络中的长短时记忆网络和量子条件主方程的联系，得到二者的等价关系。同时利用量子系统产生的散粒噪声谱的数据，解决求解量子条件主方程时方程无限循环闭合的难题，实现循环神经网络对量子条件主方程的模拟。
需要说明的是，该三个参数与长短时记忆网络的三个参数进行对应，是因为：量子条件主方程和循环神经网络是在展开计算图上是等价的，即图4和图5(下述示例性实施例将详细进行展开)；同时，由于长短时记忆网络是与量子输运系统相关的，而散粒噪声谱则是用于描述该量子输运系统/输运过程，因此利用散粒噪声谱作为长短时记忆网络的输入参数x t。
也就是说，x t参数就是网络的输入参数，是一个序列数据，散粒噪声谱也是一个序列数据，在实际的操作中，就把散粒噪声谱这个序列数据当作是x t输入到网络中，也就是说第一步输入散粒噪声谱的第一个数据，第二步输入散粒噪声谱的第二个数据，以此类推。φ和网络参数的对应要从宏观的角度来看，h的前一步和这一步两个步骤之间的变化是通过φ联系起来的，然后h参数的上一步和这一步之间的联系是通过网络参数联系起来的，不管是网络参数还是φ，他们都做了同一个事情，就是联系某一个量的上一步和这一步，然后又因为h和ρ对应，我们就把φ和网络参数对应。
在其他具体示例性实施例中，该训练后的循环神经网络或长短时记忆网络可以用于指导设计微纳量子器件的技术领域。
需要说明的是，在训练过程中，输入值x t即量子输运过程中产生的散粒噪声谱S(ω)的数据为已知参数，参数(W,b)为待训练的参数，输出值h t即量子条件主方程中的密度矩阵迹Tr[ρ (n)(t)]是未知数据。需要说明的是，输出值h t是未知的，是通过长短时记忆网络计算出来的，在计算过程中，只需给定一个初始值h 0，后面的时间步都是通过长短时记忆网络计算得到的。
具体地，下述示例性实施例首先通过推导出描述量子输运过程的量子条件主方程，然后发现量子隐马尔可夫过程和量子主方程有一定的联系，经过展开量子隐马尔可夫过程的计算图发现了其和循环神经网络之间的联系，如图2所示。
更优地，在一示例性实施例中，所述量子条件主方程由二能级量子电荷比特输运系统推导；如图3所示，所述二能级量子电荷比特输运系统包括量子点系统S和电源V，量子点系统S的左电极L与电源V的正极连接，量子点系统S的右电极R与电源V的负极连接；电 子在外部电压的激励下从量子点中流过。
所述二能级量子电荷比特输运系统的总哈密顿量为：
Figure PCTCN2021095988-appb-000034
式中，H s表示的是量子点系统S的哈密顿量，H E表示的是左电极L和右电极R的哈密顿量，H′表示的是量子点系统S和电极之间相互作用的哈密顿量。
更优地，而在又一示例性实施例中，H s、H E和H′的具体形式为：
Figure PCTCN2021095988-appb-000035
式中，s表示电子的自旋，↑,↓分别表示自旋向上和自旋向下；j表示能级，∈ j表示第j个能级的能量；
Figure PCTCN2021095988-appb-000036
分别表示电子处于第j个能级上且自旋为s的产生/湮灭算符；ω是两个电子占据同一能级但自旋不相同的库伦作用能，n j↑、n j↓、n js分别表示电子占据第j个能级且自旋为↑,↓,s时的粒子数算符；C E是与占据能级的电子数有关的电荷能；α表示电极；k表示的是电子的动量；∈ αks表示电极上动量为k的电子的能量，考虑到电极上的电子处于热统计平衡状态，其分布函数为：
Figure PCTCN2021095988-appb-000037
μ表示费米能量，考虑外部电压是对成的加在系统上的，这里费米能量等于μ L＝eV/2,μ R＝-eV/2；T表示的是温度，就是量子输运系统处于的温度，k B表示玻尔兹曼常数；
Figure PCTCN2021095988-appb-000038
表示α电极上自旋为s、动量为k的电子的产生算符；c αks表示α电极上自旋为s、动量为k的电子的湮灭算符；τ αkj表示系统和环境之间的相互作用强度，h.c.表示厄米共轭。
更优地，在一示例性实施例中，假设量子点系统S和环境之间的相互作用不是很强，可以把H′当作微扰来处理，根据二阶矩累积展开和Lindblad方程，得到描述量子输运过程的量子主方程：
Figure PCTCN2021095988-appb-000039
式中，刘维尔超算符定义为：
Figure PCTCN2021095988-appb-000040
Figure PCTCN2021095988-appb-000041
G(t,τ)是与量子点系统S哈密顿量H s有关的传播子(格林函数)；量子点系统S的约化密度矩阵为ρ(t)＝Tr E[ρ T(t)]，<(…)>＝Tr E[(…)ρ E]，ρ E表示电极的密度矩阵；i表示虚数单位，ρ(t)表示在t时刻的密度矩阵，τ表示小于时间t的任意时刻，
Figure PCTCN2021095988-appb-000042
表示ρ(t)对时间的一阶导数；
如果我们对电极所处的希尔伯特空间进行划分，用E (n)表示在Δt时间内有n个电子经过量子点系统S时电极处于的空间，则电极所在的空间就可以表示为
Figure PCTCN2021095988-appb-000043
值得提的是，当n＝0时，由于没有电子经过量子点系统，此时所处的希尔伯特空间由左右两个独立的电极的子空间所张成，即
Figure PCTCN2021095988-appb-000044
把所述假设带到量子主方程(4)中，得到量子条件主方程：
Figure PCTCN2021095988-appb-000045
这里
Figure PCTCN2021095988-appb-000046
表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，，ρ (n)(t)表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，
Figure PCTCN2021095988-appb-000047
表示ρ (n)(t)对时间的一阶导数。
更优地，在一示例性实施例中，假设
Figure PCTCN2021095988-appb-000048
并在马尔可夫近似下，所述量子条件主方程改写为：
Figure PCTCN2021095988-appb-000049
式中，
Figure PCTCN2021095988-appb-000050
是电极中电子的谱函数；ρ (n)即ρ (n)(t)，
Figure PCTCN2021095988-appb-000051
表示处于第j个能级上、自旋为s的电子的产生算符，
Figure PCTCN2021095988-appb-000052
表示处于第j个能级上、自旋为s的电子湮灭算符，γ表示谱函数
Figure PCTCN2021095988-appb-000053
中的自变量。下述内容将式(6)称为量子条件主方程的改写方程。
流过量子点系统S中的电流表示为：
Figure PCTCN2021095988-appb-000054
式中，P(n,t)表示在Δt时间内由n个电子穿过量子点系统S的概率，e表示单位电荷，n 表示单位时间穿过量子点系统S的电子数目；
根据MacDonald公式，电流的散粒噪声谱表示为：
Figure PCTCN2021095988-appb-000055
式中，ω表示散粒噪声S(ω)函数中的自变量，可以类似理解为傅里叶变换中的频率。
上述示例性实施例推导出描述量子输运过程的量子条件主方程，下述内容发现量子隐马尔可夫过程和量子主方程有一定的联系，经过展开量子隐马尔可夫过程的计算图发现了其和循环神经网络之间的联系。具体地：
更优地，在一示例性实施例中，所述二能级量子电荷比特输运系统的密度矩阵在不同时刻之间的联系，利用Kraus算符即量子隐马尔可夫进行表示：即
Figure PCTCN2021095988-appb-000056
式中m表示不同的K,Km是第m个Kraus算符；该公式与所述量子主方程即公式(4)等价；
而在量子条件主方程下，将ρ(t)＝∑ nρ (n)(t)带入上式就有
Figure PCTCN2021095988-appb-000057
根据量子条件主方程的改写方程即公式(6)，可以看出ρ (n)(t+Δt)和ρ (n)(t),ρ (n-1)(t),ρ (n+1)(t)相关，因此联合上式可知：
Figure PCTCN2021095988-appb-000058
即该式与量子条件主方程的改写方程(6)有关系，而我们的目标就是构建不含时的映射
Figure PCTCN2021095988-appb-000059
下述内容对比了量子隐马尔科夫的计算图和循环神经网络的计算图，发现两者有很高的相似性。具体地：
图4为量子隐马尔可夫计算图。对于量子隐马尔科夫，密度矩阵的演化过程实际上是一个不随时间变化的参数的循环计算的过程，即每一次变换都是利用φ参数。而图5为长短时记忆网络计算图，在长短时记忆网络训练后，每一次计算的(W,b)参数不变。因此可以看到，过展开量子隐马尔可夫过程的计算图发现了其和循环神经网络(长短时记忆网络计算图)之间的联系。
具体地，长短时记忆网络是循环神经网络的一个子类，在处理时间序列数据上有很大的优势。图6示出了长短时记忆网络LSTM细胞的具体结构图。
更优地，在一示例性实施例中，所述LSTM细胞的输入值x t和输出值h t的关系，由下式方程给出：
Figure PCTCN2021095988-appb-000060
式中，(W f,W i,W c,W o,b f,b i,b c,b o)作为所述参数(W,b)；f t为遗忘门限层的输出，i t和
Figure PCTCN2021095988-appb-000061
为输入门限层的输出，O t和h t为输出门限层的输出。该部分的内容属于现有技术的具体内容，在此不进行赘述。
x t是当前的输入值，h t可以作为当前的输出值进行输出并且传入下一时刻的LSTM细胞中。
更优地，在一示例性实施例中，由于电流的散粒噪声谱(即式(8))的计算只用到了密度矩阵迹
Figure PCTCN2021095988-appb-000062
的信息，所以只能用散粒噪声谱的数据来构建密度矩阵迹之间即t-1时刻和t时刻之间的联系，即构建
Figure PCTCN2021095988-appb-000063
(构建出来的关系不含时间)；
密度矩阵在演化的过程中始终保持迹为1，因此根据ρ(t)＝∑ nρ (n)(t)可知，在量子条件主方程下(即式(5))只能保证总体密度矩阵的迹Tr[ρ(t)]＝Tr[∑ nρ (n)(t)]＝∑ nTr[ρ (n)(t)]＝1保持不变，并不能保证Tr[ρ (n)(t)]不发生变化；这个公式(Tr[ρ (n)(t)])不会恒等于1，所以才有模拟的必要；
密度矩阵的演化过程实际上是一个不随时间变化的参数的循环计算的过程，这与循环神经网络的计算思想是一致的，即循环神经网络训练后，参数(W,b)保持不变；
把Tr[ρ (n)(t)]和长短时记忆网络中的h t参数相对应，因为h t参数在经过SoftMax函数作用后也会有Tr[h t]＝Tr[∑ nh t (n)]＝∑ nTr[h t (n)]＝1，这与Tr[ρ (n)(t)]的行为相同(即整体求和为1，但是单体变化)；
长短时记忆网络中的参数(W,b)就可以充当
Figure PCTCN2021095988-appb-000064
的作用，联系上一步和下一步的关系。
我们的目标就是用二能级量子系统产生的噪声谱的数据构建这样一个关系。
但是这里还存在一个问题，在方程(6)中粒子数n的取值可以取到任意值，但是在数值实验中我们必须对n做一个有效的截断。
更优地，在一示例性实施例中，所述方法还包括以下步骤：
用Tr[ρ (n)(t)]对总电流的贡献度的方法来有效的截断n值，n表示量子条件主方程的改写方程中的粒子数；定义评估函数：
Figure PCTCN2021095988-appb-000065
式中，M是数值实验上能取到的最大粒子数值，P M对应为有M个电子流过量子点系统的概率值；
通过不断调整M的值，绘制出了E(M)随M的变化图像，如图7所示。可以根据图7来确定M的取值，在其中一示例性实施例中，取M＝50，Tr[ρ (50)(t)]对总电流的贡献只占0.4％。
更优地，所述量子输运过程中产生的散粒噪声谱的数据分为训练数据和测试数据；
利用训练数据来训练所述循环神经网络，得到训练数据的误差随迭代次数的第一关系；利用所述测试数据来测试所述循环神经网络，得到测试数据的误差随迭代次数的第二关系；
利用第一关系和第二关系确定长短时记忆网络模拟量子条件主方程的模拟效果。
具体地，图8展示了训练数据的误差随迭代次数的关系，图9展示了测试数据的误差随迭代次数的关系。从图中中可以看到，误差随着迭代次数逐渐减小直至收敛，这说明我们通过长短时记忆网络很好的构建了
Figure PCTCN2021095988-appb-000066
也就是说，我们利用长短时记忆网络很好的模拟了量子条件主方程。
显然，上述实施例仅仅是为清楚地说明所作的举例，而并非对实施方式的限定，对于所属领域的普通技术人员来说，在上述说明的基础上还可以做出其他不同形式的变化或变动。这里无需也无法对所有的实施方式予以穷举。而由此所引申出的显而易见的变化或变动仍处于本发明创造的保护范围之中。

Claims (10)

  1. 循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：包括以下步骤：
    建立一个循环神经网络，所述循环神经网络为长短时记忆网络；所述长短时记忆网络包括T个按时间顺序排列的LSTM细胞，每个LSTM细胞具有输入值x t和输出值h t，输出值h t会传入下一时刻的LSTM细胞中，LSTM细胞内具有参数(W,b)；
    将根据量子条件主方程得到的电流的散粒噪声谱，替代输入值x t；利用量子条件主方程中的密度矩阵迹，替代输出值h t；利用前后时刻即t-1时刻和t时刻的量子条件主方程中的密度矩阵迹之间联系，替代参数(W,b)；
    利用量子输运过程中产生的散粒噪声谱的数据来训练所述循环神经网络从而达到模拟量子条件主方程的目的；所述量子输运过程对应一个可实现的物理实际系统。
  2. 根据权利要求1所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：所述量子条件主方程由二能级量子电荷比特输运系统推导；所述二能级量子电荷比特输运系统包括量子点系统S和电源V，量子点系统S的左电极L与电源V的正极连接，量子点系统S的右电极R与电源V的负极连接；所述二能级量子电荷比特输运系统的总哈密顿量为：
    Figure PCTCN2021095988-appb-100001
    式中，H s表示的是量子点系统S的哈密顿量，H E表示的是左电极L和右电极R的哈密顿量，H′表示的是量子点系统S和电极之间相互作用的哈密顿量。
  3. 根据权利要求2所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：假设量子点系统S和环境之间的相互作用不是很强，把H′当作微扰来处理，根据二阶矩累积展开和Lindblad方程，得到描述量子输运过程的量子主方程：
    Figure PCTCN2021095988-appb-100002
    式中，刘维尔超算符定义为：
    Figure PCTCN2021095988-appb-100003
    Figure PCTCN2021095988-appb-100004
    G(t,τ)是与量子点系统S哈密顿量H s有关的传播子；量子点系统S的约化密度矩阵为ρ(t)＝Tr E[ρ T(t)]，<(…)>＝Tr E[(…)ρ E]，ρ E表示电极的密度矩阵；i表示虚数单位，ρ(t)表示在t时刻的密度矩阵，τ表示小于时间t的任意时刻，
    Figure PCTCN2021095988-appb-100005
    表示ρ(t)对时间的一阶导数；
    对电极所处的希尔伯特空间进行划分，用E (n)表示在Δt时间内有n个电子经过量子点系统S时电极处于的空间，则电极所在的空间就可以表示为
    Figure PCTCN2021095988-appb-100006
    把所述假设带到量子 主方程中，得到量子条件主方程：
    Figure PCTCN2021095988-appb-100007
    这里
    Figure PCTCN2021095988-appb-100008
    表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，ρ (n)(t)表示在Δt时间内由n个电子穿过量子点系统S时系统的约化密度矩阵，
    Figure PCTCN2021095988-appb-100009
    表示ρ (n)(t)对时间的一阶导数。
  4. 根据权利要求3所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：H s、H E和H′的具体形式为：
    Figure PCTCN2021095988-appb-100010
    Figure PCTCN2021095988-appb-100011
    Figure PCTCN2021095988-appb-100012
    式中，s表示电子的自旋，↑,↓分别表示自旋向上和自旋向下；j表示能级，ε j表示第j个能级的能量；
    Figure PCTCN2021095988-appb-100013
    分别表示电子处于第j个能级上且自旋为s的产生/湮灭算符；ω是两个电子占据同一能级但自旋不相同的库伦作用能，n j↑、n j↓、n js分别表示电子占据第j个能级且自旋为↑,↓,s时的粒子数算符；C E是与占据能级的电子数有关的电荷能；α表示电极；k表示的是电子的动量；ε αks表示电极上动量为k的电子的能量，考虑到电极上的电子处于热统计平衡状态，其分布函数为：
    Figure PCTCN2021095988-appb-100014
    μ表示费米能量，考虑外部电压是对成的加在系统上的，这里费米能量等于μ L＝eV/2,μ R＝-eV/2；T表示的是温度，就是量子输运系统处于的温度，k B表示玻尔兹曼常数；
    Figure PCTCN2021095988-appb-100015
    表示α电极上自旋为s、动量为k的电子的产生算符；c αks表示α电极上自旋为s、动量为k的电子的湮灭算符；τ αkj表示系统和环境之间的相互作用强度，h.c.表示厄米共轭。
  5. 根据权利要求4所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：假设
    Figure PCTCN2021095988-appb-100016
    并在马尔可夫近似下，所述量子条件主方程改写为：
    Figure PCTCN2021095988-appb-100017
    式中，
    Figure PCTCN2021095988-appb-100018
    是电极中电子的谱函数；ρ (n)即ρ (n)(t)，
    Figure PCTCN2021095988-appb-100019
    表示处于第j个能级上、自旋为s的电子的产生算符，
    Figure PCTCN2021095988-appb-100020
    表示处于第j个能级上、自旋为s的电子湮灭算符，γ表示谱函数
    Figure PCTCN2021095988-appb-100021
    中的自变量；
    流过量子点系统S中的电流表示为：
    Figure PCTCN2021095988-appb-100022
    式中，P(n,t)表示在Δt时间内由n个电子穿过量子点系统S的概率，e表示单位电荷，n表示单位时间穿过量子点系统S的电子数目；
    根据MacDonald公式，电流的散粒噪声谱表示为：
    Figure PCTCN2021095988-appb-100023
    式中，ω表示散粒噪声S(ω)函数中的自变量。
  6. 根据权利要求5所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：所述二能级量子电荷比特输运系统的密度矩阵在不同时刻之间的联系，利用Kraus算符即量子隐马尔可夫进行表示：即
    Figure PCTCN2021095988-appb-100024
    式中m表示不同的K,Km是第m个Kraus算符；该公式与所述量子主方程等价；
    而在量子条件主方程下，将ρ(t)＝∑ nρ (n)(t)带入上式就有
    Figure PCTCN2021095988-appb-100025
    根据量子条件主方程的改写方程，ρ (n)(t+Δt)和ρ (n)(t),ρ (n-1)(t),ρ (n+1)(t)相关，因此联合上式可知：
    Figure PCTCN2021095988-appb-100026
    即该式与量子条件主方程的改写方程有关系，目标就是构建不含时的映射
    Figure PCTCN2021095988-appb-100027
  7. 根据权利要求6所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：所述LSTM细胞的输入值x t和输出值h t的关系，由下式方程给出：
    f t＝σ(W f·[h t-1,x t]+b f)
    i t＝σ(W i·[h t-1,x t]+b i)
    Figure PCTCN2021095988-appb-100028
    O t＝σ(W O·[h t-1,x t]+b O)
    h t＝O t×tanh(C t)
    式中，(W f,W i,W c,W o,b f,b i,b c,b o)作为所述参数(W,b)；f t为遗忘门限层的输出，i t和
    Figure PCTCN2021095988-appb-100029
    为输入门限层的输出，O t和h t为输出门限层的输出。
  8. 根据权利要求7所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：利用散粒噪声谱的数据来构建密度矩阵迹之间即t-1时刻和t时刻之间的联系，即构建
    Figure PCTCN2021095988-appb-100030
    把Tr[ρ (n)(t)]和长短时记忆网络中的h t参数相对应；
    将长短时记忆网络中的参数(W,b)就可以充当
    Figure PCTCN2021095988-appb-100031
    的作用。
  9. 根据权利要求5所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：所述方法还包括以下步骤：
    用Tr[ρ (n)(t)]对总电流的贡献度的方法来有效的截断n值，n表示量子条件主方程的改写方程中的粒子数；定义评估函数：
    Figure PCTCN2021095988-appb-100032
    式中，M是数值实验上能取到的最大粒子数值，P M对应为有M个电子流过量子点系统的概率值；
    通过不断调整M的值，绘制出了E(M)随M的变化图像，根据所述变化图像来确定M的取值。
  10. 根据权利要求1所述的循环神经网络模拟量子输运过程中的量子条件主方程的模拟方法，其特征在于：所述量子输运过程中产生的散粒噪声谱的数据分为训练数据和测试数据；
    利用训练数据来训练所述循环神经网络，得到训练数据的误差随迭代次数的第一关系；利用所述测试数据来测试所述循环神经网络，得到测试数据的误差随迭代次数的第二关系；
    利用第一关系和第二关系确定长短时记忆网络模拟量子条件主方程的模拟效果。
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