CN114861928B - Quantum measurement method and device and computing equipment - Google Patents
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Abstract
The invention relates to a quantum measurement method, a device and a computing equipment, wherein the method comprises the steps of constructing a limited Boltzmann machine according to a target quantum system, wherein the limited Boltzmann machine comprises n input units v and m input units vAn output unit h and a plurality of connecting lines between the input unit and the output unit, and initializing the weight coefficients of each input unit, each output unit and the plurality of connecting lines, respectively denoted as a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i The method comprises the steps of containing a plurality of elements, and representing the selection probability of an ith quantum bit for each of a plurality of measurement operators; updating the weight coefficient according to a preset cost function to obtain a target weight coefficient; the invention can reduce the measurement times of the quantum state by acquiring the measurement operator in the quantum system, realize high-efficiency measurement, save time and ensure measurement accuracy.
Description
Technical Field
The present invention relates to the field of quantum measurement, and in particular, to a quantum measurement method, a device and a computing device.
Background
As the computing power of classical computers approaches a limit, quantum computing is a new technology, which has attracted tremendous interest in the scientific community and the public, and marked a potentially revolutionary advancement. Quantum computing extends the special way classical computing means that one cannot expect a quantum computer to be able to accelerate arbitrary tasks. However, early theoretical work showed that quantum computers provided exponential computational acceleration over the most well known classical algorithms in some structured problems, such as the well known large integer decomposition problem on modern encryption bases. If these results are widely used, quantum computing will have profound effects on society as the invention of classical computing.
Research into chemical and physical molecules and materials has helped humans synthesize new chemical materials, thereby achieving breakthroughs in certain fields. However, since classical computers have very limited computing power, for larger systems, classical computers often cannot be solved efficiently. Quantum computing is then presented as a candidate, and the fact that molecules and materials can be modeled by quantum computing stems from the fact that in many cases, chemical and physical describe molecules and materials by quantum mechanics.
In order to efficiently analyze the properties of molecules and materials by the current moderate-scale quantum devices with errors, multiple quantum measurements of the hamiltonian amount of the molecules are unavoidable. How to realize quantum measurement with high efficiency is a current challenge to be solved. The optimization strategies for some quantum measurements are gradually improved and perfected for some special systems. However, for the exploration of some properties of large-scale and general hamiltonian, such as finding its ground state/excited state energy, the number of quantum measurements required is still very large and not efficient to implement.
Disclosure of Invention
The object of the present invention is to solve the above-mentioned problems occurring in the prior art.
To achieve the above object, the present invention provides a quantum measurement method comprising constructing a limited Boltzmann machine according to a target quantum system, wherein the limited Boltzmann machine comprises n input units v, m output units h, and a plurality of connecting lines between the input units and the output units, wherein an ith input unit v i An ith qubit corresponding to a quantum state of the target quantum system; initializing the weight coefficients of each input unit, each output unit and a plurality of connecting lines respectively with a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i The method comprises the steps of containing a plurality of elements, and representing the selection probability of an ith quantum bit for each of a plurality of measurement operators; updating the weight coefficient according to a preset cost function to obtain a target weight coefficient; wherein the cost function is a part irrelevant to the input state in the variance function of the probability of the measuring operator; sampling to obtain a target measurement operator through the trained limited Boltzmann machine based on the target weight coefficient; and measuring the quantum state of the quantum system by adopting the obtained target measurement operator.
The invention can reduce the measurement times of the quantum state by acquiring the measurement operator in the quantum system, realize high-efficiency measurement, save time and ensure measurement accuracy.
Drawings
FIG. 1 is a schematic diagram of a prior art solution;
FIG. 2 is a flow chart of a measurement process for optimizing measurements known in the art;
FIG. 3 is a flow chart of a quantum measurement method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a restricted Boltzmann machine constructed in accordance with an embodiment of the invention;
FIG. 5 is a schematic diagram of a quantum measurement device according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a computing device according to an embodiment of the invention.
Detailed Description
The technical scheme of the invention is further described in detail through the drawings and the embodiments.
First, in the art, searching for the ground state energy of macromolecules by reducing the number of quantum measurements is of great interest in the industry. There are many different schemes to solve this problem, the basic idea being to sample the hamiltonian h= Σby means of a specific distribution j α j Q j Observability Q contained j Measurements were made. Including L1 sampling, packet measurement, classical implicit measurement, and overlapping packet measurement. The scheme includes that a group of distribution kappa is firstly determined, then a measuring operator P is sampled from the distribution each time, and then the measuring operator obtained by sampling is used for measuring under a given ground state, so that the average value of all observables under the ground state is estimated, and further an estimated value of ground state energy is obtained.
Fig. 1 gives examples of some existing schemes for optimizing quantum measurements. The Hamiltonian amount is here an H represented by 3 qubits 2 A distribution schematic of observable samples of molecules.
Fig. 1 is a sampling schematic of several known schemes of quantum measurement. Where a vertex represents an observed quantity, a black border between two vertices represents that these two observed quantities can be obtained by measuring a same measuring operator, in the figure at, for example, X 1 X 2 The oval shading in the back represents the observed quantity that a measurement operator can cover, and the numbers above the shading represent the probability of selecting the measurement operator. The form of Hamiltonian amount of water molecules selected in the graph is
For the above 4 schemes for optimizing measurements, when the measured quantum state is +.>
The variance of the measurement results was 0.9,0.56,0.74 and 0.5 in this order.
As shown in fig. 2, a process flow diagram of quantum state optimization measurement is shown. Firstly, a classical computer, i.e. a CPU, is used to sample the measurement operators P from the distribution κ, which is a superposition of tensor products of the measurement operators P1, P2, pn, i.e. the i-th qubit corresponds to the measurement operator Pi. The measurement is then carried out with the quantum computer, i.e. QPU, with the sampled measurement operators P1, P2, pn for a given ground state. Finally, solving the average value of all observables under the ground state by utilizing a classical computer CPU, and further obtaining the estimated value of the ground state energy.
In the link of sampling the measuring operator P, the prior art has a plurality of defects. Particularly, under the condition of relatively large sampling space, the whole space cannot be effectively sampled, so that the estimation of the subsequent ground state energy is not accurate enough.
Therefore, the scheme of the invention is provided, wherein the limited Boltzmann machine is utilized for sampling the measuring operator, and the sampling is better carried out for a large sampling space, so that the accuracy of quantum measurement is improved.
Fig. 3 is a flowchart of a quantum measurement method according to an embodiment of the present invention, as shown in fig. 3, the method includes the following steps:
s101: constructing a limited Boltzmann machine according to a target quantum system, wherein the limited Boltzmann machine comprises n input units v, m output units h and a plurality of connecting lines between the input units and the output units, wherein the ith input unit v i An ith qubit corresponding to a quantum state of the target quantum system.
The limited boltzmann machine is a double-layer neural network, and comprises an input layer and a hidden layer, wherein the input layer comprises a plurality of input units (or neurons), the hidden layer comprises a plurality of output units, and the input layer and the hidden layer are fully connected, i.e. each input unit of the input layer is respectively connected to each output unit of the hidden layer; however, there is no connection between the input units of the input layer, and there is no connection between the output units of the hidden layer. Fig. 4 is an embodiment of a model of a restricted boltzmann machine.
In fig. 4, it can be seen that the restricted boltzmann machine constructed includes n input units, m output units, and connecting lines therebetween. The input units are denoted as v, then the n input units may be denoted as v, respectively 1 ,v 2 ,…,v n The method comprises the steps of carrying out a first treatment on the surface of the The output units are denoted as h, and the m input units may be denoted as h, respectively 1 ,h 2 ,…,h m The method comprises the steps of carrying out a first treatment on the surface of the The connection line can be represented by the connected input unit and output unit, for example, the connection line between the 1 st input unit and the 1 st output unit is w 11 The connection between the ith input and the jth output cell is denoted as w ij 。
The restricted boltzmann machine is constructed from a target quantum system that is measured as desired, whereby the input element represents a qubit in the target quantum system, e.g. the i-th input element v i An ith qubit corresponding to a quantum state of the target quantum system.
S102: initializing the weight coefficients of each input unit, each output unit and a plurality of connecting lines to respectively obtain a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i Contains a plurality of elements, and represents the selection probability of the ith quantum bit for each of a plurality of measurement operators.
In this step, the setting of the weight coefficients is required for each input unit, each output unit and the plurality of connection lines in the structured restricted boltzmann machine, whereby in this step, the initial weight coefficient setting is performed first, i.e. for the set of the weight coefficients denoted as a i 、b j And w ij And setting initial weight values of the input unit weight coefficient, the output unit weight coefficient and the connecting wire weight coefficient which are respectively represented, so that the operation of the limited Boltzmann machine is facilitated. It should be noted that each weight coefficient is in the form of a vector。
In this step, the weight coefficient a of the i-th input unit i Contains a plurality of elements, and represents the selection probability of the ith quantum bit for each of a plurality of measurement operators.
For example, in a quantum system measurement method according to an embodiment of the present invention, a is a weight coefficient i The input unit comprises a plurality of elements, which can be a limited boltzmann machine, as one vertex, each vertex having three values 1, 2, 3, which in turn represent X, Y, Z. The multiple elements are respectively aimed at the selection probabilities of different measuring operators. Namely, X, Y and Z respectively represent a selection mode of a measurement operator, and each selection mode has a certain probability. In this example, the weight coefficient a of the input unit i May include 3 elements corresponding to the selection probabilities of X, Y, Z, respectively. Initially, the weight coefficient a may be set i Initializing to equi-probability selection, i.e. setting its initial value to
S103: updating the weight coefficient according to a preset cost function to obtain a target weight coefficient; wherein the cost function is a part irrelevant to the input state in the variance function of the probability of the measuring operator;
in the step, the weight coefficient can be effectively updated through a preset cost function, so that a target weight coefficient is obtained, the target weight coefficient is the weight coefficient of the final limited Boltzmann machine, and the probability distribution of the limited Boltzmann machine at the moment can represent the sampling probability distribution of a measuring operator.
The cost function in this step is a preset cost function, and the cost function is a part of the variance function of the probability of the measurement operator, which is irrelevant to the input state. .
In one embodiment of the invention, the cost function may be as follows:
wherein Q is j Representing an observable quantity of quantum states, p (Q j ) Representing the observed observable Q j Probability of (2); alpha j Based on the respective observables Q j Q when Hamiltonian H is obtained j Corresponding coefficients.
From the above equation, it can be seen that the cost function depends on the probability of each observables Qj.
The probability of the observability of the quantum state can be calculated through the cost function, and the observability can be some physically observable measurement. Since the cost function is obtained through the part of the variance function of the probability of the measuring operator, which is irrelevant to the input state, the smaller the variance is, the more accurate the estimated value of the observability quantity obtained by finally measuring the quantum state of the quantum system is, and the higher the precision is.
Further, the initial weight coefficient is updated according to a preset cost function, and the method comprises the following substeps.
Sub-step 1: and obtaining the current probability distribution of the input layer according to the current weight coefficient of the limited Boltzmann machine, and taking the current probability distribution as the current probability distribution of the measuring operator.
Specifically, the limited boltzmann machine has an input unit and an output unit, and an input layer is formed by a plurality of input units. Current probability distribution of input layer, boundary with input layer, output layer and hidden layer, and weight a of hidden layer i ,w ij ,b j And (5) correlation. Specifically, in some embodiments of the present invention, deriving the current probability distribution of its input layer from the current weight coefficient of the restricted boltzmann machine specifically includes: the current probability distribution p (v, h) of the input layer is determined according to the following equation:
z is a distribution function, E (v, h; a, b, w) is the energy of the Boltzmann machine network;
wherein Z can be expressed as the following formula:
Z＝∑ v,h e -E(v,h；a,b,w) wherein E (v, h; a, b, w) = - Σ j a j ·v j -∑ i ∑ j h i w ij ·v j -∑ i b i h i Is the energy of the network.
The ith qubit v sampled to a specific measurement operator can be obtained by simplification i The probability of (2) is
Wherein the method comprises the steps of
[1,0,0]Represents the X operator, [0,1,0 ]]Represents the Y operator, [0,1 ]]Representing the Z operator.
Sub-step 2: the probability of each observables Qj is determined from the current probability distribution described above.
Determining the probability of each observables from the current probability distribution, including in particular determining the observables Q from the following formula j Probability p (Q) j )：
Specifically, from the foregoing, it can be seen that the probability of the measurement operator is replaced by the probability distribution of the input layer of the restricted boltzmann machine, thereby yielding the weighting a for the input layer, the output layer and the hidden layer i ,w ij ,b j Is a cost function of (1).
Sub-step 3: substituting the probability of each observably quantity into a cost function, taking the extremum of the cost function as a target, and updating the current weight parameter according to a gradient descent method.
Specifically, after the probability of each observed quantity Qj is brought into the cost function, the cost function obtains an extremum as a target, and the gradient descent method can effectively obtain the network a with the minimum cost function i ,w ij ,b j So that the current weight coefficient can be updated.
In some embodiments of the present invention, updating the current weight parameters according to the gradient descent method includes:
and calculating the partial derivative of the cost function relative to any weight coefficient as the gradient corresponding to the weight coefficient. That is, the cost function for a is calculated as follows i ,w ij ,b j Respective gradients, obtaining a of local optimum points according to a gradient descent method i ,w ij ,b j Is a value of (2).
Wherein the gradient of the weight coefficient a, b or w
Can be expressed as follows:
according to gradient
And a preset step size eta, determining the adjustment quantity of the weight coefficient, for example +.>
And obtaining an updated value based on the current value and the adjustment amount of the weight coefficient.
By iteratively performing the above sub-steps 1 to 3 repeatedly, the weight coefficients in the restricted boltzmann machine can be updated continuously until a certain end condition is reached. The end condition may include that the iteration turns reach a certain number of times, that the function value of the cost function reaches convergence (e.g. the amount of change of the function value with respect to the previous round is smaller than a preset threshold), etc. The updated weight coefficient obtained at this time is the target weight coefficient, and the limited boltzmann machine at this time is the trained limited boltzmann machine.
Then in step S104: and based on the target weight coefficient, sampling by a trained limited Boltzmann machine to obtain a target measurement operator.
It will be appreciated that the trained constrained boltzmann machine with target weight coefficients corresponds to the state when the cost function reaches an extremum steady state. Also as previously described, the probability distribution of the restricted boltzmann machine input layer may correspond to the probability distribution of each measurement operator. Therefore, the target probability distribution of the input layer can be determined based on the target weight coefficient, the target probability distribution is used as the target probability distribution of each measuring operator, and the target measuring operator is obtained by sampling according to the target probability distribution of each measuring operator. Therefore, the whole space can be effectively sampled, and a more comprehensive measuring operator is obtained.
S105: and measuring the quantum state of the quantum system by adopting the obtained target measuring operator.
In the step, the quantum state of the quantum system can be measured through the obtained target measuring operator, and the efficiency can be ensured by measuring the quantum state due to the fact that the sampling of the measuring operator is comprehensive.
According to the quantum measurement method provided by the embodiment of the invention, the number of times of measuring the quantum state can be reduced by using a trained limited Boltzmann machine to sample a measurement operator, so that the efficient measurement is realized, the time is saved, and the measurement precision is ensured. By the method, a larger and more comprehensive probability space is considered in the field of quantum measurement, and the space is searched more comprehensively by generating larger probability distribution of the probability space through a limited Boltzmann machine.
In one embodiment, after measuring the quantum state, step S106 may also be performed: and inputting the measured value obtained by measuring the quantum state into an estimated value function so as to obtain an estimated value of the observed quantity of the quantum state, wherein the estimated value function is the same as the cost function.
In this step, the measured value of the measured quantum state is input into an estimation function, which is in the same form as the cost function, whereby an observable estimated value can be obtained.
According to another embodiment, a quantum measurement device is also provided. As shown in fig. 5, a quantum measuring device 100 of the present invention includes:
a construction module 10 for constructing a limited boltzmann machine according to a target quantum system, wherein the limited boltzmann machine comprises n input units v, m output units h, and a plurality of connecting lines between the input units and the output units, wherein the i-th input unit v i An ith qubit corresponding to a quantum state of the target quantum system;
an initialization module 20 for initializing the weight coefficients of each input unit, each output unit and a plurality of connection lines, respectively denoted as a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i The method comprises the steps of containing a plurality of elements, and representing the selection probability of an ith quantum bit for each of a plurality of measurement operators;
the obtaining module 30 updates the weight coefficient according to a preset cost function to obtain a target weight coefficient; wherein the cost function is a part irrelevant to the input state in the variance function of the probability of the measuring operator;
the sampling module 40 samples to obtain a target measurement operator by a trained limited boltzmann machine based on the target weight coefficients;
the calculation module 50 measures the quantum state of the quantum system using the obtained target measurement operator.
As shown in fig. 6, a computing device 200 includes a memory 40 and a processor 50, the memory 40 having executable code stored therein, the processor 50, when executing the executable code, implementing the method of any of claims 1-7.
The foregoing detailed description of the invention has been presented for purposes of illustration and description, and it should be understood that the invention is not limited to the particular embodiments disclosed, but is intended to cover all modifications, equivalents, alternatives, and improvements within the spirit and principles of the invention.
Claims (8)
1. A method of quantum measurement, comprising:
constructing a limited Boltzmann machine according to a target quantum system, wherein the limited Boltzmann machine comprises n input units v, m output units h and a plurality of connecting lines between the input units and the output units, wherein the ith input unit v i An ith qubit corresponding to a quantum state of the target quantum system;
initializing the weight coefficients of each input unit, each output unit and a plurality of connecting lines respectively with a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i The method comprises the steps of containing a plurality of elements, and representing the selection probability of an ith quantum bit for each of a plurality of measurement operators;
updating the weight coefficient according to a preset cost function to obtain a target weight coefficient; the cost function formula is as follows:
wherein Q is j Representing an observable amount of the quantum state, p (Q j ) Representing the observed observable Q j Probability of (2); alpha j Based on the respective observables Q j Q when Hamiltonian quantity is obtained j Corresponding coefficients;
sampling to obtain a target measurement operator through the trained limited Boltzmann machine based on the target weight coefficient;
and measuring the quantum state of the quantum system by adopting the obtained target measurement operator.
2. The method as recited in claim 1, further comprising:
and inputting the measured value obtained by measuring the quantum state into an estimation function to obtain an estimated value of the observed quantity of the quantum state, wherein the estimation function is in the same form as the cost function.
3. The method according to claim 1, characterized in that the cost function depends on the probability of the respective observables Qj; updating the weight coefficient according to a preset cost function, wherein the updating comprises the following steps:
obtaining the current probability distribution of an input layer of the limited Boltzmann machine according to the current weight coefficient of the limited Boltzmann machine, and taking the current probability distribution as the current probability distribution of a measuring operator;
determining the probability of each observability according to the current probability distribution;
substituting the probability of each observably quantity into the cost function, taking the extremum of the cost function as a target, and updating the current weight parameter according to a gradient descent method.
4. A method according to claim 3, characterized in that deriving the current probability distribution of its input layer from the current weight coefficients of the restricted boltzmann machine comprises: the current probability distribution p (v, h) of the input layer is determined according to the following equation:
wherein Z is a distribution function, E (v, h; a, b, w) is the energy of the Boltzmann machine network;
determining the probability of each observability from the current probability distribution, including determining the observability Q according to the following formula j Probability p (Q) j )：
5. The method of claim 4, wherein the partitioning function Z is represented as:
Z＝∑ v,h e -E(v,h；a,b,w) ，
the energy is expressed as:
e(v,h；a,b,w)＝-∑ j a j ·v j -∑ i ∑ j h i w ij ·v j -∑ i b i h i 。
6. a method according to claim 3, wherein updating the current weight parameters according to the gradient descent method comprises:
calculating the partial derivative of the cost function relative to any weight coefficient as a gradient corresponding to the weight coefficient;
determining the adjustment quantity of the weight coefficient according to the gradient and the preset step length;
and obtaining an updated value of the weight coefficient based on the current value of the weight coefficient and the adjustment quantity.
7. A quantum measurement device, comprising:
the construction module constructs the limited Boltzmann machine according to the target quantum system, wherein the limited Boltzmann machine comprises n input units v, m output units h and a plurality of connecting lines between the input units and the output units, and the ith input unit v i An ith qubit corresponding to a quantum state of the target quantum system;
the initial module initializes the weight coefficients of each input unit, each output unit and a plurality of connecting lines respectively with a i 、b j And w ij A representation; wherein the weight coefficient a of the ith input unit i The method comprises the steps of containing a plurality of elements, and representing the selection probability of an ith quantum bit for each of a plurality of measurement operators;
the acquisition module is used for updating the weight coefficient according to a preset cost function so as to acquire a target weight coefficient; the cost function formula is as follows:
wherein Q is j Representing an observable amount of the quantum state, p (Q j ) Representing the observed observable Q j Probability of (2); alpha j Based on the respective observables Q j Q when Hamiltonian quantity is obtained j Corresponding coefficients;
the sampling module is used for obtaining a target measurement operator through sampling through the trained limited Boltzmann machine based on the target weight coefficient;
and the calculation module is used for measuring the quantum state of the quantum system by adopting the obtained target measurement operator.
8. A computing device comprising a memory and a processor, wherein the memory has executable code stored therein, which when executed by the processor, implements the method of any of claims 1-6.
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