CN114742228B - Hybrid computing method and device based on neural network and quantum circuit - Google Patents
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Abstract
A mixed calculation method and device based on a neural network and a quantum circuit, the method comprises the following steps: acquiring Hamiltonian quantity, and representing a line for measuring the Hamiltonian quantity energy as a classical-quantum form; the classical part comprises classical parameters, and the quantum part comprises quantum parameters; classical partial calculation is performed through a neural network, and quantum partial calculation is performed through a variable component sub-circuit; initializing classical parameters and quantum parameters; according to classical parameters and quantum parameters, circularly executing target operation; the ith operation in the target operation includes: one of the classical parameter and the quantum parameter is fixed, the other parameter is regulated, and i is an integer greater than 0; when the difference between the energy values obtained by the ith and the (i-1) th target operations is as low as the threshold, the energy value of the ith time serves as the ground state energy of the quantum system. According to the method, the neural network is introduced into a classical processing flow, so that entanglement characteristics which can be expressed by an algorithm are increased, efficiency can be improved, and a target task can be completed with higher precision.
Description
Technical Field
The invention relates to the technical field of quantum computing, in particular to a hybrid computing method and device based on a neural network and a quantum circuit.
Background
In the fields of condensed state physics, quantum chemistry and the like, calculation of a molecular structure plays a vital role in understanding physical and chemical properties of molecules. One of the most fundamental properties of molecular structure is the eigenstate energy of the molecule. For example, in chemistry, the minimum eigenvalue of the hermite matrix that characterizes the molecule is the ground state energy of the system. However, the computational cost of the electronic wave function of a multi-electronic system grows exponentially with the scale of the quantum system, and the conventional method of accurately modeling it and calculating the eigenstate energy faces computational limitations in accuracy.
Based on the basic theory of quantum computation, the variable component quantum eigenvalue finder algorithm can model multiple electron wave functions in polynomial time, which gives it an opportunity to solve the problem of eigenvalue energy computation. Furthermore, an important advantage of the variable component sub-eigenvalue finder algorithm is that it has proven to have a degree of resistance to noise in quantum hardware. However, on a quantum device of the noise-containing mesoscale quantum era, the larger the expression range of the quantum state, the larger the quantum hardware resources required, and the larger the noise.
The existing variable component quantum intrinsic solver algorithm and the derivative algorithm thereof are usually focused on the parameter optimization and quantum gate form of a quantum circuit by utilizing a classical computer, the integral feedback structure is not changed, the variable component quantum intrinsic solver algorithm is still limited by the existing quantum chip resources, and the quantum entanglement characteristics which can be expressed actually are limited. For more complex, entangled deeper systems, the accuracy and resources of the prior art are limited, which is currently not addressed by the technical methods of the prior art.
Disclosure of Invention
In view of the limitation of line depth, the existing quantum chip resources have limited quantum entanglement characteristics, a deeper entangled system and Hamiltonian amount thereof are difficult to process, and noise interference of quantum devices can be caused, and the embodiment of the application provides a hybrid computing method and device based on a neural network and quantum lines, which are used for relieving the problems on the quantum devices in a noisy mesoscale quantum era.
In a first aspect, the present application provides a hybrid computing method based on a neural network and a quantum circuit, including:
acquiring Hamiltonian quantity of a minimum eigenvalue to be solved of a target quantum system, and representing a line for measuring the Hamiltonian quantity energy into a form comprising a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical part calculation is performed through a neural network, and the quantum part calculation is performed through a variable component sub-line;
initializing the classical parameters and the quantum parameters;
and performing target operations in a circulating way according to the classical parameters and the quantum parameters, wherein the ith operation in the target operations comprises the following steps: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter; wherein i is an integer greater than 0;
and when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the (i-1) th target operation is lower than a preset threshold value, taking the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu quantity.
Preferably, when the i value is 1, the current first parameter is an initialized first parameter, and the current second parameter is an initialized second parameter; when the i value is greater than 1, the current first parameter is the first parameter after the i-1 operation adjustment, and the current second parameter is the second parameter after the i-1 operation adjustment.
Preferably, the first parameter is the classical parameter and the second parameter is the quantum parameter.
Preferably, the fixing the first parameter, and adjusting the second parameter includes: fixing the first parameter and optimizing the second parameter through a parameter transfer rule.
Preferably, the fixing the adjusted second parameter, and adjusting the first parameter includes: fixing the adjusted second parameter, and optimizing the first parameter through a neural network by adopting a gradient descent method; the neural network samples according to the probability distribution of the first parameter, so that an energy value is obtained. And analytically find the gradient with respect to the parameterized probability distribution.
Preferably, the i-th target operation obtains an energy value of the system, including: and carrying out quantum measurement on the whole current neural network to obtain an expected value as an energy value.
Preferably, the neural network employs a limited boltzmann machine.
Preferably, the variable component sub-circuit includes: one or more lines operating on qubits, the lines comprising single quantum gates and multiple quantum gates; wherein the single quantum gate is a logic gate for manipulating a single qubit, and the multiple quantum gate is a logic gate for manipulating multiple qubits.
In a second aspect, the present application provides a hybrid computing device based on a neural network and quantum wires, comprising:
the acquisition module is used for acquiring the Hamiltonian quantity of the minimum eigenvalue to be solved of the target quantum system, and representing a line for measuring the Hamiltonian quantity energy into a form comprising a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical part calculation is performed through a neural network, and the quantum part calculation is performed through a variable component sub-line;
the initialization module is used for initializing the classical parameters and the quantum parameters;
and the operation module is used for circularly executing target operations according to the classical parameters and the quantum parameters, wherein the ith operation in the target operations comprises the following steps: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter; wherein i is an integer greater than 0;
and the determining module is used for determining the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu quantity when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the (i-1) th target operation is lower than a preset threshold value.
According to the method, the neural network is introduced into a classical processing flow, so that entanglement characteristics which can be expressed by an algorithm are increased, efficiency can be improved, and a target task can be completed with higher precision.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present invention, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is an application schematic diagram of a technical solution provided in an embodiment of the present application;
FIG. 2 is a schematic diagram of method steps provided in an embodiment of the present application;
FIG. 3 is a schematic diagram of a method process according to an embodiment of the present application;
fig. 4 is a schematic diagram of an apparatus according to an embodiment of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
For the purpose of facilitating an understanding of the embodiments of the present invention, reference will now be made to the following description of specific embodiments, taken in conjunction with the accompanying drawings, which are not intended to limit the embodiments of the invention.
Fig. 1 is an application schematic diagram of a technical solution provided in an embodiment of the present application. As shown in fig. 1, the solution task of the ground state energy of the quantum system can be completed by the method provided by the technical scheme of the application. The ground state energy of a quantum system can be considered as the task of solving the minimum eigenvalue of hamiltonian. Eigenvalues are an important concept in linear algebra, assuming a is an n-th order square matrix, if there are a number m and a non-zero n-dimensional column vector x such that ax=mx holds, then m is said to be one eigenvalue or eigenvalue of a. In quantum mechanics, let a be a linear transformation of vector space, and if a vector sum X obtained by a transformation of a certain non-zero vector in space is only a constant factor, i.e., ax=kx, k is called a eigenvalue of a.
Fig. 2 is a schematic diagram of method steps provided in an embodiment of the present application. As shown in fig. 2, the hybrid computation method based on the neural network and the quantum wire may include:
step S201: acquiring Hamiltonian quantity of a minimum eigenvalue to be solved of a target quantum system, and representing a line for measuring the Hamiltonian quantity energy into a form comprising a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical partial computation is performed by a neural network and the quantum partial computation is performed by a variable component sub-line. Hamiltonian is used to represent the ground state energy of the quantum system.
Specifically, the ground state energy of the quantum system represented by hamiltonian can be expressed as the following formula:
wherein, theta represents classical parameters, phi represents quantum parameters, H represents Hamiltonian quantity, U represents a similar transformation matrix,
the complex conjugate of U is characterized by,<ψ0| characterizes the left vector, |ψ0>The right vector is characterized.
Wherein the correlation of the similarity transformation matrix is explained as: let A and B be n-order matrices, if there is a reversible matrix P, P is the result -1 Ap=b, the matrices a and B are similar, the reversible matrix P is a similar transformation matrix for transforming a into B, and the operation P is performed on a -1 The AP is said to perform a similarity transformation on a.
In this application, the minimum eigenvalue of hamiltonian is solved by employing a classical-quantum hybrid algorithm. The classical part is processed by adopting a neural network method, the quantum part is processed by adopting a variable component sub-circuit, and the variable component sub-circuit is a quantum algorithm which depends on adjustable parameters.
In some possible implementations, the neural network employs a limited boltzmann machine (restricted Boltzmann machine, RBM). An RBM is a randomly generated neural network that can learn a probability distribution through an input dataset. The Hamiltonian amount matrix is subjected to hermitian transformation through the RBM, so that entanglement relevance in the Hamiltonian amount is reduced to the extent that the existing quantum computing chip resources can be effectively processed, but the measurement result is required to be normalized so as to ensure that the eigenvalue of the original Hamiltonian amount is not changed by matrix transformation.
Wherein the normalization process may be expressed according to the following equation:
<ψ|u + (θ)u(θ)|ψ>
the final energy expression can be expressed as:
in some possible embodiments, the variable component sub-circuit comprises:
one or more lines operating on qubits, the lines comprising single quantum gates and multiple quantum gates; wherein the single quantum gate is a logic gate for manipulating a single qubit, and the multiple quantum gate is a logic gate for manipulating multiple qubits.
Quantum circuits, i.e. circuits that operate on qubits, are made up of quantum logic gates. In quantum circuits, the circuits are connected by time, and are operated upon by encountering logic gates. Whereas each of the quantum logic gates constituting the quantum wire is a unitary matrix, the entire quantum wire is also a unitary matrix.
Step S202: initializing the classical parameters and the quantum parameters.
In some possible embodiments, the first parameter of the classical part may be initialized by assigning a random value, and the second parameter of the quantum part may be initialized using the estimated result of the Hatree-Fock.
Step S203: and performing target operations in a circulating way according to the classical parameters and the quantum parameters, wherein the ith operation in the target operations comprises the following steps: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of a classical parameter and a quantum parameter, and the second parameter is the other parameter except the first parameter in the classical parameter and the quantum parameter; wherein i is an integer greater than 0.
When the i value is 1, the current first parameter is an initialized first parameter, and the current second parameter is an initialized second parameter; when the i value is greater than 1, the current first parameter is the first parameter after the i-1 operation adjustment, and the current second parameter is the second parameter after the i-1 operation adjustment.
The first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter which is determined outside the first parameter in the classical parameter and the quantum parameter. It can be understood that in the present application, the ith operation in the target operations performed in a circulating manner may adjust the parameters of the neural network part by fixing the parameters of the variable component sub-circuits first, or may adjust the parameters of the variable component sub-circuits by fixing the parameters of the neural network part first, that is, fixing the classical parameters, adjusting the quantum parameters, fixing the adjusted quantum parameters, and adjusting the classical parameters; the method can also be used for fixing quantum parameters, adjusting classical parameters, fixing the adjusted classical parameters and adjusting quantum parameters.
In a more specific example, the first parameter is the classical parameter and the second parameter is the quantum parameter.
The fixing the first parameter, and adjusting the second parameter includes: fixing the first parameter and optimizing the second parameter by a parameter transfer rule (parameter-shiftstring).
Classical parameters were fixed and quantum parameters were optimized by the parameter-shiftstring method. The parameter-shift method converts the gradient descent calculation into two quantum circuits transferred with parameters to complete the calculation, and finally, each quantum bit is measured through a plurality of single-bit or multi-bit parametric sub-gates, and the expected value of the bubble operator is taken as output. In some more specific embodiments, the fixing the adjusted second parameter, and adjusting the first parameter includes:
fixing the adjusted second parameter, and optimizing the first parameter through a neural network by adopting a gradient descent method; wherein,,
and sampling according to probability distribution given by parameters by using a neural network, thereby obtaining an energy value. And analytically find the gradient with respect to the parameterized probability distribution.
The method comprises the steps of sampling according to probability distribution given by parameters by using a neural network, so that an energy value is a strategy of energy measurement in the application, and obtaining gradients and optimizing by solving the gradients related to the parameterized probability distribution analytically.
Step S204: and when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the (i-1) th target operation is lower than a preset threshold value, taking the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu quantity.
In some more specific embodiments, the ith target operation results in a system energy value comprising: and carrying out quantum measurement on the whole current neural network to obtain an expected value as an energy value.
The variable component sub-algorithm itself comprises a loss function to be optimized, and comprises two parts of Hamiltonian quantity and quantum state, and the two parts of Hamiltonian quantity and quantum state are parameterized at the same time. According to the invention, the neural network is added into the existing classical-quantum mixing method, and more specifically, the neural network is added into the classical processing flow in the existing classical-quantum mixing method, so that parameters in a variable component sub-line are processed, parameters in the neural network are processed, entanglement characteristics of quantum states represented by the mixed line are improved, and the task of eigenvalue solving can be completed better. Meanwhile, the invention utilizes the neural network to reduce the influence of noise, saves the resources of quantum equipment and can achieve higher calculation precision.
Based on the hybrid computing method based on the neural network and the quantum wire provided in the above embodiment, in this embodiment, a hybrid computing device based on the neural network and the quantum wire is provided, and in particular, fig. 4 shows an optional block diagram of the hybrid computing device based on the neural network and the quantum wire, where the device is divided into one or more program modules, and the one or more program modules are stored in a storage medium and executed by one or more processors, to complete the present invention. Program modules in the present invention refer to a series of computer program instruction segments capable of performing specific functions, and are more suitable than programs themselves for describing the execution of a hybrid computing device based on neural networks and quantum circuits in a storage medium, and the following description will specifically describe the functions of each program module in this embodiment. The device specifically comprises:
the obtaining module 401 is configured to obtain a hamiltonian amount of a minimum eigenvalue to be solved of the target quantum system, and represent a line for measuring the energy of the hamiltonian amount as a form including a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical part calculation is performed through a neural network, and the quantum part calculation is performed through a variable component sub-line;
an initialization module 402, configured to initialize the classical parameter and the quantum parameter;
an operation module 403, configured to perform a target operation in a loop according to the classical parameter and the quantum parameter, where an ith operation in the target operation includes: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter; wherein i is an integer greater than 0;
and the determining module 404 is configured to determine the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu amount when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the i-1 th target operation is lower than a preset threshold.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises an element.
It will be understood by those skilled in the art that all or part of the steps for implementing the above embodiments may be implemented by hardware, or may be implemented by a program for instructing relevant hardware, and the program may be stored in a computer readable storage medium, where the storage medium may be a read-only memory, a magnetic disk or an optical disk, etc.
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 (9)
1. The hybrid computing method based on the neural network and the quantum circuit is characterized by comprising the following steps of:
the Hamiltonian quantity of the ground state energy to be solved of the target quantum system is obtained, and a line for measuring the Hamiltonian quantity energy is expressed to be in a form comprising a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical part calculation is performed through a neural network, and the quantum part calculation is performed through a variable component sub-line; the line for measuring the Hamiltonian energy is expressed as the following formula:
wherein, theta represents classical parameters, phi represents quantum parameters, H represents Hamiltonian quantity, U represents a similar transformation matrix,
the complex conjugate of U is characterized by,<ψ 0 the I characterizes the left vector, the I ψ 0 >Characterizing a right vector;
initializing the classical parameters and the quantum parameters;
and performing target operations in a circulating way according to the classical parameters and the quantum parameters, wherein the ith operation in the target operations comprises the following steps: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter; wherein i is an integer greater than 0;
and when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the (i-1) th target operation is lower than a preset threshold value, taking the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu quantity.
2. The method of claim 1, wherein when the i value is 1, the current first parameter is an initialized first parameter and the current second parameter is an initialized second parameter; when the i value is greater than 1, the current first parameter is the first parameter after the i-1 operation adjustment, and the current second parameter is the second parameter after the i-1 operation adjustment.
3. The method of claim 1, wherein the first parameter is the classical parameter and the second parameter is the quantum parameter.
4. A method according to claim 3, wherein said fixing the first parameter and adjusting the second parameter comprises:
fixing the first parameter and optimizing the second parameter through a parameter transfer rule.
5. A method according to claim 3, wherein fixing the adjusted second parameter, adjusting the first parameter comprises:
fixing the adjusted second parameter, and optimizing the first parameter through a neural network by adopting a gradient descent method; wherein,,
the neural network samples according to the probability distribution of the first parameter, thereby obtaining an energy value, and analytically finds a gradient with respect to the parameterized probability distribution.
6. A method according to claim 3, wherein the ith target operation yields an energy value for the system comprising: and carrying out quantum measurement on the whole current neural network to obtain an expected value as an energy value.
7. The method of claim 1, wherein the neural network employs a limited boltzmann machine.
8. The method of claim 1, wherein the variable component sub-circuit comprises:
one or more lines operating on qubits, the lines comprising single quantum gates and multiple quantum gates;
wherein the single quantum gate is a logic gate for manipulating a single qubit, and the multiple quantum gate is a logic gate for manipulating multiple qubits.
9. A hybrid computing device based on a neural network and quantum wires, the device comprising:
the acquisition module is used for acquiring the Hamiltonian quantity of the minimum eigenvalue to be solved of the target quantum system, and representing a line for measuring the Hamiltonian quantity energy into a form comprising a classical part and a quantum part; the classical part comprises classical parameters and the quantum part comprises quantum parameters; the classical part calculation is performed through a neural network, and the quantum part calculation is performed through a variable component sub-line; the line for measuring the Hamiltonian energy is expressed as the following formula:
wherein, theta represents classical parameters, phi represents quantum parameters, H represents Hamiltonian quantity, U represents a similar transformation matrix,
the complex conjugate of U is characterized by,<ψ 0 the I characterizes the left vector, the I ψ 0 >Characterizing a right vector;
the initialization module is used for initializing the classical parameters and the quantum parameters;
and the operation module is used for circularly executing target operations according to the classical parameters and the quantum parameters, wherein the ith operation in the target operations comprises the following steps: fixing a first parameter, adjusting a second parameter, fixing the adjusted second parameter, and adjusting the first parameter, wherein the first parameter is one of the classical parameter and the quantum parameter, and the second parameter is the other parameter; wherein i is an integer greater than 0;
and the determining module is used for determining the energy value of the target quantum system obtained by the ith target operation as the ground state energy of the quantum system represented by the Ha Midu quantity when the difference between the energy value of the target quantum system obtained by the ith target operation and the energy value obtained by the (i-1) th target operation is lower than a preset threshold value.
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