Information Processing Method and Apparatus, Electronic Device, and Medium Based on Quantum System

Abstract

The present disclosure provides an information processing method, apparatus, electronic device, computer-readable storage medium, and computer program product based on a quantum system, relating to the field of computers, and particularly to the field of quantum computer technology. The implementation solution is as follows: determining a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, where the Pauli operator expansion of the Hamiltonian includes a plurality of Pauli operators and a plurality of decomposition coefficients corresponding one-to-one to the plurality of Pauli operators; determining the sum of the absolute values of the plurality of decomposition coefficients; performing a first operation, where the first operation includes the following steps: based on the sum of the absolute values and the plurality of decomposition coefficients, determining a probability distribution corresponding to the plurality of Pauli operators; and sampling the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on the sampling result.

Description

Technical Field

[0001] The present disclosure relates to the field of computers, and more particularly to the field of quantum computer technology. Specifically, it relates to an information processing method, apparatus, electronic device, computer-readable storage medium, and computer program product based on a quantum system. Background Art

[0002] Currently, quantum computers are moving towards large-scale and practical applications. An important application of quantum computing is quantum simulation, that is, simulating the dynamic evolution of a quantum system. There are many applications of quantum simulation, and one of the key applications is to extract the classical information of observables. Summary of the Invention

[0003] The present disclosure provides an information processing method, apparatus, electronic device, computer-readable storage medium, and computer program product based on a quantum system.

[0004] According to one aspect of the present disclosure, there is provided an information processing method based on a quantum system, including: determining a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, the Pauli operator expansion of the observable including a plurality of Pauli operators and a plurality of decomposition coefficients corresponding to the plurality of Pauli operators one by one, where n is a positive integer; determining the sum of the absolute values of the plurality of decomposition coefficients; performing a first operation, the first operation including the following steps: based on the sum of the absolute values and the plurality of decomposition coefficients, determining a probability distribution of the plurality of Pauli operators; and sampling the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on a sampling result.

[0005] According to another aspect of the present disclosure, there is provided an information processing apparatus based on a quantum system, including: a first determination unit configured to determine a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, the Pauli operator expansion of the observable including a plurality of Pauli operators and a plurality of decomposition coefficients corresponding to the plurality of Pauli operators one by one, where n is a positive integer; a second determination unit configured to determine the sum of the absolute values of the plurality of decomposition coefficients; a first execution unit configured to perform a first operation, the first operation including the following steps: a first determination subunit configured to determine a probability distribution of the plurality of Pauli operators based on the sum of the absolute values and the plurality of decomposition coefficients; and a second determination subunit configured to sample the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on a sampling result.

[0006] According to another aspect of the present disclosure, there is provided an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; the memory stores instructions executable by the at least one processor, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute the method described in the present disclosure.

[0007] According to another aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing computer instructions for causing a computer to execute the method described in the present disclosure.

[0008] According to another aspect of the present disclosure, there is provided a computer program product including a computer program which, when executed by a processor, implements the method described in the present disclosure.

[0009] According to one or more embodiments of the present disclosure, based on the plurality of decomposition coefficients obtained by decomposition, the probability distribution corresponding to the plurality of Pauli operators obtained by decomposition can be determined, and thus, based on the probability distribution, sampling is performed on the plurality of Pauli operators to obtain the expected value of the target quantum system for this observable, thereby saving computational resources to a certain extent.

[0010] It should be understood that the content described in this part is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it used to limit the scope of the present disclosure. Other features of the present disclosure will become easily understandable through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] The drawings exemplarily illustrate embodiments and form a part of the specification, and are used together with the written description of the specification to explain the exemplary embodiments of the embodiments. The illustrated embodiments are for illustrative purposes only and do not limit the scope of the claims. In all the drawings, the same reference numerals refer to similar but not necessarily identical elements.

[0012] Figure 1 A flowchart of an information processing method based on a quantum system according to an embodiment of the present disclosure is shown;

[0013] Figure 2 A flowchart of obtaining an expected value by selecting a corresponding scheme according to an embodiment of the present disclosure is shown;

[0014] Figure 3 A block diagram of an information processing apparatus based on a quantum system according to an embodiment of the present disclosure is shown; and

[0015] Figure 4 A block diagram of an exemplary electronic device capable of implementing the embodiments of the present disclosure is shown. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0016] The following describes exemplary embodiments of the present disclosure with reference to the accompanying drawings. Various details of the embodiments of the present disclosure are included to facilitate understanding, and they should be considered merely exemplary. Therefore, those of ordinary skill in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope of the present disclosure. Similarly, descriptions of well-known functions and structures are omitted below for clarity and conciseness.

[0017] In the present disclosure, unless otherwise specified, the use of terms such as "first" and "second" to describe various elements is not intended to limit the positional relationship, temporal relationship, or importance relationship of these elements. Such terms are only used to distinguish one element from another. In some examples, the first element and the second element may refer to the same instance of the element, and in certain cases, based on the context description, they may also refer to different instances.

[0018] In the description of various examples in the present disclosure, the terms used are only for the purpose of describing specific examples and are not intended to be limiting. Unless the context clearly indicates otherwise, if the number of elements is not specifically limited, the element may be one or more. In addition, the term "and / or" used in the present disclosure covers any one and all possible combinations of the listed items.

[0019] Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.

[0020] To date, various different types of computers in use are based on classical physics as the theoretical basis for information processing, referred to as traditional computers or classical computers. Classical information systems use binary data bits, which are the easiest to implement physically, to store data or programs. Each binary data bit is represented by 0 or 1, called a bit or a byte, as the smallest information unit. Classical computers themselves have inevitable weaknesses: one is the most basic limitation of energy consumption during the computing process. The minimum energy required for logic elements or storage units should be several times that of kT to avoid malfunction due to thermal fluctuations; the second is information entropy and heat generation energy consumption; the third is that when the wiring density of computer chips is very large, according to the Heisenberg uncertainty relation, when the uncertainty of the electron position is very small, the uncertainty of the momentum will be very large. The electrons are no longer bound, and there will be quantum interference effects, which can even damage the performance of the chip.

[0021] A quantum computer is a type of physical device that follows the properties and laws of quantum mechanics to perform high-speed mathematical and logical operations, store, and process quantum information. When a device processes and computes quantum information and runs quantum algorithms, it is a quantum computer. Quantum computers follow unique quantum dynamics laws (especially quantum interference) to achieve a new mode of information processing. For parallel processing of computational problems, quantum computers have an absolute speed advantage over classical computers. The transformation applied to each superposition component by a quantum computer is equivalent to a classical computation. All these classical computations are completed simultaneously and superimposed with a certain probability amplitude to give the output result of the quantum computer. This kind of computation is called quantum parallel computing. Quantum parallel processing greatly improves the efficiency of quantum computers, enabling them to complete tasks that classical computers cannot, such as the factorization of a very large natural number. Quantum coherence is essentially utilized in all quantum super-fast algorithms. Therefore, quantum parallel computing using quantum states instead of classical states can achieve an operation speed and information processing function that classical computers cannot match, while saving a large amount of computing resources.

[0022] With the rapid development of quantum computer technology, due to its powerful computing power and fast operation speed, the application scope of quantum computers is becoming wider and wider. For example, chemical simulation refers to the process of mapping the Hamiltonian of a real chemical system to a physically operable Hamiltonian, and then modulating parameters and evolution time to find the eigenstate that can reflect the real chemical system. For example, in the research and development of high-performance batteries, it is necessary to estimate the energy density of the positive and negative electrode materials by solving the ground state and excited state of molecules. By second quantization of the chemical molecular formula of the positive and negative electrode materials, the Hamiltonian H can be obtained, thereby determining the ground state and excited state of the material, and then estimating the energy density of the material to achieve the purpose of shortening the research and development cycle of new batteries and reducing the trial-and-error cost. When simulating an n-electron chemical system on a classical computer, it involves the solution of a 2 n -dimensional Schrödinger equation, and the computational amount will increase exponentially with the increase in the number of electrons in the system. Therefore, classical computers have a very limited role in chemical simulation problems. To break through this bottleneck, it is necessary to rely on the powerful computing power of quantum computers. The Variational Quantum Eigensolver (VQE) algorithm is an efficient quantum algorithm for chemical simulation on quantum hardware and is one of the most promising applications of quantum computers in the near future, opening up many new fields of chemical research.

[0023] A core computational process of the variational quantum eigensolver algorithm VQE is to estimate the expectation value Tr[Oρ], where ρ is an n - qubit quantum state generated by a quantum computer, and the n - qubit observable O is the Hamiltonian of a real chemical system mapped to a physically operable Hamiltonian. The above process is the most general form of quantum computing to extract classical information and is the core step of reading classical information from quantum information.

[0024] For example, when simulating and solving the ground - state energy of an n - qubit closed physical system by the VQE algorithm, a parameterized trial wave function |Ψ(θ)> is prepared on a quantum device, and then an optimization algorithm in classical machine learning (such as the gradient - descent method) is used to continuously adjust and optimize the parameter θ to minimize the expectation value <Ψ(θ)|H|Ψ(θ)>. That is, the ground - state energy E0 can be expressed as:

[0025]

[0026] The classical part in the VQE algorithm (i.e., using the optimization algorithm in classical machine learning to optimize the parameter θ) has very high computational efficiency. Therefore, to accelerate the VQE algorithm, it is necessary to experimentally and efficiently estimate the expectation value of the Hamiltonian (i.e., the ground - state energy of the Hamiltonian) <h>:= <Ψ(θ)|H|Ψ(θ)> is a very important task.

[0027] Therefore, according to an embodiment of the present disclosure, an information processing method based on a quantum system is provided. Figure 1 The flowchart of the information processing method based on the quantum system according to the embodiment of the present disclosure is shown, as Figure 1 shown, the method 100 includes: determining the Pauli operator expansion of the observable corresponding to the target quantum system of n qubits, the Pauli operator expansion of the observable includes a plurality of Pauli operators and a plurality of decomposition coefficients corresponding to the plurality of Pauli operators one by one, the n is a positive integer (step 110); determining the sum of the absolute values of the plurality of decomposition coefficients (step 120); and performing a first operation, the first operation includes the following steps (step 130); based on the sum of the absolute values and the plurality of decomposition coefficients, determining the probability distribution of the plurality of Pauli operators (step 1301); and sampling the plurality of Pauli operators based on the probability distribution to determine the expected value of the target quantum system for the observable based on the sampling result (step 1302).

[0028] According to the embodiment of the present disclosure, based on the plurality of decomposition coefficients obtained by decomposition, the probability distribution corresponding to the plurality of Pauli operators obtained by decomposition can be determined, so as to sample the plurality of Pauli operators based on the probability distribution to obtain the expected value of the target quantum system for the observable, thereby saving computing resources to a certain extent.

[0029] It can be understood that according to the embodiment of the present disclosure, it can be widely applied to all quantum applications that need to estimate the expected value in the form of Tr[Oρ], where ρ is the quantum state of n qubits generated by a quantum device.

[0030] According to some embodiments, the observable includes the Hamiltonian corresponding to the target quantum system of n qubits. Therefore, the n - qubit observable O can be any physically expressible Hamiltonian.

[0031] In fact, unless the Hamiltonian H can be expanded in a direct - product form, it is experimentally very difficult to directly estimate the Hamiltonian expectation value <h>For. In order to estimate experimentally <h>, the Hamiltonian H can be expanded as a weighted sum of Pauli operators, as shown in Equation (1):

[0032]

[0033] In Equation (1), denotes the set of Pauli operators for n qubits (hereinafter referred to as the Pauli basis), and c P = Tr[HP] is a real number representing the weight (i.e., the decomposition coefficient) corresponding to the corresponding Pauli operator P. In this set of Pauli operators, the number of elements in the n-qubit Pauli basis is |P n | = 4 n . Since the set of Pauli operators P n constitutes a basis for the n-qubit operator space, any n-qubit operator can be expanded in the form of Equation (1). Therefore, Equation (1) can be called the Pauli basis expansion of the Hamiltonian H. That is, given the Hamiltonian H corresponding to any system, it can be decomposed according to Equation (1), and the expansion coefficients c P can be calculated and stored using a classical computer. In fact, only the Pauli terms corresponding to non-zero coefficients need to be recorded and stored.

[0034] Using Equation (1), the expectation value <h>It can be further expressed as shown in Formula (2):

[0035]

[0036] That is, the estimated expected value <h>The task is converted into the process of estimating a set of Pauli operator expectation values {<Ψ(θ)|P|Ψ(θ)>: P ∈ P n &c P ≠ 0}.

[0037] It can be understood that in the embodiments of determining the ground state energy of the Hamiltonian, the quantum state |Ψ(θ)> can be understood as the quantum state obtained in an optimization process, and this quantum state can be generated by a parameterized quantum circuit. In obtaining the expectation value corresponding to the quantum state |Ψ(θ)> <h>After that, combined with the optimization algorithms in classical machine learning (such as the gradient descent method), continuously adjust and optimize the parameter θ to minimize the expected value <Ψ(θ)|H|Ψ(θ)>, so as to obtain the ground state energy E0.

[0038] It can be conceived that all Pauli operators in the set S = {P: c P ≠ 0} formed by decomposing are usually treated equally. That is, for each Pauli operator in the set S = {P: c P ≠ 0}, estimate its corresponding expected value respectively, and then determine the target expected value corresponding to the Hamiltonian. For estimating the expected value of the quantum state |Ψ(θ)> generated by the n-qubit quantum device in the VQE algorithm is taken as an example to illustrate. First, the n-qubit Hamiltonian H in the form of formula (1) and its Pauli basis expansion can be determined, and the error value ε and the non-confidence level δ can be determined. The error value ε is given by the experimenter, recording the accepted estimated error value; the non-confidence level δ is given by the experimenter, recording the confidence level of accepting wrong judgments, so as to ensure that there is a probability of more than 1 - δ that the estimated expected value is located in <h>-ε, <h>within the interval of +ε. Then, perform the following steps:

[0039] Step 1: Statistically decompose the obtained multiple Pauli operators to form a set of Pauli operators S = {P: cP ≠ 0}.

[0040] Step 2: For each Pauli operator P in the set S, estimate its expected value using the following method := <Ψ(θ)|P|Ψ(θ)>

[0041] Step 2.1: Call a quantum device to generate the quantum state Ψ(θ), measure this quantum state based on the Pauli operator P, and record the measurement result b i ∈ {-1, 1}

[0042] Step 2.2: Repeat Step 2.1 a total of N (a positive integer) times to obtain a set of measurement results Using this data, calculate:

[0043]

[0044] In fact, is Approximate estimation.

[0045] Step 3: Use the data set obtained in Step 2 Calculate

[0046]

[0047] Step 4: Output as the expected value <h>Unbiased estimation.

[0048] In some embodiments, Since the quantum effect disappears after the quantum state is measured and it can no longer participate in the calculation, the number of quantum states consumed in this scheme (i.e., the number of times the quantum device is called) is:

[0049]

[0050] where |S| represents the number of elements in set S, that is, the number of non-zero coefficient terms in the expansion of Hamiltonian H in the Pauli basis. It can be seen that in the worst case, |S| = |P n | = 4 n .

[0051] However, for a given Hamiltonian H, it can be seen that if the coefficient c of a certain Pauli operator P P is very small, then its corresponding expected value< / h> Target expected value <h>has limited influence; conversely, if the coefficient c of a certain Pauli operator P P is very large, then its corresponding expected value< / h> Target expected value <h>The impact is very significant. That is to say, the focus can be placed on those Pauli operators with "high weights". Therefore, a probability distribution is constructed from the decomposition coefficients {c P}, and these probability values represent the weights of the corresponding Pauli operators. Then, using the Monte Carlo sampling (with replacement) method, only the expected values of those Pauli terms that are easily sampled are estimated. Here, "easily sampled" corresponds to those Pauli terms with large weights. The principle of Monte Carlo sampling ensures that only a part of the Pauli terms in the set (rather than all) need to be sampled and their expected values estimated, and after weighting, they can well approximate the target expected value <h>。

[0052] To use the Monte Carlo sampling idea, first, a probability distribution Pr(·) defined on the set S = {P : c P ≠ 0} formed by the multiple Pauli operators obtained by decomposition needs to be introduced. This probability distribution can well characterize the weights of these multiple Pauli operators. Specifically, for the Pauli basis expansion formula (1) of the given Hamiltonian H, a new variable is defined, representing the sum of the absolute values of the multiple decomposition coefficients corresponding to the multiple Pauli operators one by one:

[0053]

[0054] Based on the variable Δ, the probability distribution can be defined as:

[0055]

[0056] Since Pr(P) ≥ 0 and ∑ P∈S Pr(P) = 1, Pr(P) defined as above is indeed a probability distribution defined on the set S. Using this probability distribution, formula (2) can be expressed as shown in formula (3):

[0057]

[0058] where sign(c P ) represents the sign of the coefficient c P : if c P is negative, sign(c P ) = -1; if c P is positive, sign(c P ) = 1. It can be understood that c P is not 0. The above formula expresses the expected value <h>Denoted as the random variable X P := sign(c P )·Δ·The expected value form of <Ψ(θ)|P|Ψ(θ)>. Starting from this formula, we can use the Monte Carlo sampling method to estimate the target expected value <h>。

[0059] Therefore, in the present disclosure, based on the multiple decomposition coefficients obtained by decomposition, the probability distribution corresponding to the multiple Pauli operators obtained by decomposition can be determined, so as to sample the multiple Pauli operators based on the probability distribution, obtain the expected value of the target quantum system for this observable, thereby saving computational resources to a certain extent.

[0060] According to some embodiments, sampling the multiple Pauli operators based on the probability distribution to determine the expected value of the target quantum system for the observable based on the sampling result includes: repeatedly performing the second operation a total of L times to obtain the first value obtained each time the second operation is completed, where L is a positive integer; and determining the expected value of the target quantum system for the observable based on all the first values obtained after the L times of the second operation. The second operation includes the following steps: sampling among the multiple Pauli operators according to the probability distribution to obtain a first Pauli operator; measuring the first quantum state corresponding to the target quantum system based on the first Pauli operator to obtain a measurement result, where the first quantum state is determined based on the information to be processed of the target quantum system; and determining the first value based on the sum of the absolute values, the sign of the decomposition coefficient corresponding to the first Pauli operator, and the measurement result.

[0061] Experimentally, after each quantum state is measured, its quantum effect disappears and cannot participate in the calculation anymore. Therefore, we use the number of quantum states consumed by the scheme (i.e., the number of times the quantum device is called) as the complexity of the scheme. This complexity represents the consumption degree of hardware resources such as quantum devices and classical computer memories and processors.

[0062] Therefore, according to some embodiments, the execution times L of the second operation can be determined based on the following formula:

[0063]

[0064] where Δ is the sum of the absolute values, ε is the error tolerance of the preset expected value, and 1 - δ is the preset confidence level.

[0065] According to some embodiments, determining the expected value of the target quantum system for the observable based on all the first values obtained after the L operations includes:

[0066]

[0067] where X l represents the first value obtained by the l-th time of the second operation.

[0068] In an exemplary embodiment according to the present disclosure, continuing with the expectation value of the quantum state |Ψ(θ)> generated by an n-qubit quantum device in the VQE algorithm First, an n-qubit Hamiltonian H in the form shown in Equation (1) and its Pauli basis expansion can be determined, and an error value ε and a non-confidence level δ can be determined. The error value ε is given by the experimenter, recording the accepted estimated error value; the non-confidence level δ is given by the experimenter, recording the confidence level of accepting a wrong judgment, such that there is a probability of more than 1 - δ that the estimated expectation value lies within <h>-ε, <h>within the interval of +ε. Then, perform the following steps:

[0069] Step 1: Data preprocessing:

[0070] Step 1.1: Statistically decompose the obtained multiple Pauli operators to form a set of Pauli operators S = {P: c P ≠ 0}.

[0071] Step 1.2: According to the Pauli operator expansion of H, calculate the sum of the absolute values of the multiple decomposition coefficients corresponding to the multiple Pauli operators, denoted as Δ, and then calculate the probability distribution Pr(·).

[0072] Step 1.3: Determine the total number of sampling times

[0073] Step 2: Repeat the following steps L times, and let l denote the l-th round of data.

[0074] Step 2.1: Sampling with replacement from the set S according to the probability distribution Pr(·) to obtain the Pauli operator P l .

[0075] Step 2.2: Call the quantum device to generate the quantum state Ψ(θ), and perform measurements based on the Pauli operator P l to obtain the measurement result b l ∈ {-1, 1}.

[0076] Step 2.3: Calculate from the measurement result and store the data.

[0077] Step 3: Using the data set {X l} obtained in Step 2, calculate to obtain:

[0078]

[0079] Step 4: Output as the expected value <h>Unbiased estimate.

[0080] It can be understood that the absolute value calculation, the sampling process, and the process of obtaining the expected value based on the measurement results can be efficiently performed on a classical computer, which will not be elaborated here.

[0081] It should be understood that the above-described embodiments are merely an exemplary implementation manner according to the method of the present disclosure, and various forms of processes shown above can also be used, reordering, adding, or deleting steps. For example, the steps recorded in the present disclosure can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved, which will not be limited herein.

[0082] By comparing with L total and N total It can be seen that the coefficient of the scheme complexity changes from |S| to |Δ 2 |. For the scheme that treats all Pauli operators in set S equally, the coefficients in the H Pauli basis decomposition do not affect the number of samplings, that is, this information is not fully utilized. In the present disclosure, this information is fully utilized to construct a Hamiltonian ground state energy estimation scheme based on Monte Carlo sampling, which can significantly reduce the number of quantum states consumed by the scheme in many cases.

[0083] Since the new scheme does not treat all Pauli terms in set S equally, but considers the coefficients of each Pauli term, its complexity depends on the coefficients {c P}. Therefore, it can be further thought that there is a possibility for the experimenter to select a suitable method according to the actual situation of the Hamiltonian H.

[0084] Specifically, according to some embodiments, performing the first operation includes: determining the square value of the sum of the absolute values; and in response to determining that the square value is less than the number of Pauli operators of the plurality of Pauli operators, performing the first operation.

[0085] According to some embodiments, it further includes: in response to determining that the square value is not less than the number of Pauli operators of the plurality of Pauli operators, performing a third operation. The third operation includes the following steps: repeating the fourth operation N times in total to obtain the second value obtained each time the fourth operation is completed, where N is a positive integer; and based on all the second values obtained after the N times of the fourth operation, determining the expected value of the target quantum system for the observable. The fourth operation includes: for each Pauli operator of the plurality of Pauli operators, measuring the first quantum state corresponding to the target quantum system based on the Pauli operator to obtain the measurement result as the second value.

[0086] Figure 2 A flowchart of obtaining an expected value by selecting a corresponding solution according to an embodiment of the present disclosure is shown. As Figure 2 shown, in method 200, after obtaining the square value of the sum of the absolute values of the decomposition coefficients obtained by decomposing the Pauli operator through steps 210-230, i.e., |Δ 2 |, by comparing the number of Pauli operators |S| in the set S with this square value |Δ 2 | (i.e., step 240), corresponding operations (i.e., step 250 or step 260) are performed to achieve the purpose of always obtaining the expected value with less computing resources.

[0087] According to some embodiments, the number of executions N of the fourth operation is determined based on the following formula:

[0088]

[0089] where ε is the preset error tolerance of the expected value, and 1 - δ is the preset confidence level.

[0090] According to some embodiments, determining the expected value of the target quantum system for the observable based on all the second numerical values obtained after the N - th fourth operation includes:

[0091]

[0092] where, b i is the second numerical value obtained after the i - th fourth operation, c P is the decomposition coefficient corresponding to the Pauli operator P, and P n is the set of Pauli operators formed by the multiple Pauli operators.

[0093] Specifically, in some examples, when |Δ 2 | << |S| (<< means much less than), the solution of performing the first operation has a significant advantage over the solution of performing the third operation, and the number of quantum states consumed can be greatly reduced. Therefore, when the experimenter calculates and finds that |Δ 2 | << |S|, the solution of performing the first operation can be selected; if |Δ 2 | >> |S|, the solution of performing the third operation can be selected; if |Δ 2 | ≈ |S|, any solution can be selected according to the actual situation.

[0094] In fact, the situation of |Δ 2 | << |S| exists. The following considers two special cases to illustrate the importance of having the selection ability. Case 1: The solution of performing the first operation is much better than the solution of performing the first operation. Assume c P = 1 / |S|, that is, all Pauli terms in set S have the same weight. Through calculation, it can be found that Δ = ∑ P∈S |c P | = 1, which means that the scheme for performing the first operation only requires times of sampling. If S ≈ 4 n , then the scheme for performing the first operation is exponentially accelerated. Case 2: The scheme for performing the third operation is much better than the scheme for performing the first operation. Assume c P = 1 / |S| k , that is, all Pauli terms in set S have the same weight but are relatively small. Through calculation, it can be found that Δ = ∑ P∈S |c P | = |S| k-1 , which means that the scheme for performing the first operation requires times of sampling. When k becomes larger, the number of quantum states required by the scheme for performing the first operation exponentially increases.

[0095] Therefore, the embodiments according to the present disclosure have strong practicability and can be widely applied to small and medium-sized quantum devices with hundreds of physical qubits integrated thereon, endowing experimenters with the advantage of selecting a suitable expected value estimation scheme according to the Hamiltonian H, continuously improving the operation efficiency of recent quantum algorithms, and further using these algorithms to achieve more valuable applications and accelerating the industrialization process of quantum computing.

[0096] According to an embodiment of the present disclosure, as Figure 3 shown, there is also provided an information processing apparatus 300 based on a quantum system, including: a first determination unit 310 configured to determine a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, the Pauli operator expansion of the observable including a plurality of Pauli operators and a plurality of decomposition coefficients corresponding to the plurality of Pauli operators one by one, where n is a positive integer; a second determination unit 320 configured to determine the sum of the absolute values of the plurality of decomposition coefficients; a first execution unit 330 configured to perform a first operation, and the first operation includes the following steps: a first determination subunit 3301 configured to determine a probability distribution of the plurality of Pauli operators based on the sum of the absolute values and the plurality of decomposition coefficients; and a second determination subunit 3302 configured to sample the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on the sampling result.

[0097] Here, the operations of the above units 310 to 330 of the information processing apparatus 300 based on the quantum system are respectively similar to the operations of steps 110 to 130 described above, and will not be elaborated here.

[0098] According to an embodiment of the present disclosure, there is also provided an electronic device, a readable storage medium, and a computer program product.

[0099] Referring Figure 4 , the structural block diagram of the electronic device 400 that can be used as a server or a client of the present disclosure will now be described. It is an example of a hardware device that can be applied to various aspects of the present disclosure. The electronic device is intended to represent various forms of digital electronic computer devices, such as, laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as, personal digital processors, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0100] As Figure 4 shown, the electronic device 400 includes a computing unit 401, which can perform various appropriate actions and processes according to the computer program stored in the read-only memory (ROM) 402 or the computer program loaded from the storage unit 408 into the random access memory (RAM) 403. In the RAM 403, various programs and data required for the operation of the electronic device 400 can also be stored. The computing unit 401, the ROM 402, and the RAM 403 are connected to each other through a bus 404. The input / output (I / O) interface 405 is also connected to the bus 404.

[0101] A plurality of components in the electronic device 400 are connected to the I / O interface 405, including: an input unit 406, an output unit 407, a storage unit 408, and a communication unit 409. The input unit 406 can be any type of device that can input information into the electronic device 400. The input unit 406 can receive input digital or character information, and generate key signal inputs related to the user settings and / or function controls of the electronic device, and can include, but is not limited to, a mouse, a keyboard, a touch screen, a trackpad, a trackball, a joystick, a microphone, and / or a remote control. The output unit 407 can be any type of device that can present information, and can include, but is not limited to, a display, a speaker, a video / audio output terminal, a vibrator, and / or a printer. The storage unit 408 can include, but is not limited to, a magnetic disk, an optical disk. The communication unit 409 allows the electronic device 400 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks, and can include, but is not limited to, a modem, a network card, an infrared communication device, a wireless communication transceiver, and / or a chipset, such as a Bluetooth device, an 802.11 device, a WiFi device, a WiMax device, a cellular communication device, and / or the like.

[0102] The computing unit 401 can be various general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of the computing unit 401 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 401 executes the various methods and processes described above, such as method 100. For example, in some embodiments, method 100 can be implemented as a computer software program tangibly embodied in a machine-readable medium, such as the storage unit 408. In some embodiments, part or all of the computer program can be loaded and / or installed onto the electronic device 400 via the ROM 402 and / or the communication unit 409. When the computer program is loaded into the RAM 403 and executed by the computing unit 401, one or more steps of method 100 described above can be executed. Alternatively, in other embodiments, the computing unit 401 can be configured to execute method 100 in any other suitable manner (e.g., by means of firmware).

[0103] Various embodiments of the systems and techniques described above in this document can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a dedicated or general-purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit the data and instructions to the storage system, the at least one input device, and the at least one output device.

[0104] The program code for implementing the methods of the present disclosure can be written in any combination of one or more programming languages. These program codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when the program code is executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code can be executed entirely on the machine, partially on the machine, as an independent software package partially on the machine and partially on a remote machine, or entirely on a remote machine or server.

[0105] In the context of this disclosure, a machine-readable medium can be a tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium can be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of the machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0106] In order to provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and a pointing device (e.g., a mouse or a trackball) by which the user can provide input to the computer. Other kinds of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0107] The systems and techniques described herein can be implemented in a computing system that includes backend components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes frontend components (e.g., a user computer having a graphical user interface or a web browser through which the user can interact with an implementation of the systems and techniques described herein), or a computing system that includes any combination of such backend components, middleware components, or frontend components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), the Internet, and a blockchain network.

[0108] A computer system may include a client and a server. The client and the server are generally far from each other and usually interact via a communication network. The relationship between the client and the server is generated by computer programs running on respective computers and having a client-server relationship with each other. The server may be a cloud server, a server of a distributed system, or a server incorporating a blockchain.

[0109] It should be understood that various forms of the processes shown above can be used, steps can be reordered, added or deleted. For example, the steps described in this disclosure can be executed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this is not limited herein.

[0110] Although embodiments or examples of the present disclosure have been described with reference to the accompanying drawings, it should be understood that the above methods, systems and devices are merely exemplary embodiments or examples, and the scope of the present invention is not limited by these embodiments or examples, but is only defined by the authorized claims and their equivalent scope. Various elements in the embodiments or examples can be omitted or replaced by their equivalent elements. In addition, the steps can be executed in an order different from that described in the present disclosure. Further, the various elements in the embodiments or examples can be combined in various ways. Importantly, with the evolution of technology, many of the elements described herein can be replaced by equivalent elements that emerge after the present disclosure.< / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h> < / h>

Claims

1. An information processing method based on a quantum system, comprising: Determining a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, the Pauli operator expansion of the observable including a plurality of Pauli operators and a plurality of decomposition coefficients corresponding one-to-one to the plurality of Pauli operators, where n is a positive integer; Determining the sum of the absolute values of the plurality of decomposition coefficients; Performing a first operation, the first operation comprising the following steps: Based on the sum of the absolute values and the plurality of decomposition coefficients, determining a probability distribution of the plurality of Pauli operators; And Sampling the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on the sampling result.

2. The method according to claim 1, wherein, Sampling the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on the sampling result includes: Repeatedly performing a second operation a total of L times to obtain a first value obtained each time the second operation is performed, where L is a positive integer; and Based on all the first values obtained after the L times of performing the second operation, determining an expected value of the target quantum system for the observable, where The second operation comprises the following steps: Sampling among the plurality of Pauli operators according to the probability distribution to obtain a first Pauli operator; Measuring a first quantum state corresponding to the target quantum system based on the first Pauli operator to obtain a measurement result, where the first quantum state is determined based on information to be processed of the target quantum system; and Based on the sum of the absolute values, the sign of the decomposition coefficient corresponding to the first Pauli operator, and the measurement result, determining the first value.

3. The method according to claim 2, wherein, The number of executions L of the second operation is determined based on the following formula: where Δ is the sum of the absolute values, ε is a preset error tolerance of the expected value, and 1 - δ is a preset confidence level.

4. The method according to claim 2, wherein, Determine the expected value of the target quantum system for the observable based on the following formula including: Among them, X l represents the first numerical value obtained from the l-th said second operation.

5. The method according to any one of claims 1-4, wherein, Performing the first operation includes: Determining the square value of the sum of the absolute values; and In response to determining that the square value is less than the number of Pauli operators of the plurality of Pauli operators, performing the first operation.

6. The method according to claim 5, further comprising: In response to determining that the square value is not less than the number of Pauli operators of the plurality of Pauli operators, performing a third operation, the third operation comprising the following steps: Repeatedly performing a fourth operation a total of N times to obtain a second value obtained each time the fourth operation is performed, where N is a positive integer; and Based on all the second values obtained after the N times of performing the fourth operation, determining an expected value of the target quantum system for the observable, where The fourth operation includes: for each Pauli operator among the plurality of Pauli operators, measuring the first quantum state corresponding to the target quantum system based on the Pauli operator to obtain a measurement result as the second value.

7. The method according to claim 6, wherein, The number of executions N of the fourth operation is determined based on the following formula: where ε is a preset error tolerance of the expected value, and 1 - δ is a preset confidence level.

8. The method according to claim 6, wherein, Determine the expected value of the target quantum system for the observable based on the following formula including: Among them, b i is the second value obtained after the i-th fourth operation, c P is the decomposition coefficient corresponding to the Pauli operator P, P n is the set of Pauli operators formed by the multiple Pauli operators.

9. The method according to claim 1, wherein The observable includes a Hamiltonian corresponding to a target quantum system of n qubits.

10. An information processing apparatus based on a quantum system, comprising: A first determination unit, configured to determine a Pauli operator expansion of an observable corresponding to a target quantum system of n qubits, where the Pauli operator expansion of the observable includes a plurality of Pauli operators and a plurality of decomposition coefficients corresponding to the plurality of Pauli operators one by one, and n is a positive integer; A second determination unit, configured to determine the sum of the absolute values of the plurality of decomposition coefficients; A first execution unit, configured to execute a first operation, where the first operation includes the following steps: A first determination subunit, configured to determine a probability distribution of the plurality of Pauli operators based on the sum of the absolute values and the plurality of decomposition coefficients; And A second determination subunit, configured to sample the plurality of Pauli operators based on the probability distribution to determine an expected value of the target quantum system for the observable based on a sampling result.

11. The device according to claim 10, wherein The second determination subunit includes: An execution subunit, configured to repeatedly execute a second operation L times to obtain a first value obtained each time the second operation is executed, where L is a positive integer; and A third determination subunit, configured to determine an expected value of the target quantum system for the observable based on all the first values obtained after the L times of the second operation, where The second operation includes the following steps: Sampling among the plurality of Pauli operators according to the probability distribution to obtain a first Pauli operator; Measuring a first quantum state corresponding to the target quantum system based on the first Pauli operator to obtain a measurement result, where the first quantum state is determined based on information to be processed of the target quantum system; and Determining the first value based on the sum of the absolute values, the sign of the decomposition coefficient corresponding to the first Pauli operator, and the measurement result.

12. The apparatus according to claim 11, wherein, The number of executions L of the second operation is determined based on the following formula: where Δ is the sum of the absolute values, ε is a preset error tolerance of the expected value, and 1 - δ is a preset confidence level.

13. The device according to claim 11, wherein, Determine the expected value of the target quantum system for the observable based on the following formula including: Among them, X l represents the first numerical value obtained from the l-th said second operation.

14. The device according to any one of claims 10 - 13, wherein, Executing the first operation includes: Determining a squared value of the sum of the absolute values; and In response to determining that the squared value is less than the number of Pauli operators of the plurality of Pauli operators, executing the first operation.

15. The apparatus according to claim 14, further comprising: A second execution unit, configured to, in response to determining that the squared value is not less than the number of Pauli operators of the plurality of Pauli operators, execute a third operation, where the third operation includes the following steps: Repeatedly executing a fourth operation N times to obtain a second value obtained each time the fourth operation is executed, where N is a positive integer; and Determining an expected value of the target quantum system for the observable based on all the second values obtained after the N times of the fourth operation, where The fourth operation includes: for each Pauli operator among the plurality of Pauli operators, measuring the first quantum state corresponding to the target quantum system based on the Pauli operator to obtain a measurement result as the second value.

16. The device according to claim 15, wherein, The number of executions N of the fourth operation is determined based on the following formula: where ε is a preset error tolerance of the expected value, and 1 - δ is a preset confidence level.

17. The device according to claim 15, wherein, Determine the expected value of the target quantum system for the observable based on the following formula including: wherein, b i is the second value obtained after the i-th fourth operation, and c P is the decomposition coefficient corresponding to the Pauli operator P, and P n is the set of Pauli operators formed by the plurality of Pauli operators.

18. The device according to claim 10, wherein The observable includes the Hamiltonian corresponding to the target quantum system of n qubits.

19. An electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the method according to any one of claims 1-9.

20. A non-transitory computer-readable storage medium storing computer instructions, wherein, The computer instructions are used to cause the computer to execute the method according to any one of claims 1-9.

21. A computer program product, comprising a computer program, wherein, The computer program, when executed by a processor, implements the method according to any one of claims 1-9.

Images