Information processing method and device based on quantum system

Abstract

The present disclosure provides an information processing method and device based on a quantum system, which relates to the field of quantum computing technology, especially to quantum simulation technology and the field of extracting classical information based on quantum devices. The specific implementation scheme is: based on the Hamiltonian, multiple subcircuits of the quantum system and the forward and reverse ordering of the multiple subcircuits are determined; the multiple subcircuits in the forward order are used to construct a first quantum circuit, and the multiple subcircuits in the reverse order are used to construct a second quantum circuit; the first expected result of the quantum system for the target observable quantity is obtained when the first quantum circuit simulates the first quantum state of the quantum system at the evolution time t; the second expected result of the quantum system for the target observable quantity is obtained when the second quantum circuit simulates the second quantum state of the quantum system at the evolution time t; based on the first expected result and the second expected result, the expected value of the target observable quantity is obtained. Based on this method, the simulation accuracy of the quantum system is effectively improved.

Description

Technical Field

[0001] The present disclosure relates to the field of quantum computing technology, and in particular to the field of quantum simulation and extraction of classical information based on quantum devices. Background Art

[0002] At present, quantum computing technology is moving towards scale and practical application. Quantum simulation is a core application of quantum computing, that is, simulating the dynamic evolution of quantum systems. Efficient and practical quantum simulation methods not only have good application prospects in quantum chemistry research and development of new drugs and batteries, but are also the core sub-steps of several common quantum algorithms in quantum machine learning. Furthermore, estimating the expected value of a quantum system under a certain observable is an important and practical operation in common quantum algorithms.

[0003] As quantum technology is in the gradual development stage, the existing quantum devices have a small number of qubits and are greatly affected by noise, resulting in limited accuracy. Therefore, how to use fewer qubits and basic single-qubit quantum gates or two-qubit quantum gates to achieve the desire to extract observable quantities has become an important consideration for recent quantum algorithms. Summary of the invention

[0004] The present disclosure provides a quantum system-based information processing method and device.

[0005] According to one aspect of the present disclosure, there is provided a method for information processing based on a quantum system, comprising:

[0006] Determine multiple subcircuits of the quantum system based on the Hamiltonian, and forward sorting and reverse sorting of the multiple subcircuits; wherein the multiple subcircuits in the forward sorting are used to construct a first quantum circuit, and the multiple subcircuits in the reverse sorting are used to construct a second quantum circuit;

[0007] Obtaining a first expected result of a target observable quantity of the quantum system when the first quantum circuit simulates a first quantum state of the quantum system at an evolution time t; and

[0008] Obtaining a second expected result of the quantum system on the target observable when the second quantum circuit simulates the second quantum state of the quantum system at the evolution time t;

[0009] Based on the first expected result and the second expected result, an expected value of the target observable quantity is obtained.

[0010] According to another aspect of the present disclosure, there is provided an information processing device based on a quantum system, comprising:

[0011] A determination module, used to determine multiple subcircuits of the quantum system based on the Hamiltonian, and a forward sorting and a reverse sorting of the multiple subcircuits; wherein the multiple subcircuits in the forward sorting are used to construct a first quantum circuit, and the multiple subcircuits in the reverse sorting are used to construct a second quantum circuit;

[0012] A first acquisition module is used to acquire a first expected result of a target observable quantity of the quantum system when the first quantum circuit simulates the first quantum state of the quantum system at the evolution time t; and

[0013] A second acquisition module is used to obtain a second expected result of the quantum system on the target observable quantity when the second quantum circuit simulates the second quantum state of the quantum system at the evolution time t;

[0014] The estimation module is used to obtain an expected value of a target observable quantity based on the first expected result and the second expected result.

[0015] According to another aspect of the present disclosure, there is provided an electronic device, comprising:

[0016] at least one processor; and

[0017] a memory communicatively connected to at least one processor; wherein,

[0018] The memory stores instructions that can be executed by at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform an information processing method based on a quantum system.

[0019] According to another aspect of the present disclosure, there is provided a quantum computing device, comprising:

[0020] At least one Quantum Processing Unit (QPU);

[0021] a memory coupled to at least one QPU and configured to store executable instructions,

[0022] The instructions are executed by at least one quantum processing unit to enable the at least one quantum processing unit to perform an information processing method based on a quantum system.

[0023] According to another aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to cause a computer to execute an information processing method based on a quantum system.

[0024] According to another aspect of the present disclosure, a computer program product is provided, including a computer program, which implements an information processing method based on a quantum system when executed by a processor.

[0025] The solution provided in this embodiment realizes the evolution of forward and reverse quantum circuits through the first quantum circuit and the second quantum circuit, which can eliminate or mitigate the errors of the two quantum circuits, thereby effectively improving the simulation accuracy of the estimated value of the observable quantity.

[0026] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0028] Figure 1 is a schematic diagram of the structure of a quantum circuit in an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0029] Figure 2 is a flowchart of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0030] Figure 3 is a schematic diagram of the structure of a quantum circuit in an information processing method based on a quantum system according to another embodiment of the present disclosure;

[0031] Figure 4 is a schematic structural diagram of a sub-circuit of an information processing method based on a quantum system according to another embodiment of the present disclosure;

[0032] Figure 5a is a schematic diagram of the overall process of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0033] Figure 5b is a schematic diagram of a forward circuit structure of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0034] Figure 5c is a schematic diagram of the reverse circuit structure of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0035] Figure 6a is a schematic diagram of the overall process of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0036] Figure 6b is a schematic diagram of a forward circuit structure of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0037] Figure 6c is a schematic diagram of the reverse circuit structure of an information processing method based on a quantum system according to an embodiment of the present disclosure;

[0038] Figure 7 is a schematic diagram of the structure of an information processing device based on a quantum system according to an embodiment of the present disclosure;

[0039] Figure 8 It is a block diagram of an electronic device used to implement the information processing method based on quantum system according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0040] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0041] The terms "first", "second", etc. in the disclosed embodiments are used to distinguish similar objects, and are not necessarily used to describe a specific order or precedence. In addition, the terms "including" and "having" and any variations thereof are intended to cover non-exclusive inclusions. For example, a series of steps or units are included. The method, system, product, or device is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products, or devices.

[0042] For simulating the dynamic evolution of a quantum system, specifically, for a quantum system whose evolution is determined by a certain Hamiltonian H, the quantum state of the quantum system at the evolution time t is |ψ(t)>=e -iHt |ψ(0)>, where |ψ(0)> represents the initial state of the quantum system, which can also be called a pure state. is an imaginary number, U = e -iHt is the evolved unitary matrix. The goal of quantum simulation is to realize the evolved unitary matrix U=e by designing quantum circuits. -iHt , and then the state of this quantum system at evolution time t is prepared with a certain accuracy |ψ(t)>. Therefore, how to use basic quantum gates such as single-qubit quantum gates or two-qubit quantum gates to obtain higher simulation accuracy in order to extract the expectation of the target observable quantity has become a problem that needs to be solved urgently. Based on this goal, the embodiment of the present disclosure proposes a method to improve the simulation accuracy to extract the classical information of expectation.

[0043] A quantum circuit includes multiple sub-circuits, and different sub-circuits will construct different quantum circuits if they are sorted in different orders. Since the forward-sorted quantum circuit and the reverse-sorted quantum circuit will each produce errors in the process of seeking expectations after simulating the Hamiltonian. Therefore, if the expected values ​​are estimated separately through the evolution of the forward quantum circuit and the reverse quantum circuit, and then the expected values ​​estimated by the two quantum circuits are combined to determine the final expected value, the errors generated by the two quantum circuits can be offset or mitigated to a certain extent, so that the expected value of the observable quantity estimated based on the quantum simulation has a higher accuracy. Based on this technical concept, the present disclosure constructs a quantum circuit with two sub-circuits arranged in opposite orders to improve the simulation accuracy.

[0044] like Figure 1 FIG. 1 is a schematic diagram of the structure of a quantum circuit designed in an embodiment of the present disclosure, which includes two quantum circuits. The subcircuits used in the two quantum circuits are the same, but the subcircuits are arranged in opposite orders. Figure 1 The method includes two sub-circuits, the first quantum circuit and the second quantum circuit. The two quantum circuits each contain N sub-circuits, and the expectations of observable quantities are extracted by the two quantum circuits. The first expected result of the observable quantity is obtained by running the first quantum circuit, and the second expected result of the observable quantity is obtained by running the second quantum circuit, thereby obtaining the final expectation of the observable quantity.

[0045] like Figure 2 FIG. 1 is a flow chart of an information processing method based on a quantum system in an embodiment of the present disclosure, including:

[0046] S201, determining multiple subcircuits of a quantum system based on the Hamiltonian, and a forward sorting and a reverse sorting of the multiple subcircuits, wherein the multiple subcircuits in the forward sorting are used to construct a first quantum circuit, and the multiple subcircuits in the reverse sorting are used to construct a second quantum circuit.

[0047] The system Hamiltonian is decomposed into several sub-Hamiltonians, and then the sub-Hamiltonians are arranged in a certain order. Based on the arrangement order of the sub-Hamiltonians, multiple sub-circuits arranged in the corresponding order are obtained. These sequentially arranged sub-circuits constitute a forward-ordered quantum circuit. This forward-ordered quantum circuit is used as the first quantum circuit, and another quantum circuit with the sub-circuit arrangement order opposite to that of the first quantum circuit is used as the second quantum circuit.

[0048] S202, obtaining a first expected result of a quantum system for a target observable quantity when a first quantum circuit simulates a first quantum state of the quantum system at an evolution time t; and obtaining a second expected result of a quantum system for a target observable quantity when a second quantum circuit simulates a second quantum state of the quantum system at an evolution time t.

[0049] It should be noted that the present disclosure does not limit the order of obtaining the two expected results, that is, the first expected result can be obtained first, or the second expected result can be obtained first, and under certain conditions, the first expected result and the second expected result can also be obtained at the same time.

[0050] S203: Obtain an expected value of the target observable quantity based on the first expected result and the second expected result.

[0051] The two expected results obtained by quantum measurement can be recognized and processed by a classical computer. In this case, both quantum circuits are in the quantum device and act on the initial pure state of the quantum system |ψ(0)> to obtain the first expected result and the second expected result.

[0052] In the embodiments of the present disclosure, two quantum circuits are constructed at the same time, and the expected results obtained by performing quantum simulations on the two quantum circuits are obtained. Since the forward-ordered quantum circuit and the reverse-ordered quantum circuit will each produce errors in the process of seeking expectations after simulating the Hamiltonian. The present disclosure obtains the expected value of the target observable quantity by evolving the forward and reverse quantum circuits, and then estimating the expected values ​​and processing the two respectively, which can offset or mitigate the errors generated by the two quantum circuits to a certain extent, so that the expected value of the observable quantity estimated based on the quantum circuit has higher accuracy. And the present disclosure does not need to introduce additional quantum bits, and can use basic quantum gates to realize quantum circuits, which can improve the estimation accuracy of expectations with the same number of quantum gates.

[0053] Among them, the positive and reverse order of the sorting sequence of each sub-circuit is based on the relative relationship between the two, that is, as long as in two quantum circuits, except for the opposite arrangement order of each other's sub-circuit, other elements are the same, any one of the two quantum circuits can be used as a quantum circuit with positive order sorting, and the other quantum circuit can be used as a quantum circuit with reverse order sorting.

[0054] To facilitate understanding of how to determine multiple sub-circuits of a quantum system based on the Hamiltonian, the present disclosure describes two schemes, a first-order product formula and a randomized product formula:

[0055] 1) First-order product formula

[0056] Since the evolution of a quantum system over time is determined by the Hamiltonian of the system, the realization of quantum simulation requires determining the Hamiltonian of the quantum system and the evolution time t of the dynamic evolution of the quantum system. Therefore, constructing a subcircuit based on the first-order product method can be implemented as follows: determining the Hamiltonian, the evolution time t, and the number of time periods into which the evolution time t is divided.

[0057] Since the determined Hamiltonian of a quantum system cannot be used directly to construct a quantum circuit, it is necessary to decompose the Hamiltonian of the quantum system to obtain multiple sub-Hamiltonians so as to use basic quantum gates to construct a quantum circuit. During implementation, multiple sub-circuits can be determined based on multiple sub-Hamiltonians, the evolution time t, and the number of time periods.

[0058] The disclosed embodiment adopts a combination of multiple sub-Hamiltonians, the evolution time t, and the number of time periods into which the evolution time t is divided to determine multiple sub-circuits, thereby obtaining a first quantum circuit and a second quantum circuit. By dividing the evolution time t into multiple time periods, the extraction accuracy of classical information can be improved. In addition, on this basis, adding two quantum circuits, one in forward order and the other in reverse order, can further improve the expected simulation accuracy of the observed quantity.

[0059] For example, the Hamiltonian H of a quantum system can usually be expanded into the sum of many sub-Hamiltonians in the form of Pauli tensors. Its expression is shown in formula (1):

[0060]

[0061] In equation (1), the Hamiltonian H is L sub-Hamiltonians H k H k is the kth sub-Hamiltonian, k∈[1,L].

[0062] After the Hamiltonian is decomposed into sub-Hamiltonians, the sorting order of the sub-Hamiltonians in equation (1) is the forward sorting order of the sub-circuit corresponding to the sub-Hamiltonian. After that, the sub-circuit is further constructed using the first-order product method. In this method, the evolved unitary matrix is ​​expressed as shown in equation (2). For ease of processing, equation (2) can be approximated as shown in equation (3):

[0063]

[0064]

[0065] Wherein, t in the above equations (2) and (3) is the evolution time t, that is, the total simulation time of the quantum system. is an imaginary number, where H k represents the kth sub-Hamiltonian, and the symbol Π represents the quadrature. That is the sub-Hamiltonian H k The corresponding subcircuit.

[0066] In addition, in the first-order product method, the evolution time t can be divided into r segments to further improve and ensure the accuracy of the overall simulation. After the evolution time is divided into r segments, its expression is shown in formula (4):

[0067]

[0068] In formula (4), the parameters have been explained above and will not be repeated here.

[0069] Thus, in the first-order product, by increasing r, the simulation can be controlled to reach any accuracy, thereby obtaining an estimate of <ψ(t)|O|ψ(t)> of a specified accuracy, where It can be realized with basic quantum gates. It can be understood as the sub-Hamiltonian H k The corresponding subcircuit.

[0070] On the basis of dividing the evolution time t into r segments, accordingly, in the embodiment of the present disclosure, the first quantum circuit includes r positive-sequence circuit groups connected in series, wherein each positive-sequence circuit group includes a plurality of sub-circuits sorted in a forward direction; the second quantum circuit includes r reverse-sequence circuit groups connected in series, wherein each reverse-sequence circuit group includes a plurality of sub-circuits sorted in a reverse direction; wherein r is the number of time segments.

[0071] By dividing the evolution time t into r segments, the first quantum circuit and the second quantum circuit constructed include r identical circuit groups, so that the quantum simulation based on r control can achieve arbitrary accuracy, thereby obtaining an estimated value of the expected observable quantity of specified accuracy. In the embodiment of the present disclosure, on the basis of the accuracy that can be achieved by the first-order product method, the first quantum circuit and the second quantum circuit are further superimposed and used, so that higher accuracy expectations can be obtained than the first-order product method when the number of quantum gates is the same.

[0072] For example Figure 3 As shown, it is a schematic diagram of the structure of the first quantum circuit and the second quantum circuit constructed based on the first-order product method. Figure 3 In the example, the first quantum circuit and the second quantum circuit each include r circuit groups. The first quantum circuit includes r positive sequence circuit groups, each positive sequence circuit group includes L sub-circuits, and the L sub-circuits are arranged in a forward sorting order. Figure 3 The subcircuits in the second quantum circuit are arranged in the order of 1-L. Similarly, the second quantum circuit includes r reverse circuit groups. Each reverse circuit group includes L subcircuits, and the L subcircuits are arranged in the reverse order. Figure 3 The subcircuits in are sorted in the order of L-1.

[0073] In this embodiment, the forward sorting order of the subcircuits may be defaulted to the sorting order of decomposing the Hamiltonian into multiple sub-Hamiltonians, that is, the subcircuits are sorted according to the order of the sub-Hamiltonians obtained by formula (1).

[0074] The first-order product method controls the desired simulation accuracy by dividing the number of time periods r. This method is particularly suitable for situations where the number of terms in the Hamiltonian expansion is relatively small.

[0075] 2) Randomized product formula

[0076] In the disclosed embodiment, since the evolution of a quantum system over time is determined by the Hamiltonian of the system, the implementation method for determining each subcircuit based on the randomized product method can be: determining the Hamiltonian, the evolution time t, and the number of samplings required for the specified simulation accuracy. Since the determined quantum system Hamiltonian cannot be used directly to construct a quantum circuit, it is necessary to decompose the quantum system Hamiltonian by the number of terms to obtain multiple sub-terms of the quantum system Hamiltonian. Each sub-term corresponds to a sub-Hamiltonian, and thus multiple sub-Hamiltonians can be determined based on the Hamiltonian. Afterwards, multiple sub-circuits are determined based on multiple sub-Hamiltonians, the evolution time t, and the number of samplings.

[0077] For example, the Hamiltonian H of a quantum system can usually be expanded into the sum of many sub-Hamiltonians in the form of Pauli tensors. Its expression is shown in equation (5):

[0078]

[0079] In equation (5), the Hamiltonian H is L sub-Hamiltonians H k The sum of, ∑ is the sum symbol, H k is the kth sub-Hamiltonian, each sub-term H k The maximum singular value of is equal to 1, and the coefficient h k greater than zero, k∈[1,L].

[0080] The randomized product method mainly samples according to the probability distribution of formula (6) to obtain h k :

[0081] p j =h j / ∑ j h j (6)

[0082] In formula (6), p j =h j / ∑ j h j That is, the coefficient h j Divide by the total coefficient sum, and you get the coefficient h j The weight we get is the coefficient h j The probability distribution of j That is h k .

[0083] After the probability distribution of each coefficient is obtained based on the method in the above formula (6), random sampling is performed on [1,…,L] based on the probability distribution to obtain j n , and then get the corresponding subcircuit After that, the evolved unitary matrix can be expressed as shown in formula (7). For ease of processing, after N samplings, formula (7) can be approximated as shown in formula (8):

[0084]

[0085]

[0086] This achieves a more easily implementable subcircuit using a series of To simulate the target quantum gate e -iHt .

[0087] Wherein, t in the above equations (7) and (8) is the evolution time t, that is, the total simulation time of the quantum system. is an imaginary number, in formula (7) H k represents the kth sub-Hamiltonian, and the symbol Π represents the quadrature. The λ in the j h j .

[0088] The randomized product method controls the simulation to any precision by sampling the total number of times N, thereby obtaining an estimate of <ψ(t)|O|ψ(t)> of a specified precision. This method is particularly suitable for cases where the number of terms in the Hamiltonian expansion is particularly large.

[0089] In the disclosed embodiment, multiple sub-circuits are determined by combining multiple sub-Hamiltonians, evolution time t and sampling number, thereby obtaining a first quantum circuit and a second quantum circuit. In this method, the simulation accuracy can be controlled by controlling the sampling number, and the desired simulation accuracy can be further improved by the forward and reverse first quantum circuit and the second quantum circuit.

[0090] In the randomized product approach, the forward and reverse ordering of multiple subcircuits can be determined based on the following method:

[0091] As described in the above formulas (5) and (6), based on the sub-Hamiltonian, the weight ratio of the coefficients in each sub-Hamiltonian can be calculated respectively, and the obtained results are used as the weight coefficients of multiple sub-circuits. Then, based on the obtained weight coefficients, the probability distribution of the weight coefficients of multiple sub-circuits is constructed; then, based on the probability distribution of the weight coefficients of each sub-circuit, the sampling range ([1,…,L]) is randomly sampled to obtain the sorting order j of each sub-circuit. n .

[0092] The sorting order of each subcircuit is sorted in positive order to obtain a forward sorting; and the sorting order of each subcircuit is sorted in reverse order to obtain a reverse sorting.

[0093] In the disclosed embodiment, random sampling is performed based on the probability distribution of weight coefficients of multiple sub-circuits to determine the arrangement order of each sub-circuit, so that the order of sub-circuits in the quantum circuit is not affected by a fixed ordering method, and the structure of the quantum circuit is more suitable for extracting the expectation of the target observable quantity, thereby improving the simulation accuracy of the expectation.

[0094] The previous section introduced how to determine subcircuits and how to determine the order of subcircuits. The following describes a method for determining the expected result based on two quantum circuits.

[0095] In some embodiments, based on the determined first quantum circuit and second quantum circuit, corresponding expected results can be obtained respectively, including a first expected result and a second expected result. The specific implementation methods are as follows.

[0096] 1) Get the first expected result:

[0097] Obtaining a first expected result of a target observable by a quantum system when a first quantum circuit simulates a first quantum state of a quantum system at an evolution time t can be implemented as follows:

[0098] Obtain n first quantum measurement values, where n is a positive integer greater than 1. Each first quantum measurement value is determined by the quantum computer based on the following method: applying the first quantum circuit to the initial state of the quantum system to obtain the first quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the first quantum state and the target observable to obtain the quantum measurement value of the target observable.

[0099] The quantum computer may also be a first quantum computer that executes a first quantum circuit, and a second quantum computer that executes quantum measurement. Of course, the first quantum computer and the second quantum computer may also be the same quantum computer.

[0100] An average of n first quantum measurement values ​​is determined as a first expected result, and the first quantum measurement values ​​of n target observable quantities obtained by n quantum measurements are averaged, and the obtained average is taken as the first expected result.

[0101] by Figure 1 Taking the first quantum circuit constructed by the randomized product formula shown as an example, the first quantum circuit can be run multiple times and repeatedly. Each time the first quantum circuit is run, a first quantum measurement value will be obtained. The multiple first quantum measurement values ​​are averaged and the obtained average is used as the first expected result.

[0102] by Figure 3Taking the first quantum circuit constructed based on the first-order product method as an example, the first quantum circuit can be repeatedly run n times to obtain n first quantum measurement values, and then the n first quantum measurement values ​​are averaged to obtain the first expected result.

[0103] By obtaining the first quantum measurement value multiple times and then averaging the multiple quantum measurement values ​​to determine the first expected result, rather than directly taking the quantum measurement value obtained once as the first expected result, accidental errors can be eliminated, thereby improving the accuracy of the first expected result to a certain extent.

[0104] 2) Get the second expected result:

[0105] Similar to the method of obtaining the first expected result, the process of obtaining the second expected result is different from that of obtaining the first expected result in that the quantum circuit used is different. Specifically, the second quantum circuit is applied to a given pure state to obtain the second expected result of the target observable, which can be implemented as follows:

[0106] Obtain m second quantum measurement values, where m is a positive integer greater than 1. Each second quantum measurement value is determined based on the following method:

[0107] The second quantum circuit is applied to the initial state of the quantum system to obtain the second quantum state of the quantum system at the evolution time t, and quantum measurement is performed based on the second quantum state and the target observable to obtain the second quantum measurement value of the target observable.

[0108] Determine the average of the m second quantum measurement values ​​as the second expected result, average the second quantum measurement values ​​of the m target observable quantities obtained through m quantum measurements, and take the average value as the second expected result.

[0109] by Figure 1 Taking the second quantum circuit constructed by the randomized product formula shown as an example, the second quantum circuit can be run multiple times and repeatedly. Each time the second quantum circuit is run, a second quantum measurement value will be obtained. The multiple second quantum measurement values ​​are averaged and the obtained average is used as the second expected result.

[0110] by Figure 3 Taking the second quantum circuit constructed based on the first-order product method as shown, the first quantum circuit can be repeatedly run m times to obtain m second quantum measurement values, and then the m second quantum measurement values ​​are averaged to obtain the second expected result.

[0111] By obtaining the second quantum measurement values ​​multiple times and then averaging the multiple quantum measurement values ​​to determine the second expected result, rather than directly taking the quantum measurement value obtained once as the second expected result, accidental errors can be eliminated, thereby improving the accuracy of the second expected result to a certain extent.

[0112] It should be noted that the values ​​of n and m mentioned above may be the same or different.

[0113] After determining two quantum circuits composed of multiple subcircuits in opposite order, the two quantum circuits are used to obtain a first expected result and a second expected result. For these two expected results, in the embodiment of the present disclosure, an expected value of the target observation is obtained based on the first expected result and the second expected result. Figure 1 and Figure 3 For example, after obtaining the first expected result and the second expected result, the average of the first expected result and the second expected result can be obtained as the expected value of the target observable quantity.

[0114] The disclosed embodiment sets the method for processing the first expected result and the second expected result obtained as taking the average, and takes the average of the first expected result and the second expected result as the expected value of the target observable quantity, rather than directly taking the first expected result or the second expected result as the expected value of the target observable quantity, so that the expected value of the target observable quantity finally obtained is more accurate and the simulation accuracy is higher.

[0115] In summary, the average of the first expected result and the second expected result is taken as the final estimated value of the target observable. Since the first quantum circuit and the second quantum circuit will each produce errors in the process of obtaining the expected results through quantum simulation. By evolving the forward and reverse quantum circuits, estimating their respective expected results and averaging them, the errors generated by the first expected result and the second expected result can be offset or mitigated to a certain extent, thereby making the expected value of the target observable obtained based on quantum simulation more accurate.

[0116] In some embodiments, the subcircuits for constructing the first quantum circuit and the second quantum circuit include a single-bit rotation gate and a controlled NOT gate (CONT). Thus, the single-bit rotation gate and the controlled NOT gate are relatively basic and easy-to-implement quantum gates, and using such quantum gates can easily implement quantum circuits for quantum simulation, thereby facilitating the improvement of the desired efficiency of extracting target observable quantities.

[0117] In some embodiments, quantum computing is to perform a series of operator operations on n qubits (quantum bits) to obtain the final measurement result. Any quantum computing program can be represented by a series of quantum circuits and non-parallel classical calculations. For example, the structure of the subcircuit in the present disclosure is as follows: Figure 4As shown in the figure, the n straight lines in the horizontal row in the circuit diagram represent n qubits, and from left to right they represent the time sequence. Generally, a two-qubit gate has two input terminals and two output terminals, which input the states of two qubits. Of the two input terminals, one is the control terminal and the other is the target terminal. The corresponding qubits are called control qubit and target qubit. Figure 4 For the first CONT gate, the first qubit is the control end, and the corresponding qubit is called the control qubit. The second qubit is the target end, and the corresponding qubit is called the target qubit. Its output depends on the interaction between the two qubits. Such a structure also leads to the fact that the two-qubit gate is often used to prepare entangled states. The CNOT gate is widely used, which is equivalent to the XOR gate in the classical circuit. The effect it produces is: if the control qubit is in |1>, the target qubit is flipped 180 degrees and inverted, that is, an Xgate is applied (equivalent to the aforementioned single-bit rotation gate); if the control qubit is in |0>, no operation is taken. Since the effects of quantum gates are all linear. And each evolved unitary matrix U corresponds to a valid quantum gate, that is, the effect for the quantum gate is unitary, so it is necessary to use a single quantum gate and a controlled NOT gate to construct an arbitrary gate to realize the quantum operation gate of any evolved unitary matrix.

[0118] It should be noted that Figure 4 The internal structure of only one subcircuit in the embodiment of the present disclosure is illustrated. During implementation, the internal structure of each subcircuit depends on the corresponding sub-Hamiltonian.

[0119] To facilitate a systematic understanding of the solution provided by the embodiments of the present disclosure, the following examples are respectively used to illustrate the two quantum circuits of forward sorting and reverse sorting of randomized product formulas, and the two quantum circuits of forward sorting and reverse sorting based on first-order product formulas to extract the expectation of target observable quantities.

[0120] Example 1) Perform quantum simulation based on randomized product subcircuits to extract the expected value of the target observable quantity. The implementation process is as follows: Figure 5a As shown, including the following:

[0121] S501, input the Hamiltonian H of the system to be simulated, the observable O, the Trotter number N required according to the simulation accuracy, and the evolution time t.

[0122] S502, construct probability distribution p j =h j / ∑ j h j , with probability pj Sampling the integer j in {1,2,…,L} N times yields {j1,j2,…,j N}.

[0123] S503, define the first quantum circuit as Defining the second quantum circuit

[0124] in Based on the subcircuit of single-qubit or two-qubit quantum gate combination, prepare the quantum circuit U F (t) and U B (t), each of which contains N subcircuits. B The subcircuit in (t) is U F (t) Reverse arrangement of the neutron circuit.

[0125] S504, respectively, the quantum circuit U F (t) and U B (t) acts on a given pure state |ψ(0)> and calculates and

[0126] in, The operation means taking the positive sign, that is, (-iHt) is changed to (iHt).

[0127] Based on the randomized product scheme, the first quantum circuit is Figure 5b As shown, the second quantum circuit is Figure 5c shown.

[0128] Figure 5b In the figure, it is shown that based on the randomized product scheme and the sub-Hamiltonian, the N subcircuits are sorted in positive order to obtain the first quantum circuit, which includes A sub-circuit.

[0129] akin, Figure 5c In , it is shown that based on the randomized product scheme and the sub-Hamiltonian, the N subcircuits are reversely sorted to obtain the second quantum circuit. The subcircuits of the second quantum circuit are arranged in the opposite order to that of the first quantum circuit.

[0130] For example, the order of the first sub-quantum circuit is {H1,H2,…,H N}, then the order of the second sub-quantum circuit is {H N ,H N-1 ,…,H1}.

[0131] S505, calculation

[0132] S506, output E est as an estimate of <ψ(t)|O|ψ(t)>.

[0133] It should be noted that, among the above steps, except step S503 and step S504 which need to be executed on a quantum computer, the other steps can also be implemented on a classical computer.

[0134] The embodiments of the present disclosure can be used to simulate a variety of quantum systems and have the characteristics of universality. A one-dimensional, chain-like Hamiltonian is selected as the quantum system to be simulated by the present disclosure, which can be written as in the form of formula (9):

[0135]

[0136] Where n is the number of quantum bits in the system, p1p2p3∈{x,y,z}, represents the Pauli matrix on the kth quantum bit, h k is a set of coefficients greater than zero selected randomly. For the observable quantity O, the embodiment of the present disclosure selects the Yixin model of the following formula (10):

[0137]

[0138] In the numerical experiment, n=6 and the evolution time t=10 are set. In order to compare the simulation accuracy improvement effect with other schemes, the embodiment of the present disclosure uses the first-order product method as scheme 1 and the randomized product method as scheme 2 to simulate the same Hamiltonian respectively, and selects the same observable O. The three methods including the scheme of the present disclosure are limited to use the same circuit depth.

[0139] The following table shows the percentage of accuracy improvement of the present disclosure compared to Scheme 1 and Scheme 2. For a given observable O and a quantum system H to be simulated, the present disclosure randomly generates 1000 pure states as the initial state of the system, and averages the absolute errors of the expected estimates obtained by the two schemes. The accuracy improvement shown in the table below is an average improvement after 1000 simulation experiments (the comparison accuracy improvement is the accuracy improvement of the present disclosure scheme compared to Scheme 1 and Scheme 2, respectively).

[0140] Experimental protocol Average estimation error Improved contrast accuracy Solution 1 0.35 17％ Solution 2 0.33 12％ This public scheme 0.29 -

[0141] Table 1 Results of numerical experiment 1 (the number of subcircuits in the three schemes is 10800)

[0142] It can be seen that when the circuit depth is the same, the disclosed scheme has a significant accuracy advantage over the traditional randomized scheme, and maintains the advantages over the original product scheme in the case of complex Hamiltonian.

[0143] Example 2) Perform quantum simulation based on the subcircuit of the first-order product formula to extract the expected value of the target observable quantity. The implementation process is as follows Figure 6a As shown, including the following:

[0144] S601, input the Hamiltonian H of the system to be simulated, the observable O, the simulation time t, and the number of segments (Trotter steps) r into which the simulation time t is divided, i.e. the number of determined time periods.

[0145] S602, define the first quantum circuit The second quantum circuit

[0146] in Based on the subcircuit of single-qubit or two-qubit quantum gate combination, prepare the quantum circuit U F (t) and U B (t), each of which contains Lr subcircuits. Each L subcircuit is called a circuit group, U B (t) The subcircuit in the circuit group is U F (t) Reverse order of subcircuits in a circuit group.

[0147] S603, respectively, the quantum circuit U F (t) and U B (t) acts on a given pure state |ψ(0)> and calculates the value of and

[0148] Among them, based on the first-order product solution, the first quantum circuit is as follows Figure 6b As shown, the second quantum circuit is Figure 6c shown.

[0149] Figure 6b , it is shown that when the evolution time t is divided into r segments, the first quantum circuit includes r positive sequence circuit groups. Each positive sequence circuit group has the same structure, and each positive sequence circuit group includes L sub-circuits. In the positive sequence circuit group, Each of them is a subcircuit, and each subcircuit is in accordance with {H1, H2, ..., H L} Sort the subcircuits.

[0150] akin, Figure 6cIn FIG. 1 , it is shown that when the evolution time t is divided into r segments, the second quantum circuit includes r reverse circuit groups. Each reverse circuit group has the same structure, and each reverse circuit group includes L subcircuits. In the reverse circuit group, Each of them is a subcircuit, and each subcircuit is in accordance with {H1, H2, ..., H L} to sort the subcircuits in reverse order.

[0151] S604, calculation

[0152] S605, output E est as an estimate of <ψ(t)|O|ψ(t)>.

[0153] It should be noted that, among the above steps, except step S602 and step S603 which need to be executed on a quantum computer, the other steps can also be implemented on a classical computer.

[0154] The embodiments of the present disclosure can be used to simulate a variety of quantum systems and have the characteristics of universality. A one-dimensional, ring-shaped Heisenberg model is selected as the quantum system to be simulated by the present disclosure. The Heisenberg model is a commonly used model in physics, and its Hamiltonian can be written as shown in formula (11).

[0155]

[0156] Where n is the number of quantum bits in the system, represents the Pauli matrix on the kth quantum bit, h k is a coefficient related to the environmental magnetic field. k The value of is 0. Because the system is a ring structure, n+1 represents the first quantum bit. For the observable quantity O, the embodiment of the present disclosure selects the Yixin model in the form of formula (12):

[0157]

[0158] In the above numerical experiments, n=6 and simulation time t=10 are set. In order to compare the effects, the present disclosure uses the first-order product method as Scheme 1 and the high-order Trotter-Suzuki product method as Scheme 3, and simulates the same Hamiltonian with the second-order Trotter-Suzuki product method in Scheme 1 and Scheme 3, and selects the same observable O. The three methods for comparison all use the same circuit depth (subcircuit 2, 3, 4). The numbers of them are 1260, 1890, and 2520 respectively).

[0159] Tables 2, 3, and 4 show the percentage of the second-order Trotter-Suzuki product method accuracy improvement of the disclosed solution compared to Solution 1 and Solution 3. For a given observable O and a quantum system H to be simulated, 1000 pure states are randomly generated as the initial state of the system, and the absolute errors of the expected estimates obtained by the three solutions are averaged. The accuracy improvement shown in the table below is an average improvement after 1000 simulation experiments (the comparison accuracy improvement is the accuracy improvement of the disclosed solution compared to Solution 1 and Solution 3, respectively).

[0160] Experimental protocol Average estimation error Improved contrast accuracy Solution 1 0.1023 27.27％ Solution 3 0.2061 63.90％ This public scheme 0.0744 -

[0161] Table 2 Results of numerical experiment 2 (three schemes The number of is 1260)

[0162] Experimental protocol Average estimation error Improved contrast accuracy Solution 1 0.0562 42.17％ Solution 3 0.1269 74.39％ This public scheme 0.0325 -

[0163] Table 3 Results of numerical experiment 3 (three schemes The number of them is 1890)

[0164]

[0165]

[0166] Table 4 Results of numerical experiment 4 (three schemes The number of is 2520)

[0167] It can be seen that as the number of Trotter steps increases, the overall simulation accuracy of the observable estimate is higher. When the circuit depth required for each scheme is the same, the accuracy advantage of the disclosed scheme becomes more obvious.

[0168] Based on the same inventive concept, the embodiment of the present disclosure also provides an information processing device based on a quantum system, such as Figure 7 As shown, including:

[0169] A determination module 701 is used to determine multiple subcircuits of a quantum system based on the Hamiltonian, and a forward order and a reverse order of the multiple subcircuits; wherein the multiple subcircuits in the forward order are used to construct a first quantum circuit, and the multiple subcircuits in the reverse order are used to construct a second quantum circuit;

[0170] A first acquisition module 702 is used to acquire a first expected result of a target observable quantity of a quantum system when a first quantum circuit simulates a first quantum state of the quantum system at an evolution time t; and

[0171] A second acquisition module 703 is used to obtain a second expected result of the quantum system for the target observable when the second quantum circuit simulates the second quantum state of the quantum system at the evolution time t;

[0172] The estimation module 704 is used to obtain an expected value of the target observable quantity based on the first expected result and the second expected result.

[0173] In some embodiments, the determining module includes:

[0174] A first determination submodule is used to determine the Hamiltonian, the evolution time t, and the number of time periods into which the evolution time t is divided;

[0175] A second determination submodule, configured to determine a plurality of sub-Hamiltonians based on the Hamiltonian;

[0176] The third determination submodule is used to determine a plurality of sub-circuits based on a plurality of sub-Hamiltonians, the evolution time t, and the number of time periods.

[0177] In some embodiments, the determining module includes:

[0178] The fourth determination submodule is used to determine the Hamiltonian, the evolution time t, and the number of samplings required for the specified simulation accuracy;

[0179] A fifth determination submodule, configured to determine a plurality of sub-Hamiltonians based on the Hamiltonian;

[0180] The sixth determination submodule is used to determine a plurality of sub-circuits based on a plurality of sub-Hamiltonians, the evolution time t, and the sampling number.

[0181] In some embodiments, the estimation module is used to obtain the average of the first expected result and the second expected result as the expected value of the target observable.

[0182] In some embodiments, the first acquisition module includes:

[0183] A first acquisition submodule is used to acquire n first quantum measurement values, where n is a positive integer greater than 1; wherein each first quantum measurement value is determined by the quantum computer based on the following device: applying a first quantum circuit to an initial state of a quantum system to obtain a first quantum state of the quantum system at an evolution time t, and performing quantum measurement based on the first quantum state and a target observable quantity to obtain a first quantum measurement value of the target observable quantity;

[0184] The second acquisition submodule is used to determine the average of the n first quantum measurement values ​​as the first expected result.

[0185] In some embodiments, the second acquisition module includes:

[0186] A third acquisition submodule is used to obtain m second quantum measurement values, where m is a positive integer greater than 1; wherein each second quantum measurement value is determined by the quantum computer based on the following device: applying the second quantum circuit to the initial state of the quantum system to obtain the second quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the second quantum state and the target observable to obtain the second quantum measurement value of the target observable;

[0187] The fourth acquisition submodule is used to determine the average of the m second quantum measurement values ​​as the second expected result.

[0188] In some embodiments, the first quantum circuit includes r positive-sequence circuit groups connected in series, wherein each positive-sequence circuit group includes a plurality of subcircuits sorted in a positive direction;

[0189] The second quantum circuit includes r reverse order circuit groups connected in series, wherein each reverse order circuit group includes a plurality of sub-circuits arranged in reverse order; wherein r is the number of time periods.

[0190] In some embodiments, the determining module includes:

[0191] A construction submodule, used for constructing a probability distribution of weight coefficients of a plurality of subcircuits;

[0192] A sampling submodule, for randomly sampling a sampling range based on the probability distribution of the weight coefficient of each subcircuit, to obtain a sorting order of each subcircuit;

[0193] A first sorting submodule is used to sort the sorting order of each subcircuit in a positive order to obtain a forward sorting order; and

[0194] The second sorting submodule is used to sort the sorting order of each subcircuit in reverse order to obtain a reverse sorting.

[0195] In some embodiments, each sub-circuit includes a single-bit rotation gate and a controlled NOT gate.

[0196] For the description of specific functions and examples of each module and submodule of the device in the embodiment of the present disclosure, reference can be made to the relevant description of the corresponding steps in the above method embodiment, which will not be repeated here.

[0197] The disclosed solution also provides a non-transitory computer-readable storage medium storing computer instructions, which, when executed by at least one quantum processing unit, causes the at least one quantum processing unit to execute the above method of applying a quantum computing device.

[0198] The disclosed solution also provides a computer program product, including a computer program, which implements the above method applied to a classical computing device when executed by a processor;

[0199] Alternatively, the computer program, when executed by at least one quantum processing unit, implements a method applied to a quantum computing device.

[0200] The disclosed solution also provides a quantum computing device, the quantum computing device comprising:

[0201] at least one quantum processing unit;

[0202] a memory coupled to at least one QPU and configured to store executable instructions,

[0203] The instructions are executed by at least one quantum processing unit to enable the at least one quantum processing unit to perform a method applied to a quantum computing device.

[0204] It can be understood that the quantum processing unit (QPU) used in the disclosed solution, which may also be called a quantum processor or a quantum chip, may involve a physical chip including a plurality of quantum bits interconnected in a specific manner.

[0205] Moreover, it is understood that the quantum bit described in the present disclosure may refer to the basic information unit of a quantum computing device. The quantum bit is contained in the QPU and generalizes the concept of the classical digital bit.

[0206] According to an embodiment of the present disclosure, the present disclosure also provides a classic computing device (hereinafter, the classic computing device is specifically an electronic device as an example for explanation), a readable storage medium and a computer program product.

[0207] According to an embodiment of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.

[0208] Figure 8 A schematic block diagram of an example electronic device 800 that can be used to implement an embodiment of the present disclosure is shown. The electronic device is intended to represent various forms of digital computers, 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 assistants, 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 required herein.

[0209] like Figure 8As shown, the device 800 includes a computing unit 801, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 802 or a computer program loaded from a storage unit 808 into a random access memory (RAM) 803. In the RAM 803, various programs and data required for the operation of the device 800 can also be stored. The computing unit 801, the ROM 802, and the RAM 803 are connected to each other via a bus 804. An input / output (I / O) interface 805 is also connected to the bus 804.

[0210] A number of components in the device 800 are connected to the I / O interface 805, including: an input unit 806, such as a keyboard, a mouse, etc.; an output unit 807, such as various types of displays, speakers, etc.; a storage unit 808, such as a disk, an optical disk, etc.; and a communication unit 809, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 809 allows the device 800 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0211] The computing unit 801 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 801 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, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 801 performs the various methods and processes described above, such as information processing methods based on quantum systems. For example, in some embodiments, the processing method of the multimedia data stream may be implemented as a computer software program, which is tangibly contained in a machine-readable medium, such as a storage unit 808. In some embodiments, part or all of the computer program may be loaded and / or installed on the device 800 via ROM 802 and / or a communication unit 809. When the computer program is loaded into RAM 803 and executed by the computing unit 801, one or more steps of the information processing method based on the quantum system described above may be performed. Alternatively, in other embodiments, the computing unit 801 may be configured to perform information processing methods based on quantum systems in any other appropriate manner (e.g., by means of firmware).

[0212] Various implementations of the systems and techniques described above herein 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 chips (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations 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 special purpose 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 data and instructions to the storage system, the at least one input device, and the at least one output device.

[0213] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0214] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or equipment, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, 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 disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0215] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types 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).

[0216] The systems and techniques described herein may be implemented in a computing system that includes back-end 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 front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may 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), and the Internet.

[0217] A computer system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The relationship of client and 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 combined with a blockchain.

[0218] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0219] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for information processing based on a quantum system, comprising: Determine multiple subcircuits of a quantum system based on a Hamiltonian, and a forward sorting and a reverse sorting of the multiple subcircuits; wherein the multiple subcircuits in the forward sorting are used to construct a first quantum circuit, and the multiple subcircuits in the reverse sorting are used to construct a second quantum circuit, wherein the Hamiltonian is decomposed into multiple sub-Hamiltonians, and a forward sorting of the multiple subcircuits is obtained based on a sorting order of the multiple sub-Hamiltonians, wherein the reverse sorting is opposite to the sorting order of the forward sorting, and wherein each of the sub-Hamiltonians corresponds to a subcircuit; Obtaining a first expected result of a target observable quantity of the quantum system when the first quantum circuit simulates a first quantum state of the quantum system at an evolution time t; and Obtaining a second expected result of the target observable by the quantum system when the second quantum circuit simulates a second quantum state of the quantum system at an evolution time t; Based on the first expected result and the second expected result, an expected value of the target observable quantity is obtained.

2. The method according to claim 1, wherein: The method for determining a plurality of sub-circuits of a quantum system based on the Hamiltonian comprises: Determining the Hamiltonian, the evolution time t, and the number of time periods into which the evolution time t is divided; Determining a plurality of sub-Hamiltonians based on the Hamiltonian; The plurality of sub-circuits are determined based on the plurality of sub-Hamiltonians, the evolution time t, and the number of the time periods.

3. The method according to claim 1, wherein: The method for determining a plurality of sub-circuits of a quantum system based on the Hamiltonian comprises: Determine the Hamiltonian, the evolution time t, and the number of samples required for specifying simulation accuracy; Determining a plurality of sub-Hamiltonians based on the Hamiltonian; The plurality of sub-circuits are determined based on the plurality of sub-Hamiltonians, the evolution time t, and the sampling number.

4. The method according to any one of claims 1 to 3, wherein: The obtaining the expected value of the target observation quantity based on the first expected result and the second expected result includes: An average of the first expected result and the second expected result is obtained as the expected value of the target observable quantity.

5. The method according to any one of claims 1 to 3, wherein: The obtaining of a first expected result of a target observable quantity of the quantum system when the first quantum circuit simulates a first quantum state of the quantum system at an evolution time t comprises: Obtaining n first quantum measurement values, where n is a positive integer greater than 1; wherein each first quantum measurement value is determined by a quantum computer based on the following method: applying the first quantum circuit to an initial state of the quantum system to obtain a first quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the first quantum state and the target observable to obtain the first quantum measurement value of the target observable; An average of the n first quantum measurement values ​​is determined as the first expected result.

6. The method according to any one of claims 1 to 3, wherein: The step of applying the second quantum circuit to a given pure state to obtain a second expected result of the observed quantity comprises: Obtaining m second quantum measurement values, where m is a positive integer greater than 1; wherein each second quantum measurement value is determined by the quantum computer based on the following method: applying the second quantum circuit to the initial state of the quantum system to obtain a second quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the second quantum state and the target observable to obtain the second quantum measurement value of the target observable; An average of the m second quantum measurement values ​​is determined as the second expected result.

7. The method according to claim 2, wherein the first quantum circuit comprises r positive-sequence circuit groups connected in series, wherein each positive-sequence circuit group comprises the plurality of sub-circuits arranged in the forward direction; The second quantum circuit includes r reverse order circuit groups connected in series, wherein each reverse order circuit group includes the multiple sub-circuits arranged in the reverse order; wherein r is the number of the time periods.

8. The method according to claim 3, determining the forward order and the reverse order of the plurality of sub-circuits, comprising: constructing a probability distribution of weight coefficients of the plurality of subcircuits; Based on the probability distribution of the weight coefficient of each sub-circuit, the sampling range is randomly sampled to obtain the sorting order of each sub-circuit; Sorting the sorting order of each subcircuit in positive order to obtain the forward sorting; and, The reverse sorting is obtained by sorting the sorting order of each sub-circuit in reverse order.

9. The method according to any one of claims 1 to 3, wherein each sub-circuit comprises a single-bit rotation gate and a controlled NOT gate.

10. An information processing device based on a quantum system, comprising: A determination module, used for determining a plurality of subcircuits of a quantum system based on a Hamiltonian, and a forward sorting and a reverse sorting of the plurality of subcircuits; wherein the plurality of subcircuits in the forward sorting are used to construct a first quantum circuit, and the plurality of subcircuits in the reverse sorting are used to construct a second quantum circuit, wherein the Hamiltonian is decomposed into a plurality of sub-Hamiltonians, and a forward sorting of the plurality of subcircuits is obtained based on a sorting order of the plurality of sub-Hamiltonians, wherein the reverse sorting is opposite to the sorting order of the forward sorting, and wherein each of the sub-Hamiltonians corresponds to a subcircuit; A first acquisition module is used to acquire a first expected result of a target observable quantity of the quantum system when the first quantum circuit simulates a first quantum state of the quantum system at an evolution time t; and A second acquisition module, used for acquiring a second expected result of the quantum system for the target observable quantity when the second quantum circuit simulates the second quantum state of the quantum system at the evolution time t; An estimation module is used to obtain an expected value of the target observable quantity based on the first expected result and the second expected result.

11. The device according to claim 10, wherein: The determining module comprises: A first determination submodule, used to determine the Hamiltonian, the evolution time t, and the number of time periods into which the evolution time t is divided; A second determination submodule, configured to determine a plurality of sub-Hamiltonians based on the Hamiltonian; The third determination submodule is configured to determine the plurality of sub-circuits based on the plurality of sub-Hamiltonians, the evolution time t, and the number of the time periods.

12. The device according to claim 10, wherein: The determining module comprises: A fourth determination submodule, used to determine the Hamiltonian, the evolution time t and the number of samplings required for specifying the simulation accuracy; a fifth determination submodule, configured to determine a plurality of sub-Hamiltonians based on the Hamiltonian; The sixth determination submodule is used to determine the multiple sub-circuits based on the multiple sub-Hamiltonians, the evolution time t and the sampling number.

13. The device according to any one of claims 10 to 12, wherein: The estimation module is used to obtain the average of the first expected result and the second expected result as the expected value of the target observable quantity.

14. The device according to any one of claims 10 to 12, wherein: The first acquisition module includes: A first acquisition submodule is used to acquire n first quantum measurement values, where n is a positive integer greater than 1; wherein each first quantum measurement value is determined by the quantum computer based on the following device: applying the first quantum circuit to the initial state of the quantum system to obtain a first quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the first quantum state and the target observable quantity to obtain the first quantum measurement value of the target observable quantity; The second acquisition submodule is used to determine the average of the n first quantum measurement values ​​as the first expected result.

15. The device according to any one of claims 10 to 12, wherein: The second acquisition module includes: A third acquisition submodule is used to acquire m second quantum measurement values, where m is a positive integer greater than 1; wherein each second quantum measurement value is determined by the quantum computer based on the following device: applying the second quantum circuit to the initial state of the quantum system to obtain a second quantum state of the quantum system at the evolution time t, and performing quantum measurement based on the second quantum state and the target observable quantity to obtain the second quantum measurement value of the target observable quantity; The fourth acquisition submodule is used to determine the average of the m second quantum measurement values ​​as the second expected result.

16. The device according to claim 11, wherein the first quantum circuit comprises r positive sequence circuit groups connected in series, wherein each positive sequence circuit group comprises the plurality of sub-circuits arranged in the forward direction; The second quantum circuit includes r reverse order circuit groups connected in series, wherein each reverse order circuit group includes the multiple sub-circuits arranged in the reverse order; wherein r is the number of the time periods.

17. The apparatus according to claim 12, wherein the determining module comprises: A construction submodule, used to construct a probability distribution of weight coefficients of the plurality of subcircuits; A sampling submodule, for randomly sampling a sampling range based on the probability distribution of the weight coefficient of each subcircuit, to obtain a sorting order of each subcircuit; A first sorting submodule is used to sort the sorting order of each subcircuit in a positive order to obtain the forward order; and The second sorting submodule is used to sort the sorting sequence of each subcircuit in reverse order to obtain the reverse sorting.

18. The device according to any one of claims 10 to 12, wherein each sub-circuit comprises a single-bit rotation gate and a controlled NOT gate.

19. An electronic device comprising: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed 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 perform the method according to any one of claims 1 to 9.

20. A quantum computing device comprising: At least one quantum processing unit QPU; a memory coupled to the at least one QPU and configured to store executable instructions, The instructions are executed by the at least one quantum processing unit to enable the at least one quantum processing unit to perform the method of any one of claims 1-9.

21. 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.

22. A computer program product comprising a computer program, which, when executed by a processor, implements the method according to any one of claims 1 to 9.

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