Method and system for determining electronic state density of material
By combining quantum computers and classical computers, the initial random states of qubits are generated and time evolution processed, which solves the high complexity and high cost problems when classical computers calculate the density of electronic states of materials, and achieves more efficient and accurate calculations.
Patent Information
- Application Number
- CN202510340341.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-21
- Publication Date
- 2025-07-08
AI Technical Summary
In the prior art, when calculating the electronic state density of materials through classical computers, the calculation complexity is high and the calculation order is large, resulting in problems such as large demand for computing resources, high calculation cost and long-term consumption.
By combining quantum computers and classical computers, random numbers are generated and the initial random states of qubits are generated. Hamiltonians performs time evolution processing with multiple time steps, and combined with the measurement results of auxiliary qubits, the electron state density of the material is determined.
The calculation efficiency and accuracy of the electronic density of states of the material are improved, the demand for computing resources is reduced, and the calculation time is reduced.
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Figure CN120280053A_ABST
Abstract
Description
Technical Field
[0001] The present disclosure relates to the field of quantum computing, and particularly to a method and system for determining the electronic state density of a material. Background Art
[0002] The electronic state density, abbreviated as the density of electronic energy states, refers to the number of electronic states within a unit energy interval under the condition that the electronic energy levels are quasi-continuously distributed, and is a key physical quantity reflecting the electronic state and properties of a material. The electrical, optical, transport and other properties of a material can be further predicted through the electronic state density of the material.
[0003] Currently, the electronic state density of a material can be calculated by a classical computer. One way to calculate the electronic state density of a material by a classical computer is: diagonalize the Hamiltonian matrix in the material to obtain the energy spectrum of the electrons in the material, and sum and analyze the energy spectrum of the electrons in the material to obtain the electronic state density of the material. When the number of electrons in the material increases, the dimension of the Hamiltonian increases at least linearly, and diagonalizing the Hamiltonian becomes a difficult step to complete, and the efficiency of classical calculation for predicting the electronic state density will be greatly reduced; another way can also be: generate an initial random state of the electrons in the material by a classical computer, evolve the random state according to the Hamiltonian evolution operator over time to obtain the random state at each time step, and perform a Fourier transform on the inner product of the initial random state and the evolved random state by a classical computer to obtain the electronic state density. Although this method avoids the time-consuming diagonalization step, it is necessary to construct a Hamiltonian and a random state containing millions of electrons to accurately predict the electronic state density of the material, which greatly consumes the operating memory of the classical computer, and the number of steps for time evolution usually reaches thousands, resulting in a long time-consuming problem.
[0004] The following technical problems exist in the prior art: in the process of calculating the electronic state density of a material by a classical computer, the calculation complexity is high and the calculation magnitude is large, resulting in large requirements for computing resources, high computing costs and long computing times in the determination process. Summary of the Invention
[0005] The present disclosure provides a method and system for determining the electronic state density of a material, which realizes the calculation of the electronic state density of the material by combining a quantum computer and a classical computer, improves the calculation efficiency and accuracy of the electronic state density of the material, and reduces the requirements for computing resources.
[0006] According to one aspect of the present disclosure, the present disclosure provides a method for determining the electronic state density of a material, including:
[0007] Generate random numbers by a classical computer, and the number of the random numbers is determined based on the number of electrons of the target material;
[0008] Generate an initial random state of qubits based on the random numbers by a quantum computer, perform time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determine the measurement results corresponding to each of the time steps during the time evolution processing of the auxiliary qubits;
[0009] Based on the classical computer, based on the measurement results corresponding to each of the time steps of the auxiliary qubits, determine the inner product of the random state corresponding to each of the time steps and the initial random state, and determine the electronic state density of the target material through the inner products of the random states corresponding to multiple time steps and the initial random state.
[0010] Optionally, the generating an initial random state of qubits based on the random numbers includes:
[0011] Apply an H gate and at least one random rotation gate to each qubit in the initial state in sequence by the quantum computer to obtain an initial random state composed of multiple qubits, where the at least one random rotation gate includes one or more of a random rotation Z gate, a random rotation X gate, and a random rotation Y gate, and the rotation angle of any one of the random rotation gates is the random number.
[0012] Optionally, the performing time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material and determining the measurement results corresponding to each of the time steps during the time evolution processing of the auxiliary qubits includes:
[0013] Execute a first quantum circuit by the quantum computer, perform time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determine the first measurement result corresponding to each of the time steps during the time evolution processing of the auxiliary qubits;
[0014] Execute a second quantum circuit by the quantum computer, perform time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determine the second measurement result corresponding to each of the time steps during the time evolution processing of the auxiliary qubits.
[0015] Optionally, during the time evolution of any time step, apply an H gate to the initial state of the auxiliary qubit, perform the time evolution processing of the current time step on the initial random state or the random state corresponding to the previous time step, and then apply an H gate after the time evolution processing, and measure the auxiliary qubit to obtain the first measurement result corresponding to the current time step.
[0016] Optionally, during the time evolution at any time step, an H gate and a phase gate are sequentially applied to the initial state of the auxiliary qubit, the time evolution process of the current time step is performed on the initial random state or the random state of the previous time step, and after the time evolution process, an H gate is applied, and the auxiliary qubit is measured to obtain a second measurement result corresponding to the current time step.
[0017] Optionally, determining the inner product of the random state corresponding to each time step and the initial random state based on the measurement results respectively corresponding to the auxiliary qubit at each time step includes: determining the real part data corresponding to each time step based on the first measurement result corresponding to the auxiliary qubit at each time step; determining the imaginary part data corresponding to each time step based on the second measurement result corresponding to the auxiliary qubit at each time step; and determining the inner product of the random state corresponding to each time step and the initial random state based on the real part data and the imaginary part data respectively corresponding to each time step.
[0018] Optionally, performing time evolution processing on the initial random state for multiple time steps based on the Hamiltonian of the target material includes: performing Pauli basis decomposition on the Hamiltonian of the target material by the quantum computer to obtain a plurality of sub-Hamiltonians, and any one of the sub-Hamiltonians includes one or more Pauli matrices; splitting the evolution operator corresponding to the Hamiltonian into time evolution operators corresponding to each of the sub-Hamiltonians; and performing evolution processing on the initial random state or the random state of the previous time step based on the time evolution operator corresponding to each sub-Hamiltonian to obtain the random state of the qubit at the current time step.
[0019] Optionally, performing evolution processing on the initial random state or the random state of the previous time step based on the time evolution operator corresponding to each sub-Hamiltonian to obtain the random state of the qubit at the current time step includes: mapping the time evolution operator corresponding to each sub-Hamiltonian to obtain a quantum operation gate, and applying the quantum operation gate to the initial random state or the random state of the previous time step to obtain the random state of the qubit at the current time step.
[0020] Optionally, determining the electronic state density of the target material by the inner product of the random states corresponding to multiple time steps and the initial random state includes: performing Fourier transform on the inner product of the random states corresponding to multiple time steps and the initial random state by the classical computer to obtain the electronic state density of the target material.
[0021] According to another aspect of the present disclosure, the present disclosure provides a system for determining the electronic state density of a material, including: a classical computer and a quantum computer; wherein,
[0022] The classical computer is configured to generate random numbers, and the number of the random numbers is determined based on the number of electrons of the target material;
[0023] The quantum computer is configured to read the random numbers from the classical computer, generate an initial random state of qubits based on the random numbers, perform time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determine the measurement results respectively corresponding to each of the time steps during the time evolution processing of an auxiliary qubit, and store the measurement results of the auxiliary qubit corresponding to each of the time steps into the classical computer;
[0024] The classical computer is further configured to determine the inner product of the random state corresponding to each of the time steps and the initial random state based on the measurement results respectively corresponding to each of the time steps of the auxiliary qubit, and determine the electronic state density of the target material through the inner products of the random states and the initial random state corresponding to multiple time steps.
[0025] In the technical solution of the embodiment of the present disclosure, for a target material composed of 2 N electrons, random numbers required in the determination process of the electronic state density are generated by a classical computer, an initial random state composed of N qubits is generated by a quantum computer, and time evolution processing is performed on the initial random state composed of qubits based on the Hamiltonian of the target material. During the above time evolution processing, an auxiliary qubit is introduced, and the measurement results respectively corresponding to each time step during the time evolution processing of the auxiliary qubit are measured. The classical computer converts the measurement results of the auxiliary qubit corresponding to each time step during the time evolution processing into the inner product of the random state and the initial random state corresponding to each time step during the time evolution processing, and obtains the electronic state density of the target material through the inner products respectively corresponding to multiple time steps. The present disclosure determines the electronic state density of a material by combining the advantages of exponential - level parallel processing and storage of a quantum computer and the data - processing advantages of a classical computer. The quantum computer can implement data processing related to a target material composed of 2 N electrons through the processing of N qubits. Compared with generating and storing 2 N random complex numbers in a classical computer, the amount of data to be processed and the amount of calculation are reduced, as well as the memory and resources occupied are reduced, and the calculation time for the electronic state density is improved.
[0026] 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 understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] To more clearly illustrate the technical solutions in the embodiments of the present disclosure, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present disclosure. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can be obtained based on these drawings.
[0028] Figure 1 is a flowchart of a method for determining the electronic state density of a material provided by an embodiment of the present disclosure;
[0029] Figure 2 is a schematic diagram of a random state generation circuit provided by an embodiment of the present disclosure;
[0030] Figure 3 is a schematic diagram of the first sub-circuit in the first quantum circuit provided by an embodiment of the present disclosure;
[0031] Figure 4 is a schematic diagram of the second sub-circuit in the second quantum circuit provided by an embodiment of the present disclosure;
[0032] Figure 5 is a schematic diagram of a method for determining the inner product of a random state at any time step and an initial random state provided by an embodiment of the present disclosure;
[0033] Figure 6 is a flowchart of another method for determining the electronic state density of a material provided by an embodiment of the present disclosure;
[0034] Figure 7 is a schematic diagram of an evolution circuit provided by an embodiment of the present disclosure;
[0035] Figure 8 is a schematic diagram of another evolution circuit provided by an embodiment of the present disclosure;
[0036] Figure 9 is a flowchart of another method for determining the electronic state density of a material provided by an embodiment of the present disclosure;
[0037] Figure 10 is a schematic diagram of the structure of a system for determining the electronic state density of a material provided by an embodiment of the present disclosure. Detailed implementation manners
[0038] To enable those skilled in the art to better understand the solutions of the present disclosure, the following will clearly and completely describe the technical solutions in the embodiments of the present disclosure in conjunction with the accompanying drawings in the embodiments of the present disclosure. Obviously, the described embodiments are only some embodiments of the present disclosure, rather than all embodiments. Based on the embodiments in the present disclosure, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present disclosure.
[0039] It should be noted that the terms "first", "second", etc. in the description, claims and above-mentioned drawings of the present disclosure are used to distinguish similar objects, and do not necessarily need to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged under appropriate circumstances, so that the embodiments of the present disclosure described here can be implemented in an order other than those illustrated or described here. In addition, the terms "comprising" and "having" and any variations thereof are intended to cover non-exclusive inclusion. For example, a process, method, system, product or device comprising a series of steps or units does not necessarily have to be limited to those steps or units clearly listed, but may include other steps or units not clearly listed or inherent to these processes, methods, products or devices.
[0040] Regarding the problems of high computational complexity and large computational magnitude in the process of a classical computer determining the electronic state density of a material, which lead to large computational resource requirements, high computational costs and long time consumption in the determination process.
[0041] The present disclosure provides a method for determining the electronic state density of a material. Refer to Figure 1 , Figure 1 is a flowchart of a method for determining the electronic state density of a material provided by an embodiment of the present disclosure. As Figure 1 shown, the method includes:
[0042] S110. Generate random numbers through a classical computer, and the number of the random numbers is determined based on the number of electrons of the target material.
[0043] In some embodiments of the present disclosure, the target material may include one or more of one-dimensional materials, two-dimensional materials, and three-dimensional materials. For example, one-dimensional materials may include, but are not limited to, carbon nanotubes, two-dimensional materials may include, but are not limited to, graphene, and three-dimensional materials may include, but are not limited to, silicon, etc.
[0044] The target material may be a material composed of 2 N electrons, and the number of electrons of the target material can be determined based on the atomic type and the number of atoms in the target material, where N is a positive integer.
[0045] The classical computer generates a first number of random numbers, and the first number can be determined based on the number of electrons of the target material. Taking the target material including 2 NTaking an electron as an example, the number of random numbers can be a multiple of N. For example, the number of random numbers can be N, 2N, 3N, etc. Optionally, the classical computer is configured with a random number generator to generate a first number of random numbers through the random number generator. Optionally, the above random numbers are between 0 and 2π. Generating random numbers determined based on the number of electrons of the target material by the classical computer provides a data basis for the quantum computer to process qubits.
[0046] S120. Based on the random numbers, the quantum computer generates an initial random state of the qubits, performs a time evolution process with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determines the measurement results corresponding to each of the time steps during the time evolution process for the auxiliary qubits.
[0047] The quantum computer processes a second number of qubits to generate an initial random state composed of the second number of qubits. The initial random state is a kind of quantum random state. The quantum random state can be a quantum random state composed of N qubits, and the quantum random state can represent 2 N random complex numbers, and each qubit has a random phase and amplitude. Correspondingly, for the target material of 2 N electrons, the second number can be N.
[0048] For the target material including 2 N electrons, the quantum computer only needs to generate and store N qubits. Compared with generating and storing 2 N random complex numbers in the classical computer, the amount of processed data and the amount of calculation are reduced, and the occupied storage space is reduced.
[0049] In some embodiments of the present disclosure, the quantum computer processes N qubits respectively through executing a random state generation circuit to obtain the initial random state of the qubits. The random state generation circuit may include setting operation gates, and the setting operation gates may include an H gate and a random rotation gate, where the random rotation gate is generated based on the above random numbers.
[0050] In some embodiments of the present disclosure, generating the initial random state of the qubits based on the random numbers includes: sequentially applying an H gate and at least one random rotation gate to each qubit in the initial state through the quantum computer to obtain the initial random state of the multiple qubits, where the at least one random rotation gate includes one or more of a random rotation Z gate, a random rotation X gate, and a random rotation Y gate, and the rotation angle of any one of the random rotation gates is the any one of the random numbers.
[0051] The quantum computer sets N qubits to the initial state, that is, the |0> state. Optionally, the qubits can be initialized by applying an H gate to the qubits.
[0052] For each qubit, apply the H gate and at least one random rotation gate to the initial state of the qubit. The at least one random rotation gate can be one or more of a random rotation Z gate, a random rotation X gate, and a random rotation Y gate. Here, the type and number of the random rotation gates are not limited. For example, apply the H gate and the random rotation Z gate to the initial state of each qubit in sequence; for another example, apply the H gate, the random rotation Z gate, and the random rotation X gate to the initial state of each qubit in sequence; for still another example, apply the H gate, the random rotation Z gate, the random rotation X gate, and the random rotation Y gate to the initial state of each qubit in sequence.
[0053] Exemplarily, referring to Figure 2 , Figure 2 is a schematic diagram of a random state generation circuit provided by an embodiment of the present disclosure. Figure 2 It is only a circuit for generating an initial random state composed of three qubits. Taking Figure 2 as an example, for N qubits, the quantum computer reads 2N random numbers from the classical computer, and generates N random rotation X gates {R i} based on the N random numbers {φ x (φ i )}, generates N random rotation Z gates {R i (θ z )} based on the N random numbers {θ i}, and for the N qubits, apply the H gate, the random rotation Z gate {R z (θ i )}, and the random rotation X gate {R x (φ i )} respectively to obtain the ground states of the N qubits, and the initial random state of the qubits formed by the ground states of the N qubits It should be noted that the number of random numbers satisfies the generation requirements of at least one type of random rotation gate.
[0054] In some embodiments of the present disclosure, by applying the H gate to the initial state of the qubit, the initial state of the qubit is converted into a superposition state. By applying at least one random rotation gate to the superposition state of the qubit, randomness is introduced into the quantum state of the qubit, making the subsequent generation of the initial random state have a certain degree of randomness and complexity.
[0055] S130. Through the classical computer, based on the measurement results respectively corresponding to the auxiliary qubits at each time step, determine the inner product of the random state corresponding to each time step and the initial random state, and determine the electronic state density of the target material through the inner products of the random states corresponding to multiple time steps and the initial random state.
[0056] The initial random state of qubits is processed by time evolution on a quantum computer, and the time evolution processing includes time evolution processing of multiple time steps. The time evolution of the state can be the change of the quantum state of the material over time, and the change rule is determined by the Hamiltonian of the system. The Hamiltonian of the material can form its own time evolution operator. Acting the time evolution operator on the quantum state can realize the time evolution of the state.
[0057] Among them, the time step can be determined based on the energy range of the target material and the number of steps. Specifically, the energy range of the target material is pre-stored in a classical computer, and the quantum computer obtains the energy range of the target material from the classical computer. The energy resolution is determined based on the energy range of the target material and the number of steps. Based on the conversion relationship between the energy resolution and the time step, the time step is determined. Specifically, △E = 2π / △t, where △E is the energy resolution, △t is the time step, △E = Q / m, where Q is the energy range, and the energy ranges of different materials are different, and m is the number of steps.
[0058] The quantum computer introduces auxiliary qubits during the process of processing the initial random state of qubits by time evolution, measures the auxiliary qubits corresponding to each time step during the time evolution process, obtains the measurement results of the auxiliary qubits, and further determines the inner product of the random states corresponding to each time step and the initial random state during the time evolution process through the measurement results of the auxiliary qubits. The inner product can be the inner product of quantum states, which refers to a mathematical operation of projecting one quantum state onto another quantum state. In some embodiments of the present disclosure, the inner product of the random states corresponding to each time step and the initial random state is determined by determining the measurement data of the auxiliary qubits at each time step.
[0059] In some embodiments of the present disclosure, a quantum circuit corresponding to time evolution processing is preset, and the quantum computer executes the above quantum circuit to implement time evolution processing on the initial random state of the quantum bits. It can be understood that the inner product of the random state corresponding to each time step and the initial random state consists of real part data and imaginary part data. Optionally, a first quantum circuit and a second quantum circuit corresponding to time evolution processing are preset, where the first quantum circuit can be a quantum circuit for obtaining the first measurement result of the auxiliary quantum bit, and the first measurement result of the auxiliary quantum bit is configured to generate the real part data of the above inner product. The second quantum circuit can be a quantum circuit for obtaining the second measurement result of the auxiliary quantum bit, and the second measurement result of the auxiliary quantum bit is configured to generate the imaginary part data of the above inner product. In some embodiments of the present disclosure, the quantum computer obtains the first measurement result and the second measurement result of the auxiliary quantum bit by setting the first quantum circuit and the second quantum circuit respectively. The classical computer generates the real part data and the imaginary part data that make up the above inner product through the first measurement result and the second measurement result, and forms the inner product of the random state corresponding to each time step and the initial random state through the real part data and the imaginary part data, and further obtains the electronic state density of the target material through the above inner products corresponding to multiple time steps respectively.
[0060] The present disclosure combines a quantum computer and a classical computer, and respectively utilizes the advantages of exponential parallel processing and storage of the quantum computer and the data processing advantages of the classical computer to implement the calculation of the electronic state density of materials. This method can be executed by a processing system for the electronic state density of materials. The classical computer and the quantum computer here can be separate computer devices, and they are communicatively connected; or, they can be computing components integrated in the same computing system. For example, the computing system can include at least one quantum computer component and at least one classical computer component, and data transmission can be achieved between the quantum computer component and the classical computer component. The connection method is not limited.
[0061] In some embodiments of the present disclosure, performing time evolution processing on the initial random state for multiple time steps based on the Hamiltonian of the target material, and determining the measurement results corresponding to each time step of the auxiliary quantum bit during the time evolution processing, includes: executing the first quantum circuit by the quantum computer, performing time evolution processing on the initial random state for multiple time steps based on the Hamiltonian of the target material, and determining the first measurement result corresponding to each time step of the auxiliary quantum bit during the time evolution processing; executing the second quantum circuit by the quantum computer, performing time evolution processing on the initial random state for multiple time steps based on the Hamiltonian of the target material, and determining the second measurement result corresponding to each time step of the auxiliary quantum bit during the time evolution processing.
[0062] The first quantum circuit includes first sub - circuits corresponding to multiple time steps respectively; the initial random state of a qubit can be processed by time evolution through the first sub - circuit of the first time step to obtain the final state of the qubit at the first time step, that is, the random state at the first time step; through the first sub - circuit of the second time step, the random state at the first time step is processed by time evolution to obtain the final state of the qubit at the second time step, that is, the random state at the second time step; through the first sub - circuit of the third time step, the random state at the second time step is continuously processed by time evolution, and so on, until the final state of the qubit at the last time step is obtained as the final state of the qubit in the whole time - evolution process.
[0063] The structures of the first sub - circuits corresponding to different time steps are the same. Exemplarily, see Figure 3 , Figure 3 which is a schematic diagram of the first sub - circuit of the first quantum circuit provided by the embodiments of the present disclosure.
[0064] During the time - evolution process of any time step, the quantum state of the auxiliary qubit is initialized to the initial state, that is, the |0> state, and the H - gate is applied to the initial state of the auxiliary qubit to convert the initial state of the auxiliary qubit into a superposition state. The auxiliary qubit is used as the control end. When the auxiliary qubit is in the |1> state, the time - evolution process of the current time step is performed on the initial random state or the random state of the previous time step. Among them, for the first time step, when the auxiliary qubit is in the |1> state, the time - evolution process of the current time step is performed on the initial random state. In other time steps except the first time step, the time - evolution process of the current time step is performed on the random state of the previous time step. After the time - evolution process, the H - gate is applied to the auxiliary qubit again, and the first measurement result corresponding to the current time step is obtained by measuring the auxiliary qubit. Among them, the first measurement result can be the first probability that the auxiliary qubit is in the |0> state.
[0065] During the above - mentioned time - evolution process, applying the H - gate to the initial state of the auxiliary qubit can be expressed as which represents converting the initial state |0> of the auxiliary qubit into a superposition state According to the state of the auxiliary qubit, it is determined whether the initial random state or the random state of the previous time step performs the time - evolution process. Figure 3 In the formula, the symbol U represents the time - evolution process. where H represents the Hamiltonian of the target material, and t i represents the i - th time step. Correspondingly, the auxiliary qubit can be expressed as Applying another H - gate to the auxiliary qubit again, the auxiliary qubit can be expressed as
[0066] The second quantum circuit includes second sub - circuits corresponding to multiple time steps respectively. Similarly, through the second sub - circuit of the first time step, the initial random state of the qubit is subjected to time evolution processing to obtain the final state of the qubit at the first time step, that is, the random state at the first time step. Through the second sub - circuit of the second time step, the random state at the first time step is subjected to time evolution processing to obtain the final state of the qubit at the second time step, that is, the random state at the second time step. Through the second sub - circuit of the third time step, the random state at the second time step is continuously subjected to post - time - evolution processing, and so on, until the final state of the qubit at the last time step is obtained as the final state of the qubit in the entire time evolution processing.
[0067] The structures of the second sub - circuits corresponding to different time steps are the same. Exemplarily, see Figure 4 , Figure 4 which is a schematic diagram of the second sub - circuit in the second quantum circuit provided by the embodiments of the present disclosure.
[0068] During the time evolution process of any time step, the quantum state of the auxiliary qubit is initialized to the initial state, that is, the |0> state. The H - gate is applied to the initial state of the auxiliary qubit to convert the initial state of the auxiliary qubit into a superposition state. The phase gate is applied to the superposition - state auxiliary qubit. The phase gate remains unchanged when applied to the |0> state and gives it a phase i when applied to the |1> state, which is used to change the phase of the auxiliary qubit. The auxiliary qubit is the control end. When the auxiliary qubit is in the |1> state, the initial random state or the random state of the previous time step is subjected to the time evolution processing of the current time step. Among them, for the first time step, when the auxiliary qubit is in the |1> state, the initial random state is subjected to the time evolution processing of the current time step. In other time steps except the first time step, the random state of the previous time step is subjected to the time evolution processing of the current time step. After the time evolution processing, the H - gate is applied to the auxiliary qubit again, and the second measurement result corresponding to the current time step is obtained by measuring the auxiliary qubit; where the second measurement result can be the second probability that the auxiliary qubit is in the |0> state.
[0069] During the above - mentioned time evolution process, applying the H - gate to the initial state of the auxiliary qubit can be expressed as characterizing the conversion of the initial state |0> of the auxiliary qubit into a superposition state Applying the phase gate to the superposition - state auxiliary qubit, the auxiliary qubit can be expressed as According to the state of the auxiliary qubit, it is determined whether the initial random state or the random state of the previous time step performs time evolution processing. Figure 3 In Correspondingly, the auxiliary qubit can be represented as Applying another H gate to the auxiliary qubit again, the auxiliary qubit can be represented as
[0070] In some embodiments of the present disclosure, the quantum computer executes the first quantum circuit and the second quantum circuit respectively, and obtains the first measurement result and the second measurement result corresponding to each time step in the time evolution process of multiple time steps. That is, the measurement results corresponding to each time step in the time evolution process of the auxiliary qubit include the first measurement result and the second measurement result.
[0071] During the processing of the quantum computer, measuring the auxiliary qubit does not affect the time evolution process of the qubit. The state of the qubit is only affected by the control operation and its initial state, while the measurement of the auxiliary qubit only involves the collapse of the auxiliary qubit itself, which can ensure that after taking the inner product of the random state at a certain time step and the initial random state, the evolution of the qubit continues to proceed normally.
[0072] In some embodiments of the present disclosure, the first measurement result corresponding to each time step of the auxiliary qubit is the first probability that the auxiliary qubit is in the |0> state at each time step; the second measurement result corresponding to each time step of the auxiliary qubit is the second probability that the auxiliary qubit is in the |0> state at each time step. Correspondingly, the first measurement result of the auxiliary qubit can be represented as The second measurement result of the auxiliary qubit can be represented as Here, t i represents the i-th time step.
[0073] The quantum computer transmits the first measurement result and the second measurement result corresponding to each time step of the auxiliary qubit to the classical computer for storage, and the classical computer determines the electronic state density of the target material based on the first measurement result and the second measurement result corresponding to each time step of the auxiliary qubit.
[0074] In some embodiments of the present disclosure, through the classical computer, based on the measurement results corresponding to each time step of the auxiliary qubit, determining the inner product of the random state corresponding to each time step and the initial random state includes:
[0075] S131. Determining the real part data corresponding to each time step based on the first measurement result of the auxiliary qubit corresponding to each time step.
[0076] S132. Determining the imaginary part data corresponding to each time step based on the second measurement result of the auxiliary qubit corresponding to each time step.
[0077] Based on the real part data and the imaginary part data respectively corresponding to each of the time steps, form the inner product of the random state corresponding to each time step and the initial random state.
[0078] See Figure 5 , Figure 5 is a schematic diagram of a method for determining the inner product of the random state and the initial random state at any time step provided by an embodiment of the present disclosure.
[0079] The classical computer is preconfigured with a first mapping relationship between the real part data and the first measurement result, and a second mapping relationship between the imaginary part data and the second measurement result. Through the first mapping relationship and the first measurement result corresponding to the auxiliary qubit at each time step, the real part data corresponding to each time step is obtained, and through the second mapping relationship and the second measurement result corresponding to the auxiliary qubit at each time step, the imaginary part data corresponding to each time step is obtained, wherein the real part data and the imaginary part data respectively corresponding to each time step can form the inner product of the random state and the initial random state corresponding to each time step. Among them, the inner product of the random state and the initial random state can be expressed as Re(U) is the real part data, and Im(U) is the imaginary part data.
[0080] Among them, the first mapping relationship can be expressed as: The second mapping relationship can be expressed as:
[0081] In the above embodiment, and
[0082] Taking the first measurement result of the auxiliary qubit as an example,
[0083]
[0084] Correspondingly, the first mapping relationship can be obtained
[0085] Similarly, the second mapping relationship can be obtained
[0086] The classical computer calculates the real part data and the imaginary part data corresponding to each time step respectively through the first measurement result and the second measurement result for each time step, and then obtains the inner product of the random state and the initial random state corresponding to each time step. The above inner product can be expressed as C DOS (t).
[0087] The classical computer determines the electronic state density of the target material through the inner product of the random states corresponding to multiple said time steps and the initial random state. Specifically, through the classical computer, a Fourier transform is performed on the inner product of the random states corresponding to multiple said time steps and the initial random state to obtain the electronic state density of the target material.
[0088] The electronic state density of the target material can be characterized by the following formula:
[0089]
[0090] For the technical solutions of some embodiments of the present disclosure, for a target material composed of 2 N electrons, random numbers required in the process of determining the electronic state density are generated by a classical computer, an initial random state composed of N qubits is generated by a quantum computer, and time evolution processing is performed on the initial random state composed of qubits based on the Hamiltonian of the target material. During the above time evolution processing, auxiliary qubits are introduced, and the measurement results corresponding to each time step in the time evolution processing of the auxiliary qubits are measured. The classical computer converts the measurement results corresponding to each time step in the time evolution processing of the auxiliary qubits into the inner product of the random state and the initial random state corresponding to each time step in the time evolution processing, and the electronic state density of the target material is obtained through the inner products corresponding to multiple time steps respectively. By combining the advantages of exponential - level parallel processing and storage of the quantum computer and the data - processing advantages of the classical computer, the electronic state density of the material is determined. The quantum computer can perform data processing related to a target material composed of 2 N electrons through the processing of N qubits. Compared with generating and storing 2 N random complex numbers in a classical computer, the amount of processed data and the amount of calculation are reduced, as well as the occupied memory and resources, and the calculation time for the electronic state density is improved.
[0091] Figure 6 is a flowchart of a method for processing the electronic state density of a material according to another embodiment provided by the present disclosure. As Figure 6 shown, the method includes:
[0092] S210. Generate random numbers through a classical computer, and the number of the random numbers is determined based on the number of electrons of the target material.
[0093] S220. Generate an initial random state of qubits based on the random numbers through a quantum computer.
[0094] S230. Perform a Pauli basis decomposition on the Hamiltonian of the target material by means of the quantum computer to obtain a plurality of sub-Hamiltonians; split the evolution operator corresponding to the Hamiltonian into the time evolution operators corresponding to the respective sub-Hamiltonians; for each time evolution operator corresponding to a sub-Hamiltonian, perform an evolution process on the initial random state or the random state at the previous time step to obtain the random state of the quantum bits at each time step.
[0095] The Hamiltonian of the target material is pre-stored in the classical computer, and the method for determining the Hamiltonian of the target material is not limited herein. The Hamiltonian includes information such as the kinetic energy of the particles in the target material and the interaction energy between the particles. Taking the target material composed of 2 N electrons as an example, the Hamiltonian of the target material includes, but is not limited to, information such as single-electron terms and two-electron interaction terms.
[0096] The quantum computer obtains the Hamiltonian of the target material from the classical computer, so as to construct an evolution operator through the Hamiltonian of the target material and perform a time evolution process on the initial random state of the quantum bits.
[0097] In some embodiments of the present disclosure, the quantum computer performs a Pauli basis decomposition on the Hamiltonian of the target material to obtain a plurality of sub-Hamiltonians. Among them, each sub-Hamiltonian can be a tensor product of a plurality of Pauli matrices, and the tensor product can include one or more Pauli matrices. The Pauli matrix can be a group of two-by-two matrices and can be implemented by single-qubit quantum gate operations. The Pauli matrix includes the identity matrix, the Pauli X matrix, the Pauli Y matrix, and the Pauli Z matrix.
[0098] In some embodiments of the present disclosure, the quantum computer performs a Pauli basis decomposition on the Hamiltonian of the target material by means of the Jordan–Wigner transformation method. Correspondingly, the Hamiltonian of the target material can be expressed as H = ∑ j h j , where h j is the j-th sub-Hamiltonian.
[0099] In the time evolution process, the state of the quantum bits evolving with time is characterized by the evolution operator. Among them, the evolution operator can be expressed as e -iHt , where H is the Hamiltonian of the target material, t is the total duration corresponding to the time evolution process, and i is the imaginary unit. Based on the plurality of sub-Hamiltonians corresponding to the Hamiltonian, the quantum computer splits the evolution operator corresponding to the Hamiltonian into the time evolution operators corresponding to the respective sub-Hamiltonians, and decomposes the time evolution process into the accumulation of evolutions in multiple time steps. Specifically, it is split according to the time step Δt, and the time t is divided into m time steps, t = mΔt.
[0100] In some embodiments of the present disclosure, a quantum computer decomposes a time evolution operator based on the Trotter decomposition algorithm. Exemplarily, the time evolution operator can be decomposed into where m is the number of time steps. Correspondingly, the time evolution operator e -iHΔt corresponding to each time step can be expressed as
[0101] Correspondingly, for the time evolution operator corresponding to each sub-Hamiltonian, the initial random state or the random state of the previous time step is evolved to obtain the random state of the qubit at the current time step. Exemplarily, at the first time step, the initial random state is evolved based on the time evolution operator corresponding to each sub-Hamiltonian to obtain the random state at the first time step; at other time steps except the first time step, the random state of the previous time step is evolved based on the time evolution operator corresponding to each sub-Hamiltonian to obtain the random state corresponding to this time step.
[0102] In some embodiments of the present disclosure, the quantum computer decomposes the Hamiltonian of the target material into multiple sub-Hamiltonians, and each sub-Hamiltonian is a tensor product of multiple Pauli matrices. Through the Pauli matrices corresponding to the sub-Hamiltonians, the time evolution operator corresponding to each sub-Hamiltonian can be mapped to obtain a quantum operation gate, and the above time evolution process is realized through the quantum operation gate. Specifically, the time evolution operator corresponding to each sub-Hamiltonian is mapped into a quantum circuit of N qubits to form an evolution circuit, and the evolution circuit may include the above quantum operation gates.
[0103] Optionally, for the time evolution operator corresponding to each sub-Hamiltonian, evolving the initial random state or the random state of the previous time step to obtain the random state of the qubit at the current time step includes: mapping the time evolution operator corresponding to each sub-Hamiltonian to obtain a quantum operation gate, and applying the quantum operation gate to the initial random state or the random state of the previous time step to obtain the random state of the qubit at the current time step.
[0104] The sub-Hamiltonian may include at least one type of Pauli matrix. According to the type of Pauli matrix included in the sub-Hamiltonian, the time evolution operator corresponding to the sub-Hamiltonian is mapped to obtain a quantum operation gate corresponding to the type of Pauli matrix. Exemplarily, the Pauli X matrix is mapped to the Rx gate, the Pauli Y matrix is mapped to the Ry gate, and the Pauli Z matrix is mapped to the Rz gate.
[0105] In some embodiments of the present disclosure, the mapped quantum operation gates form an evolution circuit, and the time evolution processing for each time step can be implemented by executing the evolution circuit on a quantum computer. Correspondingly, the evolution circuit may include one or more of the above-mentioned Rx gates, Ry gates, and Rz gates and a controlled NOT gate.
[0106] In some embodiments of the present disclosure, for mapping the time evolution operator corresponding to each sub-Hamiltonian to a quantum operation gate, it includes: converting a plurality of Pauli matrices of the sub-Hamiltonian into Pauli matrices of a specific type respectively, and mapping the corresponding quantum operation gate based on the Pauli matrices of the specific type. Wherein, the Pauli matrices of the specific type include any one of the Pauli X matrix, the Pauli Y matrix, and the Pauli Z matrix. Optionally, the Pauli matrices of the specific type are Pauli Z matrices. Correspondingly, the Pauli X matrix, the Pauli Y matrix, and the identity matrix among the plurality of Pauli matrices in the sub-Hamiltonian are respectively converted into Pauli Z matrices. Specifically, the Pauli X matrix, the Pauli Y matrix, and the identity matrix can be respectively converted into Pauli Z matrices through the H gate.
[0107] Mapping the Pauli matrices of a specific type to the corresponding quantum operation gates. For example, when the Pauli matrices of the specific type are Pauli Z matrices, the corresponding quantum operation gates may include Rz gates and controlled NOT gates. It can be understood that the quantum operation gates corresponding to different types of Pauli matrices are different.
[0108] See Figure 7 and Figure 8 , Figure 7 and Figure 8 are respectively schematic diagrams of the evolution circuits provided by the embodiments of the present disclosure. As Figure 7 shown, the time evolution operator is When only the Pauli Z matrix is included in the sub-Hamiltonian, the evolution circuit constructed by Rz gates and controlled NOT gates is mapped. As Figure 8 shown, the time evolution operator is When the sub-Hamiltonian includes a Pauli X matrix, the Pauli X matrix is converted into a Pauli Z matrix through the H gate, and Rz gates and controlled NOT gates are mapped to construct the evolution circuit. In addition, when only the Pauli X matrix and the Pauli Y matrix are included in the sub-Hamiltonian, the Pauli X matrix can be converted into a Pauli Z matrix through the H gate; the Pauli Y matrix can be converted into a Pauli Z matrix through the phase gate, and Rz gates and controlled NOT gates are mapped to construct the evolution circuit.
[0109] It should be noted that Figure 7 and Figure 8 The evolution circuits shown are only for the time evolution operator corresponding to one sub-Hamiltonian. For each sub-Hamiltonian h in jcorrespond to a time evolution operator respectively. Each time evolution operator generates a corresponding evolution circuit, and each sub-Hamiltonian h j The evolution circuits corresponding respectively can be connected in sequence to form an evolution circuit of one time step. It can be understood that Figure 7 the corresponding evolution circuit performs time evolution processing on the quantum state formed by three qubits (q1, q2, and q3), and Figure 7 and Figure 8 are only schematic diagrams of the evolution circuit. The quantum operation gates mapped by the time evolution operators corresponding to the sub-Hamiltonians of the target object act on N qubits respectively to realize time evolution processing on the initial random state or the random state of the previous time step corresponding to the N qubits.
[0110] See Figure 3 and Figure 4 , Figure 3 and Figure 4 In, the "U" characterizes the above evolution circuit. The quantum computer forms a first quantum circuit by combining the above evolution circuit with the H gate and the controlled-NOT gate; forms a second quantum circuit by combining the above evolution circuit with the H gate, the phase gate, and the controlled-NOT gate.
[0111] S240. Determine the measurement results respectively corresponding to each time step in the time evolution processing of the auxiliary qubit by the quantum computer. The measurement results respectively corresponding to each time step include a first measurement result and a second measurement result.
[0112] The quantum operation gates mapped by the time evolution operators corresponding to the above sub-Hamiltonians form an evolution circuit. The quantum computer realizes time evolution processing on the initial random state of the qubit by executing the first quantum circuit and the second quantum circuit including the evolution circuit, and measures the measurement results respectively corresponding to each time step in the time evolution processing of the auxiliary qubit, that is, obtains the first measurement result and the second measurement result of the inner product of the random state corresponding to each time step and the initial random state.
[0113] S250. Based on the first measurement result and the second measurement result corresponding to each time step of the auxiliary qubit, determine the inner product of the random state corresponding to each time step and the initial random state by the classical computer, and determine the electronic state density of the target material through the inner products of the random states corresponding to multiple time steps and the initial random state.
[0114] The classical computer obtains the inner product of the random state corresponding to each time step and the initial random state through the first measurement result and the second measurement result corresponding to each time step, and further obtains the electronic state density of the target material.
[0115] In some embodiments of the present disclosure, the Hamiltonian of the target material is decomposed in the Pauli basis by a quantum computer to obtain a plurality of sub-Hamiltonians. The mapping of the time evolution operator corresponding to the sub-Hamiltonian to the quantum circuit is realized by a plurality of Pauli matrices included in the Hamiltonian, and the evolution circuit corresponding to the time evolution operator is obtained. The first quantum circuit and the second quantum circuit are constructed through the evolution circuit to realize the time evolution processing of the random state of the quantum bits by the quantum computer.
[0116] An alternative example of a method for determining the electronic state density of a material is also provided in the embodiments of the present disclosure. Figure 9 It is a flowchart of a method for determining the electronic state density of a material provided in the embodiments of the present disclosure. For a target material composed of 2 N electrons, a random state composed of N quantum bits is prepared for time evolution. First, 2N random numbers between 0 and 2π are generated by a random number generator of a classical computer, and N of the random numbers {φ i} are used to generate N random rotation X gates {R x (φ i )}, and N random numbers {θ i} are used to generate N random rotation Z gates {R z (θ i )}.
[0117] Meanwhile, the N quantum bits of the quantum computer are initialized to the |0> state, N H gates are respectively applied to the N quantum bits initialized to the |0> state, and a random rotation Z gate {R z (θ i )} and a random rotation X gate {R x (φ i )} are sequentially applied to each quantum bit to generate an initial random state composed of N quantum bits
[0118] The quantum computer decomposes the Hamiltonian H of the target material composed of 2 N electrons into a linear combination of N Pauli matrices {σ0, σ x , σ y , σ z} sub-Hamiltonians, that is, H = ∑ j h j , h j is the sub-Hamiltonian of N Pauli matrices, that is, the sub-Hamiltonian. The Pauli basis decomposition process can be realized by the Jordan–Wigner transformation method.
[0119] The quantum computer transforms the time evolution operator e -iHΔtinto a quantum circuit mapped to N qubits. Among them, the Hamiltonian H has been decomposed into a linear combination of Pauli matrix sub-Hamiltonians, and the evolution operator e can be decomposed into the cumulative product of m time-step evolutions through Trotter decomposition -iHt with each time step being Δt = t / m, and the time evolution operator e corresponding to each time step for each time step is Δt = t / m, and the time evolution operator e corresponding to each time step -iHΔt can be expressed as
[0120] The quantum computer sequentially maps m U(Δt)'s into the quantum circuit of N qubits. For each U(Δt), the mapping to the quantum circuit of N qubits is sequentially completed ; for each e -iHΔt , h j in the case where there is only the Pauli Z matrix σ z , the mapping of can be completed using CNOT gates and Rz gates, as shown in Figure 7 . For h j in addition to the case where there is the Pauli Z matrix σ z , there are also cases of the Pauli X matrix and the Pauli Y matrix. The Pauli X matrix can be converted to the Pauli Z matrix through the H gate; the Pauli Y matrix is converted to the Pauli Z matrix by applying the H gate, and the converted Pauli Z matrix is mapped to the Rz gate, and the mapping of is completed through CNOT gates and Rz gates.
[0121] The quantum computer has completed all mappings to N qubits and obtained the evolution circuit. Through the evolution circuit, the quantum circuit for the evolution of the random state at any time mΔt by the time evolution operator U(mΔt) is obtained, that is, the first quantum circuit and the second quantum circuit are constructed through the evolution circuit.
[0122] The quantum computer executes the first quantum circuit, prepares the auxiliary qubit in the initial state, applies an H gate to this auxiliary qubit, for each time step random state or initial random state, applies the time evolution process corresponding to the controlled evolution circuit, applies the H gate operation to the auxiliary qubit again, and finally measures the probability P(0) that the auxiliary qubit is in the |0> state as the first measurement result.
[0123] The quantum computer executes the second quantum circuit, prepares the auxiliary qubit in the initial state, applies an H gate to this auxiliary qubit, and then applies a phase gate to this auxiliary qubit. For each time step random state or initial random state, applies the time evolution process corresponding to the controlled evolution circuit, applies the H gate operation to the auxiliary qubit again, and finally measures the probability P(0) that the auxiliary qubit is in the |0> state as the second measurement result.
[0124] The quantum computer stores the first measurement result and the second measurement result corresponding to each time step into the classical computer. The classical computer obtains the real part data corresponding to each time step based on the first measurement result corresponding to each time step, and obtains the imaginary part data corresponding to each time step based on the second measurement result corresponding to each time step. The real part data and the imaginary part data corresponding to each time step form the inner product of the random state corresponding to each time step and the initial random state. The total number of inner products is m. Performing a fast Fourier transform on the m inner products of the m time steps can obtain the electronic state density of the target material.
[0125] Figure 10 It is a schematic diagram of a system for determining the electronic state density of a material provided by an embodiment of the present disclosure. As Figure 10 shown, the system includes: a classical computer 310 and a quantum computer 320; the connection relationship between the classical computer 310 and the quantum computer 320 is not limited herein. Among them,
[0126] The classical computer 310 is configured to generate random numbers, and the number of the random numbers is determined based on the number of electrons of the target material;
[0127] The quantum computer 320 is configured to read the random numbers from the classical computer, generate an initial random state of quantum bits based on the random numbers, perform a multi-time-step time evolution process on the initial random state based on the Hamiltonian of the target material, and determine the measurement results respectively corresponding to each time step in the time evolution process of the auxiliary quantum bits, and store the measurement results of the auxiliary quantum bits corresponding to each time step into the classical computer;
[0128] The classical computer 310 is further configured to determine the inner product of the random state corresponding to each time step and the initial random state based on the measurement results respectively corresponding to each time step of the auxiliary quantum bits, and determine the electronic state density of the target material through the inner products of the random states and the initial random state corresponding to multiple time steps.
[0129] The system for determining the electronic state density of a material provided by an embodiment of the present disclosure can execute the method for determining the electronic state density of a material provided by any embodiment of the present disclosure, and has the corresponding functional modules and beneficial effects for executing the method.
[0130] It should be understood that various forms of the processes shown above can be used, reordering, adding or deleting steps. For example, the steps recorded in the present disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired results of the technical solutions of the present disclosure can be achieved, and no limitations are made herein.
[0131] The above specific embodiments do not constitute a limitation on the protection scope of the present disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principle of the present disclosure shall be included within the protection scope of the present disclosure.
Claims
1. A method for determining the electronic state density of a material, characterized in that, Including: Generating random numbers by a classical computer, where the number of the random numbers is determined based on the number of electrons of a target material; Generating an initial random state of qubits by a quantum computer based on the random numbers, performing time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determining measurement results respectively corresponding to each of the time steps during the time evolution processing of an auxiliary qubit; By the classical computer, based on the measurement results respectively corresponding to each of the time steps of the auxiliary qubit, determining the inner product of the random state corresponding to each of the time steps and the initial random state, and determining the electron state density of the target material through the inner products of the random states corresponding to multiple time steps and the initial random state.
2. The method according to claim 1, wherein The generating the initial random state of qubits based on the random numbers includes: By the quantum computer, sequentially applying an H gate and at least one random rotation gate to each qubit in the initial state, to obtain an initial random state formed by multiple qubits, where the at least one random rotation gate includes one or more of a random rotation Z gate, a random rotation X gate, and a random rotation Y gate, and the rotation angle of any one of the random rotation gates is any one of the random numbers.
3. The method according to claim 1, wherein The performing time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material and determining measurement results respectively corresponding to each of the time steps during the time evolution processing of the auxiliary qubit includes: By the quantum computer, executing a first quantum circuit, performing time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determining a first measurement result corresponding to each of the time steps during the time evolution processing of the auxiliary qubit; By the quantum computer, executing a second quantum circuit, performing time evolution processing with multiple time steps on the initial random state based on the Hamiltonian of the target material, and determining a second measurement result corresponding to each of the time steps during the time evolution processing of the auxiliary qubit.
4. The method according to claim 3, wherein During the time evolution process of any time step, applying an H gate to the initial state of the auxiliary qubit, performing the time evolution processing of the current time step on the initial random state or the random state corresponding to the previous time step, and applying an H gate again after the time evolution processing, and measuring the auxiliary qubit to obtain the first measurement result corresponding to the current time step.
5. The method according to claim 3, wherein During the time evolution process of any time step, sequentially applying an H gate and a phase gate to the initial state of the auxiliary qubit, performing the time evolution processing of the current time step on the initial random state or the random state of the previous time step, and applying an H gate again after the time evolution processing, and measuring the auxiliary qubit to obtain the second measurement result corresponding to the current time step.
6. The method according to claim 3, characterized in that, The determining the inner product of the random state corresponding to each of the time steps and the initial random state based on the measurement results respectively corresponding to each of the time steps of the auxiliary qubit includes: Determine the real part data corresponding to each time step based on the first measurement result of the auxiliary qubit corresponding to each time step; Determine the imaginary part data corresponding to each time step based on the second measurement result of the auxiliary qubit corresponding to each time step; Determine the inner product of the random state corresponding to each time step and the initial random state based on the real part data and the imaginary part data respectively corresponding to each time step.
7. The method according to claim 1, wherein The time evolution process of performing multi-time step on the initial random state based on the Hamiltonian of the target material includes: Perform Pauli basis decomposition on the Hamiltonian of the target material by the quantum computer to obtain a plurality of sub-Hamiltonians, and any one of the sub-Hamiltonians includes one or more Pauli matrices; Split the evolution operator corresponding to the Hamiltonian into time evolution operators corresponding to each of the sub-Hamiltonians; Based on the time evolution operator corresponding to each sub-Hamiltonian, perform an evolution process on the initial random state or the random state of the previous time step to obtain the random state of the qubit at the current time step.
8. The method according to claim 7, wherein The process of performing an evolution process on the initial random state or the random state of the previous time step based on the time evolution operator corresponding to each sub-Hamiltonian to obtain the random state of the qubit at the current time step includes: Map the time evolution operator corresponding to each sub-Hamiltonian to obtain a quantum operation gate, and apply the quantum operation gate to the initial random state or the random state of the previous time step to obtain the random state of the qubit at the current time step.
9. The method according to claim 1, wherein The process of determining the electronic state density of the target material by the inner product of the random states corresponding to multiple time steps and the initial random state includes: Perform a Fourier transform on the inner product of the random states corresponding to multiple time steps and the initial random state by the classical computer to obtain the electronic state density of the target material.
10. A system for determining the electronic state density of a material, characterized in that, Including: A classical computer and a quantum computer; wherein, The classical computer is configured to generate random numbers, and the number of the random numbers is determined based on the number of electrons of the target material; The quantum computer is configured to read the random numbers from the classical computer, generate an initial random state of the qubit based on the random numbers, perform a multi-time step time evolution process on the initial random state based on the Hamiltonian of the target material, and determine the measurement results respectively corresponding to each time step during the time evolution process of the auxiliary qubit, and store the measurement results of the auxiliary qubit corresponding to each time step into the classical computer; The classical computer is further configured to determine the inner product of the random state corresponding to each time step and the initial random state based on the measurement results respectively corresponding to each time step of the auxiliary qubit, and determine the electronic state density of the target material by the inner product of the random states corresponding to multiple time steps and the initial random state.