Quantum computer device, method of operation, and non-temporary computer-readable storage medium

Abstract

A hybrid computer mechanism configured to perform a simulation of a chemical system includes a combination of a classical computer coupled to a quantum computer, and the hybrid computer mechanism, when in use, is configured to receive input data and generate corresponding processed output data from the input data, and is configured to (a) receive information describing the chemical system in the input data, (b) process the information describing the chemical system using a preentangler algorithm and a fixed circuit algorithm to generate a quantum Ansatz that defines initial values ​​for a quantum circuit calculation and a Hamiltonian from which a variational circuit algorithm is generated, (c) calculate a corresponding quantum circuit using the quantum Ansatz and variational circuit algorithm to generate a quantum calculation result, and (d) process the quantum calculation result to generate output data including information describing an electron trajectory simulation of the chemical system.

Description

[Technical Field]

[0001] This disclosure relates to a quantum computing device, for example, a hybrid computing device including a combination of a quantum computer and a classical binary computer coupled together. Furthermore, this disclosure relates to a method for operating such a quantum computing device. In addition, this disclosure relates to a software product recorded on a machine-readable medium, the software product being executable on the aforementioned quantum computing device for carrying out the aforementioned method. [Background technology]

[0002] Quantum computers have recently become available as noisy intermediate-scale quantum (NISQ) devices[1], and furthermore, quantum computers can be classically simulated (i.e., "emulated"). One of the technical problems with NISQ devices is that their currently available qubits are too noisy to perform the deep quantum circuits required for most useful applications of quantum computers. For example, qubit phase estimation is difficult to implement on NISQ devices. To bridge the gap between modern NISQ devices and future fault-tolerant quantum computing devices, many researchers have turned to variational quantum algorithms such as variational quantum eigensolvers (VQEs), quantum optimization algorithms, variational imaginary-time evolution algorithms, variational quantum adiabatic algorithms, and quantum neural network algorithms[2~8]. Variational quantum circuits executable using NISQ devices are typically shallower than many other types of quantum circuits executed using such devices. Due to this shallowness, variational quantum circuits exhibit a certain algorithmic resilience to noise, which is beneficial. Furthermore, such variational quantum circuits function iteratively by evaluating a given objective function of a given optimization problem on a given NISQ device, and updating the variational parameters of the variational quantum circuit by using a classical optimization algorithm.

[0003] A drawback is that designing a sufficiently expressive quantum circuit ansatz presents the problem of exponentially vanishing gradients as a function of the number of qubits used, resulting in a barren plateau that requires exponential time to escape [9]. In the presence of noise, the barren plateau becomes an even less expressive, problem-inspired ansatz as long as one attempts to train hyperlinear parameterized gates

[10] . Therefore, reducing the number of variational parameters is essential for the success of variational quantum algorithms in the near future. Vanishing gradients also presented an early challenge to deep neural networks in classical machine learning.

[0004] Generally, according to classical canonical transformation theory, the electron correlations of molecules are typically divided into two components. Static correlations have been used to quantify the portion of electron correlation associated with multiple relevant determinants whose energies are close to the Highest Occupied Molecular Orbital (HOMO) and Lowest Un-occupied Molecular Orbital (LUMO). Dynamic correlations describe the correction to the ground state resulting from excitations involving low-position core orbitals or high-position virtual orbitals. When static correlations are negligible, this is called single-reference chemistry. In such situations, the dynamic correlations can generally be adequately described by the classical coupled cluster (CC) method, provided that a sufficiently large ground system is used

[19] . Conversely, multi-reference situations arise when a single determinant is insufficient to describe the chemical bonding, even qualitatively. In practice, these situations are observed in chemical reactions, i.e., when crossing the HOMO-LUMO gap where the valence configurations of the products and reactants are almost completely lost, as well as in excited states and transition metal chemistry.

[20]

[0005] To handle the multi-reference situation, when performing quantum chemical simulations, as shown in Figure 1b, conventionally, molecular orbitals are usually divided into core (c) orbitals, active (a) orbitals, and virtual (v) orbitals. At this time, (i) Core orbitals are defined as being completely filled, (ii) Orbitals in the active space are partially filled, (iii) Orbitals in the virtual space are empty. The optimal way to assign the active space is not known and is initially based on chemical intuition. Modern computer software programs such as BLOCK

[21] and AutoCAS[22 - 25] use the Fiedler vector as a proxy for the mutual information between orbitals and also use machine learning algorithms to automate the assignment of the active space. And the Hilbert space is

[0006]

Number

[0007] To handle the multi - reference situation, many methods have been developed, such as multi - reference coupled cluster

[26] , etc. All of them are computationally expensive when executed using NISQ devices. Below, to assist in the understanding of the subject matter of this disclosure, the Canonical Transformation (CT theory) will be further explained. This disclosure defines the initial values of qubits used when executing quantum circuits on NISQ devices using the CAS - DMRG ansatz. In CT theory, for a given qubit, the initial values are given by equations (1) and (2).

[0008]

Number

[0009]

number

[0010] Here, M is the number of spin orbitals in the active space, and the physical index i j is in the range of 0 to 1, and α j , 1...D j Takes a range of values, D j is the join dimension of join j. The join dimension D of MPS is all D j Defined as the maximum value over a certain period. Objective A [j] is a matrix for j ∈ {1, M} and is a given bulk tripod tensor. The optimization cost is O(MD 3 ) can be scaled as such, and calculations up to D=1000 can be performed routinely, with the largest bond dimension reported in supercomputer chemical simulations being D=65536

[27] . In practice, much lower bond dimensions can yield highly accurate results, especially in pseudo-one-dimensional shapes, where convergence has been achieved for active spaces of up to 100 orbitals[28, 29].

[0011] A major challenge in CAS-DMRG is restoring dynamic correlations. The single-reference CC method is applicable because it assumes that a given excitation operator has fixed orbital occupations of a given reference state. One proposal to overcome this problem is the canonical transformation (CT) theory mentioned above [14, 30-33]. In CT, the CC excitation operator is replaced by the unitary operator given by equation (3). U=e T (3) Here,

[0012]

number

[0013]

number

[0014] [Number] is c ● , a ● , and v ● The indices denoted as, respectively, core space, active space, and virtual space, and the repeated indices of each term are assumed to be added together. Next, as given in equation (4), the unitary U is applied to the reference state. |ψ⟩ = U|ψ0⟩ (4) The coefficient θ needs to be optimized. Classically, this optimization proceeds as follows. That is, as given in equation (5), the exponent can be expanded.

[0015] [Number]

[0016] In a classical binary computer, an exact and efficient implementation of equation (5) is not possible. The reason for this impossibility is that an expression such as [[H,T],T] contains an N - point correlation function. Although the one - body and two - body reduced density matrices of the reference wave function can be calculated, general N - body term operations necessarily require exponential time. Therefore, in CT theory, higher - order terms are approximated by a sum of products of one - body and two - body terms using a so - called cumulant expansion

[34] . The convergence of the cumulant expansion is generally fast in the single - reference scenario but slow in the multi - reference system. Ironically, these are exactly the systems for which CAS - DMRG is particularly suitable

[35] . Thus, in order to overcome the main limitation of CT theory, an alternative method for calculating (5) must be found. Summary of the Invention Problems to be Solved by the Invention

[0017] The object of this disclosure is to provide an improved method for configuring a quantum computer device to perform quantum chemical simulations, such simulations can be used in the processes of manufacturing chemical materials and pharmaceuticals, and designing and controlling chemical manufacturing machinery. [Means for solving the problem]

[0018] According to a first aspect, a method is provided for configuring a hybrid computer mechanism to perform chemical simulations, the hybrid computer mechanism comprising a combination of a classical computer coupled with a quantum computer, the hybrid computer mechanism being configured to receive input data and generate corresponding post-processed output data from the input data when in use, and the method is (a) Configuring a classical computer to receive information describing the chemical system in the input data, (b) Constructing a classical computer to process information describing a chemical system using pre-entangler algorithms and fixed-circuit algorithms to generate a quantum Ansatz that defines initial values ​​for quantum circuit calculations, and a Hamiltonian from which a variational circuit algorithm is generated, (c) Constructing a quantum computer to compute corresponding quantum circuits and generate quantum computation results using quantum Ansatz and variational circuit algorithms, (d) Constructing a classical computer to process quantum computation results and generate output data containing information describing electron orbital simulations of chemical systems.

[0019] The present invention is advantageous in that it allows the computational load to be transferred from a quantum computer to a classical computer by using a pre-entangler, such as a parameter-free pre-entangler. Furthermore, the present invention is advantageous in that it can reduce the number of parameters in variational quantum circuit algorithms, especially as the number of qubits used in the quantum circuit increases.

[0020] Optionally, the method includes configuring a pre-entangler algorithm to function as a parameter-free pre-entangler. Further optional, the method includes configuring a pre-entangler algorithm using a Matrix Product State (MPS) algorithm. Further optional, the method includes generating a Matrix Product State (MPS) based on a unitary linear combination describing a chemical system. Optionally, the method includes configuring a hybrid computer mechanism to generate a Matrix Product State (MPS) using a Density Matrix Renormalization Group (DMRG) algorithm to capture the complete active space (CAS) for one or more nonlinear transition metal complexes contained in the chemical system. Optionally, the method includes configuring a hybrid computer mechanism to generate a Matrix Product State (MPS) by using an MPS algorithm based on sequential generation using an ancilla.

[0021] Optionally, the method involves using a quantum circuit to find the ground state of the Hamiltonian.

[0022] Optionally, the method comprises constructing a variational quantum circuit algorithm as a variational quantum eigenvalue solver based on one or more canonical transformations, and the method comprises constructing a hybrid computing mechanism to generate a density matrix renormalization group (DMRG) algorithm using a classical computer to construct static correlations in wave functions describing a chemical system, the density matrix renormalization group (DMRG) algorithm being used to generate the corresponding DMRG-QCT portion of the quantum circuit.

[0023] Optional, the method is: (i) Assigning core space, virtual space, and molecular orbitals capable of occupying the active space to the active space based on the molecular system, (ii) Approximate the ground state of the Hamiltonian using the MSRG algorithm by generating a matrix product state (MPS) description |ψ0〉 of the ground state for a given bond dimension D, (iii) Find a quantum circuit that creates the MPS description |ψ0〉 on a quantum computer, (iv) Constructing variational quantum circuits that describe dynamic correlations by coupling active orbitals in the core space and active space, (v) From the results of executing the quantum circuit, minimize the ground state energy to generate the output result, This includes configuring a hybrid computer mechanism to perform the following actions.

[0024] According to a second aspect, a hybrid computer mechanism is provided which is configured to perform chemical simulations, the hybrid computer mechanism comprising a combination of a classical computer coupled with a quantum computer, the hybrid computer mechanism being configured to receive input data and generate corresponding post-processed output data from the input data when in use, the computer mechanism (a) It is configured to receive information describing the chemical system in the input data, (b) The pre-entangler algorithm and the fixed-circuit algorithm are configured to process information describing the chemical system to generate a quantum ansatz that defines initial values ​​for quantum circuit calculations, and a variational circuit algorithm that generates a Hamiltonian therefrom, (c) Configured to use quantum Ansatz and variational circuit algorithms to compute the corresponding quantum circuit and generate quantum computation results, (d) The system is configured to process the quantum computation results and generate output data that includes information describing the electron orbital simulation of the chemical system.

[0025] Optionally, in the hybrid computer mechanism, the pre-entangler algorithm is configured to function as a parameter-free pre-entangler.

[0026] Optionally, in the hybrid computer mechanism, the pre-entangler algorithm is configured to use a matrix product state (MPS) algorithm. Further optional, the hybrid computer mechanism is configured to generate matrix product states (MPS) using a density matrix renormalization group (DMRG) algorithm to capture the fully active space (CAS) for one or more nonlinear transition metal complexes contained in the chemical system. Further optional, the hybrid computer mechanism is configured to generate matrix product states (MPS) by using an MPS algorithm based on sequential generation using ancillaries.

[0027] Optionally, a hybrid computer mechanism is configured to use quantum circuits to find the ground state of the Hamiltonian.

[0028] Optionally, the hybrid computer mechanism is configured to include a variational quantum circuit algorithm as a variational quantum eigenvalue solver based on one or more canonical transformations, and the hybrid computer mechanism is configured to use a classical computer to generate a density matrix renormalization group (DMRG) algorithm to construct static correlations in the wave function describing the chemical system, and the density matrix renormalization group (DMRG) algorithm is used to generate the corresponding DMRG-QCT portion of the quantum circuit.

[0029] Optionally, a hybrid computer mechanism, (i) Assigning core space, virtual space, and molecular orbitals capable of occupying the active space to the active space based on the molecular system, (ii) Approximate the ground state of the Hamiltonian using the MSRG algorithm by generating a matrix product state (MPS) description |ψ0〉 of the ground state for a given bond dimension D, (iii) Find a quantum circuit that creates the MPS description |ψ0〉 on a quantum computer, (iv) Constructing variational quantum circuits that describe dynamic correlations by coupling active orbitals in core space and active space, (v) From the results of executing the quantum circuit, minimize the ground state energy to generate the output result, It was configured to perform the following actions.

[0030] According to a third aspect, a non-temporary computer-readable storage medium is provided, comprising a unique computer-readable instruction executable by data processing hardware, wherein the unique computer-readable instruction, when executed using the data processing hardware, implements the method of the first aspect.

[0031] Further aspects, advantages, features, and objectives of this disclosure will become apparent from the drawings and the detailed description of exemplary embodiments, which shall be construed in conjunction with the appended claims below.

[0032] It will be recognized that the features of this disclosure can be combined in various ways without departing from the scope of this disclosure as defined in the attached claims.

[0033] Embodiments of this disclosure will be described with reference to the following drawings. [Brief explanation of the drawing]

[0034] [Figure 1A] This diagram shows a quantum computing device that includes a classical computing mechanism coupled with a quantum computing mechanism. The classical and quantum computing mechanisms work together to perform computational tasks involving the generation and execution of quantum circuits. [Figure 1B] (a) is a diagram of the general structure of a pre-entangled variational quantum algorithm, and (b) is a diagram of the spin orbit classification in the fully active space method. [Figure 2] This is a diagram of the quantum circuit used to compute DMRG-QCT. [Figure 3](a) is a diagram of a water molecule with an equilibrium bond angle, (b) is a diagram of a nitrogen dimer, (c) is a diagram of a BeH2 molecule which is the sum of a Be atom and an H2 molecule, and (d) is a diagram of a P4 system containing two H2 molecules. [Figure 4] This figure shows the absolute energy errors of different methods for approximating the ground state energy using quantum circuits. The energy errors are strictly positive in all methods, except for CCSD, which is negative for some points. Figure 4 shows (a) a water molecule in the STO-6G ground system with 14 qubits and an active space used for DMRG calculations with 5 × 2 = 10 spin orbits, (b) a nitrogen dimer in STO-6G with an active space of 12 spin orbits, (c) BeH2 in the STO-6G ground system with an active space of 10 spin orbits, and (d) the 6-31G ground system and the P4 model system with an active space containing 12 spin orbits. All plots shown in Figure 4 share the same common legend, shown separately in (a) and (b). [Figure 5] This figure shows the energy error as a function of the bond dimension D used in DMRG for a water molecule with R(OH) = 108 angstroms, where D = 16 is the exact active (i.e., no approximation at all) bond dimension used in Figure 4. [Figure 6] (a) is a figure showing the increase in the number of parameters for GUCC and DMRG-QCT Ansatz, with an inset showing the same given data normalized by the number of parameters for the GUCC Ansatz, and (b) and (c) are figures showing the scaling of the quantum circuit depth and the number of quantum gates required as a function of the number of variational parameters. [Figure 7] (a) A figure showing the fidelity of the approximate state of an N2 molecule in the ground state of a 20-qubit STO-6G ground system, created by the SEQ algorithm, with an interatomic distance NN = 1.8 angstroms. (b) A figure showing the energy error of the same molecule, with the gray area indicating an error below chemical accuracy. [Figure 8](i) (upper figure) is a diagram of a nondeterministic circuit for constructing a linear combination of unitary circuits, and (ii) (lower figure) is a diagram of a multi-qubit controlled unitary circuit, explained with respect to one-body and two-body gates. [Figure 9A] This is a table of circuit requirements for the molecules considered with respect to the molecules described in this disclosure. In the table, (●) represents the requirements for QCT-S and QCT-SD normalized to GUCC-SD. The third column contains the coupling dimension D of the MPS by DMRG and the number of layers DSEQ used by a successive unitary algorithm to approximate the MPS with a given desired accuracy. [Figure 9B] This figure shows the probability of measuring zero in an LCU circuit as shown in Figure 8. The inset data shows the convergence of k as a function of 1 / DLCU. HAF represents the ground state data of a 16-point Heisenberg antiferromagnet (HAF) chain H=Σi(XiXi+1+YiYi+1+JZZiZi+1). H2O represents the water molecule data shown in Figure 3(a) in a 14-qubit STO-6G ground system. Furthermore, the P4 system represents the results for the ground state of the P4 model system shown in Figure 3(c) in a 16-qubit STO-6G ground system. [Figure 10A] Figure 10A(I) shows the results for the ground state of a 20-spin HAF. Furthermore, (a, b) shows the Schmidt values ​​corresponding to the two algorithms without any Dmax truncation. Furthermore, (c) shows the bond dimension as a function of the number of layers. And (d) shows the convergence of fidelity corresponding to the two algorithms with Dmax=3D truncation. [Figure 10B] Figure 10B(II) shows the data for the N2 molecule. Furthermore, (a, b) shows the Schmidt values ​​corresponding to the two algorithms without any Dmax truncation. Furthermore, (c) shows the bond dimension as a function of the number of layers. And (d) shows the convergence of fidelity corresponding to the two algorithms with Dmax=3D truncation. [Figure 11]This figure includes a first row showing fidelity and a second row showing energy error for a given ground state. Panel (I) shows the results for the P4 system shown in Figure 3a in a 6-31G ground system with 16 qubits. Panel (II) shows the data for the N2 molecule shown in Figure 3b with 20 qubits. Panel (III) shows the results for the HAF with 32 spins. [Figure 12] This is a diagram illustrating the steps of a method for implementing an embodiment relating to this disclosure. [Figure 13] These are diagrams of quantum gates and their equivalents to illustrate the implementation of this disclosure. [Modes for carrying out the invention]

[0035] In the attached drawings, underlined numbers are used to indicate the element to which the underlined number is located, or to elements adjacent to the underlined number. If a number is not underlined and is accompanied by an associated arrow, the ununderlined number is used to identify the entire element that the arrow points to.

[0036] In summary, modern computing hardware, configured to use silicon-based integrated circuits and associated data memory devices for data processing, becomes more computationally powerful and faster as the feature size of its integrated circuits decreases. As circuit feature sizes approach the nanometer scale, Heisenberg's uncertainty principle and quantum effects become more pronounced in the design and operation of integrated circuits. In extreme cases, representing data using a single particle, such as an ion or photon, i.e., in the form of a qubit, represents the limit of miniaturization and provides the fastest computing performance, especially when phenomena such as superposition and entanglement are utilized. Such methods are used in modern quantum computers. An overview of quantum computation and quantum information is provided in the academic publication "Quantum computations and quantum information" by Nagy et al. (The International Journal of Parallel, Emergent and Distributed Systems, Vol 21, No. 1, Feb 2006, pp. 1-59).

[0037] In some cases, quantum computers and quantum computing systems can leverage the quantum properties of fields and particles to improve computational speed compared to classical computers, enabling the solution of computationally complex problems within timeframes suitable for practical applications. In classical data processing, where data represents, for example, real-world physical signals, many mathematical operations such as calculations of averaging, correlation, Fourier transform, and Hadamard transform are used to process the data. The data to be processed can be quite large, for example, several terabytes of information, or even several petabytes of information, acquired sequentially over a period of time, for example, from a sensor array. Processing time and the associated latency for processing the data are important factors, for example, in real-time control situations. Quantum computers can potentially be configured to process large amounts of data very efficiently. However, a challenging modern technological problem is how to configure quantum computers in a way that is optimal for implementing such data processing. For example, considering the level noise generated by various elements of quantum circuits, a technical problem is how to use quantum computers to perform computational tasks (e.g., quantum computation tasks) in such a way that the noise generated during computation does not limit the smallest achievable computational error.

[0038] Traditionally, it has been known to use a combination of classical and quantum computers when attempting to solve extremely complex problems; in this disclosure, such a combination is referred to as a quantum computing system. Classical computers use silicon integrated circuit devices configured to operate substantially at room temperature (approximately +20°C), while quantum computers are configured to be cooled to extremely low temperatures (approximately -273°C) for most efficient operation. When tackling a given computational task, the task can be divided into execution on a classical computer and execution on a quantum computer. Furthermore, for a given task, a classical computer may be more efficient than a quantum computer for handling simple computational tasks, while a quantum computer may be able to solve certain types of computational tasks that are inefficient to perform on a classical computer. However, transferring tasks between classical and quantum computers incurs a time overhead, which is preferably reduced as much as possible to achieve optimal computational performance for a quantum computing system.

[0039] When using such a tandem configuration of a classical computer and a quantum computer, it can be advantageous to perform certain arithmetic calculations on the quantum computer rather than the classical computer, for example, to increase data processing throughput. The technical problem arising from this is how to configure the quantum computer most effectively to perform certain types of arithmetic calculations so that noise generated during quantum computation does not limit the total number of quantum operations that can be performed on a quantum computation task. Thus, some embodiments of this disclosure relate to addressing the technical problem of configuring a classical computing system tandem-coupled with a quantum computer in such a way that it enables more efficient computation of input data to generate corresponding post-processed output data, and reduces computational errors in the post-processed output data while keeping quantum noise generated within the quantum computer below a threshold.

[0040] Figure 1A shows a schematic diagram of the quantum computing system 100. In some examples, the quantum computing system 100 may receive input data 101 from a data source and generate output data 102. In some cases, the input data 101 may include a real-valued function, and the output data 102 may include a predicted value of the real-valued function for a probability distribution. In some embodiments, the output data 102 may include an estimated quantum amplitude of an error below a threshold error. In some implementations, the quantum computing system 100 may include at least a classical computing system 110 (also referred to as a classical computer or binary data computer) and a quantum computer 130 communicating with the binary data computer. In some cases, the classical computing system 110 may communicate with the quantum computer 130. In some examples, the classical computing system 110 may be coupled in combination with the quantum computer 130. The classical computing system 110 may exchange data with the quantum computer 130 via one or more data links, which may be provided, for example, using a data highway. In some examples, the classical computing system 110 may include non-temporary memory and at least one electronic processor configured to execute computer-executable instructions (e.g., software instructions or program instructions) stored in the non-temporary memory. In some examples, the electronic processor may be implemented using a silicon integrated circuit that performs binary digital calculations when in use. One or more data processors may be configured to execute software instructions for processing input data 101 and generating output data 102, with assistance from a quantum computer 130 coupled to the classical computing system 110.

[0041] Memory may be non-volatile memory such as flash memory, hard disk, magnetic disk memory, optical disk memory, or any other type of non-volatile memory. Furthermore, types of memory may include, but are not limited to, random access memory ("RAM") and read-only memory ("ROM"). In some examples, the classical computing system 110 may be programmed to perform different procedures, each implemented based on different sets of instructions.

[0042] In some cases, the electronic processor of the classical computing system 110 may receive input data 101 from a data source (e.g., from a sensor or sensor network), process the input data 101 to generate quantum computer input data 103, and execute computer executable instructions to transmit the quantum computer input data 103 to the quantum computer 130. In addition, the electronic processor of the classical computing system 110 may transmit configuration data 105 that can be used to configure the quantum computer 130 (e.g., to configure one or more quantum gates of the quantum computer 130). In some cases, the configuration data 105 may be stored in the memory of the classical computing system 110. In some other cases, the electronic processing of the classical computing system 110 may generate the configuration data 105 based at least in part on data stored in the memory of the classical computing system 110. In some cases, the configuration data 105 may be provided by the user through a user interface (e.g., the user interface of the classical computing system 110).

[0043] In some examples, the input data 103 of the quantum computer may include any data related to instructions that can be executed or used by the controller of the quantum computer 130 to control and manage specific modes of operation of the quantum computer 130. In some examples, any data included in the input data 103 of the quantum computer may include instructions that can be used by a compiler (e.g., a quantum compiler) executed by the controller of the quantum computer 130, for example, to mitigate errors and manage the arrangement of qubits.

[0044] In some cases, the data source may include, for example, one or more data memory in which data is stored, a sensor mechanism configured to stream sensor data, or a user interface. In some embodiments, the data memory source may include electronic memory configured to store computer-executable data. The data may include data received from a user, another computing system (e.g., a classical or quantum computing system), or a sensor. In some examples, the sensor mechanism may include a sensor that generates sensor data in real time, data streamed from a satellite, a camera surveillance system, a genome data PCR reader, an MRI 3-D imager, an encryption device, etc. Alternatively or additionally, the input data 101 may be provided from other sources, such as financial transaction data, parameters of a physical system being modeled, etc.

[0045] The quantum computer 130 is used by the classical computing system 110 to perform particularly computationally complex tasks that would take an unacceptably long time for the classical computing system 110 to process. The quantum computer 130 may comprise one or more quantum circuits acting on qubits configured to perform any computationally complex task using quantum effects. In various implementations, the quantum computer 130 may comprise one or more qubits (e.g., an array of qubits) and one or more quantum gates. In some cases, the quantum gates may comprise one or more rotation gates. In some cases, the quantum circuits may comprise at least some of the qubits and one or more quantum gates.

[0046] In some implementations, the quantum computer 130 includes qubits in the range of 30 to 1000, more optionally in the range of 50 to 500, and various gates that allow for modifications to quantum parameters such as qubit phase (i.e., rotational operations R), and also allow for entanglement and superposition operations between qubits. In some examples, the quantum computer 130 is configured to perform quantum noise reduction to reduce quantum computation errors arising from quantum noise. Furthermore, in certain configurations of the quantum computer 130, its qubits and quantum gates are cooled to extremely low temperatures, e.g., within 1 Kelvin from absolute zero, during operation. Optionally, the quantum computer 130 is implemented using photonic devices, cryogenic superconducting gates, or ion traps, or a combination thereof. Optionally, a classical computing system 110 is spatially distant from the quantum computer 130, and data is exchanged between them via one or more data communication links, e.g., an internet data link.

[0047] In some cases, the program instructions may include quantum amplitude estimation and / or amplification algorithms (e.g., maximum likelihood amplitude estimation algorithms) and variational approximation algorithms. In some cases, at least a portion of the quantum amplitude estimation and / or amplification algorithms and variational approximation algorithms may be executed by the quantum computer 130 using one or more quantum circuits. In some examples, one or more quantum circuits of the quantum computing system may be configured at least in part based on input data 101. The quantum computer 130 may further process the outputs 104 received from one or more quantum circuits to produce results that can be used to generate output data 102.

[0048] In some implementations, the quantum computer 130 may operate by processing a series of "shots." In some cases, an initial state may be defined (ansatz), and each shot may involve creating a qubit with a defined initial state, performing a temporal sequence of quantum operations on the qubit to generate a post-processed qubit with a final state. In some cases, the initial state may be zero. In some cases, the quantum computer 130 may generate a post-processed qubit with a final state by modifying the initial state. In some cases, the quantum computer 130 may read out the final state of the post-processed qubit using a measurement operation (e.g., a quantum measurement operation).

[0049] In some implementations, the quantum computer 130 may include one or more quantum circuits configured to process qubits. In some cases, the number of quantum operations performed by the quantum circuit and / or the longest path in the quantum circuit may be referred to as the "quantum circuit depth." In some cases, the path in the quantum circuit may include a series of quantum operations performed to transform the initial quantum state into a final quantum state.

[0050] Each shot may have a temporal duration that may be limited by quantum noise occurring in the qubit, which may manifest as decoherence of the qubit. In some examples, the quantum noise occurring in the qubit increases as more quantum operations are performed in the qubit. Thus, the quantum noise may increase along with the corresponding quantum circuit depth. Despite such technical challenges, quantum computers 130 are highly effective for certain types of computational tasks. Some of the methods disclosed herein can reduce the quantum circuit depth of a quantum circuit configured to produce an output usable for computing the value of an arithmetic function based on the values ​​of one or more random variables associated with a probability distribution (e.g., marginal distribution). Advantageously, these methods can reduce the depth of the quantum circuit without significantly increasing the computation time (e.g., convergence time) and / or the error associated with the computational value.

[0051] In some cases, the configuration data 105 can be generated during the execution of the aforementioned software instructions, prior to the execution of the quantum computer 130. In some examples, the configuration data 105 may include data that can be used to configure one or more quantum circuits of the quantum computer 130, at least in part based on arithmetic functions. In some such cases, at least a portion of the software instructions may include a special compiler that generates the configuration data 105 by compiling another portion of instructions (e.g., configuration instructions) that, when executed, represent the configuration of the quantum computer 130. In some examples, the configuration data 105 may comprise data and / or instructions that can be executed by the quantum computer 130 to configure internal quantum circuits according to the configuration instructions.

[0052] For example, the TKET compiler provided by Cambridge Quantum Computing Ltd. can convert a portion of an instruction into a Hamiltonian function, which is then processed during compilation to generate a Pauli sequence from which the corresponding Pauli gadget is derived, and then this Pauli gadget is used to define the configuration connections of quantum gates in quantum computer 130, for example, thereby creating a given quantum circuit. Such a process of converting a Hamiltonian function into a configuration connection of quantum gates is described, for example, in the IBM publication "Circuit optimization of Hamiltonian simulation by simultaneous diagonalization of Pauli clusters" (Ewout van den Berg and Kristan Temme, IBM TJ Watson, Yorktown Height, NY, USA, 31 March 2020). The entire contents of this IBM publication are incorporated herein by reference and are part of this specification. Furthermore, the publication "A compact ion-trap quantum computing demonstrator" by Pogorelov et al. describes a practical implementation of quantum computer 130, and the entire contents of this publication are incorporated herein by reference and constitute part of this specification.

[0053] In some cases, the quantum compiler can convert a first quantum circuit or its symbolic form into a second quantum circuit or its symbolic form, the second quantum circuit or its symbolic form constituting an "integer gate" of the target hardware. In the implementation, the TKET compiler may reduce the corresponding quantum circuit depth (e.g., the quantum circuit depth of the second quantum circuit or its symbolic form). In some examples, the TKET compiler may reduce the quantum circuit depth by removing at least some obvious redundancy within the quantum circuit.

[0054] It will be recognized that the aforementioned software instructions can relate to a variety of computations that process data to produce technical effects, such as implementing data encryption and decryption, filtering measurement data representing measurement physical parameters to reduce stochastic noise in the data, and correlating measurement data to detect the appearance of signal features masked by stochastic noise. Thus, the quantum computing system 100 can provide technical effects when processing data.

[0055] In some applications, calculations may require the computation of arithmetic functions. In some cases, it is desirable for arithmetic calculations to be performed on the quantum computer 130 (for example, to reduce computation time). When reading out the aforementioned qubits, various methods can be used to reduce qubit readout noise, such as quantum amplitude estimation (QAE), which requires shots to be repeated in order to calculate the average of the outputs from which the best estimate of the qubit value can be calculated. To achieve optimal data processing throughput for the quantum computing system 100, it is often useful to reduce the amount of task switching between the quantum computer 130 and the classical computing system 110.

[0056] Therefore, as stated above, it will be recognized that in order to obtain the maximum performance from the quantum computing system 100, it is desirable to allow some of the aforementioned shots to be performed on the quantum computer 130, rather than using the classical computing system 110, for arithmetic calculations. This disclosure provides a particularly effective and efficient method for performing such arithmetic calculations using the quantum computer 130.

[0057] In general, embodiments of this disclosure use quantum circuits to perform quantum chemical simulations on a quantum computer apparatus that includes a classical computer mechanism operationally coupled to a quantum computer mechanism, the quantum circuit being configured to use a parameter-free pre-entangler as the initial state of the quantum algorithm. Such use of quantum circuits is employed to address electronic structure problems, and here, (i) A quantized version of the canonical transformation proposed by Yanai and Chan [J. Chem. Phys. 124, 194106 (2006)], (ii) The fully active space density matrix renormalization group and A new Ansatz is utilized, generated by a combination of these factors. This new Ansatz enables the transfer of computational load between quantum and classical computing mechanisms. When executing quantum circuits, in the neighborhood of multiple reference points within the potential energy surface of H2O, N2, BeH2, and associated P4 systems, such a strategy has been found to require 30% to 3000% fewer parameters compared to the corresponding generalized unitarily coupled cluster quantum circuits. Thus, embodiments of this disclosure utilize a novel algorithm for creating matrix product states (MPS) based on unitarily linear combinations, which is compared, for example, to a known sequential unitarily algorithm proposed by Ran in [Phys. Rev. A 101, 032310 (2020)].

[0058] This disclosure describes an orthogonal method, in particular, for finding the ground state of a chemical Hamiltonian. Embodiments of this disclosure find a parameter-free quantum circuit using classical resources (e.g., provided by classical quantum computing mechanisms) instead of pre-training the parameters of the quantum circuit, to which a variational circuit is added. For the size of the problem of practical use, it will be recognized that this initialization brings the quantum circuit close enough to the "narrow gorge" of the optimization domain to guarantee the success of the optimization.

[0059] The resulting quantum circuit used in the embodiments of this disclosure has the following two steps: (a) A pre-entangler stage, i.e., an efficient and scalable classically optimizable parameter-free circuit, and (b) The quantum Ansatz stage, i.e., the circuit following the parameterized gate, as shown in Figure 1B(a). A good pre-entangler meets the following two criteria: (I) It exists in a manifold of quantum states that is classically easy to optimize. (II) Shallow quantum circuits are found for the manifold of that quantum state. This disclosure focuses on matrix product states (MPS) as pre-entanglers, and canonical transformations (CTs)

[14] are fitted from quantum chemistry as quantum Ansatz. This disclosure describes the application of such procedures to four problems in quantum chemistry with strong electron correlations.

[0060] This disclosure implements a method for beneficially utilizing a combination of pre-entanglement and quantum Ansatz, and relates to the following features: (i) The MPS can be efficiently obtained by the density matrix renormalization group (DMRG) algorithm. DMRG is most efficient when local one-dimensional interactions are present, but this method has been shown to faithfully capture the full active space (CAS) of nonlinear transition metal complexes

[15] and has been implemented for up to 100 orbitals. (ii) There has been considerable research on the conversion of MPS to the quantum circuits that construct them. For example, Ran has developed an iterative MPS construction algorithm

[16] based on sequential generation using ancilla

[17] . In this disclosure, the main part of the MPS construction algorithm is extended by a new strategy

[18] that uses a unitary linear combination introduced to perform Hamiltonian simulations on a quantum computer. (iii) CT theory is a classical method designed to refine the wavefunction of CAS-DMRG

[14] . It is formulated as a unitary transformation

[14] . The difficulty of classically implementing them can be overcome by approximation or by using a quantum computing mechanism to perform quantum computation as proposed in this disclosure.

[0061] Next, a variational quantum eigenvalue solver based on canonical transformation theory will be described in detail in relation to embodiments of this disclosure. To overcome the difficulty of handling equation (5), it is proposed to optimize equation (5) by variation using a quantum computer mechanism. In this disclosure, after describing the DMRG-QCT method, a reconfigured version of the method capable of addressing multi-reference problems and the associated resource requirements will be described.

[0062] Next, we will describe DMRG-QCT in detail. DMRG-QCT uses DMRG to construct static correlations in a given wavefunction using a classical computer mechanism, and then uses a variational Ansatz inspired by CT, called Quantum Canonical Transformation (QCT), to add dynamic correlations. As shown in Figure 2, the DMRG-QCT method consists of two steps (i.e., STEP 1 and STEP 2), which will be described below.

[0063] In the first step, STEP 1, assuming a proper assignment of molecular orbitals to a given active space, the algorithm used approximates the ground state of the Hamiltonian using the DMRG method. The output from the DMRG method is a ground state MPS description |ψ0〉 for a given coupling dimension D. While it is also possible to use exact diagonalization to construct the pre-entangler, embodiments of this disclosure utilize DMRG because exact diagonalization is impractical in situations where a scalable algorithm is useful for dealing with real-world problems using many qubits. Quantum circuits can be found to construct the MPS on a quantum computer. It is important that the unitary description is reliable; that is, the energy error of the unitary approximation should be sufficiently small so as not to overly ignore static correlations in the MPS description. The methods for constructing the MPS on a quantum computer are described in detail in the following section.

[0064] The second step, STEP2, is to construct a variational circuit that describes the dynamic correlation by coupling the active orbitals with the orbitals in core space and virtual space. The construction of the variational circuit is defined as e in equation (3). T This is achieved by implementing the quantum circuit. T The precise circuit description is difficult to handle, and therefore an approximation, namely the first-order Trotter-Suzuki decomposition

[36] , is used.

[0065]

number

[0066]

number

[37] .

[37] points out that the variability in performance for different orderings is high when strong static correlations exist. However, in the DMRG-QCT method, the description of static correlations is already addressed by the DMRQ calculation in the active space, so the variance in performance for different orderings in the QCT case is expected to be small. Along with the approximation of U in equation (6), the goal of the DMRG-QCT method is the ground state energy given in equation (7), i.e., E(θ) = 〈ψ0|U † (θ)HU(θ)|ψ0〉 (7) The goal is to minimize this by measuring it within the quantum computer mechanism and updating q until the smallest ground state energy is found.

[0067] To understand the embodiments of this disclosure, it is helpful to consider the DMRG-QCT method as an interpolation between purely classical and purely quantum computations. By selecting an active space that includes all orbitals, a purely classical DMRG computation is given. Conversely, in the limit of an empty active space, a fully quantum-generalized unitary couple cluster (GUCC) ansatz is reconstructed, and a variant of the commonly used unitary couple cluster ansatz is suitable for multi-reference computations.

[0068] Next, the expressive power of DMRG-QCT will be described in detail. To utilize the effectiveness of the DMRG-QCT Ansatz method, four different molecular systems will be described. These systems contain points in their potential energy surface (PES) that exhibit strong multi-reference behavior [20, 38, 39]. The PES of H2O and N2 describe typical bond-breaking situations. In the first example, the one-parameter dissociation of a water molecule at an equilibrium angle is considered (see Figure 3a), and the ground state energy when two hydrogen atoms are simultaneously and symmetrically separated from the oxygen atom is considered. In the second example, the ground state PES of a nitrogen molecule parameterized by extending the bond distance of NN is considered (see Figure 3b). In the third example, the transition state of the reaction between Be and H2 is considered

[40] . The parameterization of PEW is shown in Figure 3c, where x=0 represents the equilibrium state of BeH2 in the linear configuration, and as the value of x increases, the system transitions beyond the transition point to two non-interacting systems (Be and H2). Finally, in a fourth example, a system of the P4 model with two hydrogen molecules is considered

[41] (see Figure 3d). The bond distance between HH in the two molecules is kept fixed, while this distance between the two molecules, represented by a in PES, is varied. As the value of a increases, at a=2 Bohr, the system becomes D 4h Symmetry is obtained. Such high symmetry leads to a pseudo-degeneracy of the construction and, therefore, to the presence of strong static correlations in the associated wave functions

[20] .

[0069] Embodiments of the present invention can be carried out by computing one-electron and two-electron integrals using known modern PySCF software packages

[42] . For all quantum chemical tasks, the software product ChemMPS2 is used to perform CAS-DMRG calculations [43-46]. The software product ChemMPS2 utilizes SU(2), U(1), and point group symmetries to provide a symmetric MPS description of a given ground state. To explore with high accuracy the ability of QCT variational circuits to represent dynamic correlations, the exact DMRG construction of a given ground state in active space is considered with respect to the results provided below (i.e., the coupling dimension D used by the DMRG is large enough to represent the exact state). Furthermore, once the MPS description of the ground state is obtained, the corresponding quantum circuit that constructs the MPS is obtained using a sequential unitary algorithm.

[0070] Assuming a unitary construction of the ground state in active space, the known modern software product InQuanto

[47] is used. InQuanto is a software platform designed to perform calculations for solving chemical problems on a quantum computer mechanism to generate the Jordan-Winger transform of the fermion Hamiltonian and implement the corresponding QCT Ansatz. It will be recognized that QCT involves the application of the Trotter-Suzuki decomposition.

[37] T To decompose it, two-electron excitations are ordered before one-electron excitations, and such ordering reduces the depth and complexity of the corresponding quantum circuit, thereby generating a more accurate final calculation result using the quantum computer mechanism. Configuration of two-electron excitations

[0071]

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[0072]

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[0073]

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[48] , where the modern software product Ppytket is suitable for use in decomposing the DMRG-QCT circuit into basic CNOT gates and 1-qubit unitary gates

[49] . Compiling such a Pytket also performs a certain number of optimizations, which lead to a more efficient quantum circuit being executed by the quantum circuit mechanism. To optimize the energy, in embodiments of the present disclosure, the variational parameters are iteratively updated in the QCT by using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [50-53].

[0074] An example of the results obtained using the DMRG-QCT method on the aforementioned molecules is shown in Figure 4, where the notation at the top of each plot is ( ● e, ● o) is used to specify the number of electrons and orbitals in the active space used in the DMRG calculation. Data for Hartree-Fock (HF) is shown, where configuration interaction with single and double excitations (CISD) and coupled cluster with single and double excitations (CCSD) are used, for example, as described above. The energy errors of different methods are then calculated with respect to the fully configuration interaction method at a given ground. As expected, the classical single-reference method is inferior in performance. The error of CISD is considerably larger for stretched bonds, as shown in Figure 4(a, b), and for points of high symmetry, as shown in Figure 4(c, d). CCSD becomes non-variational near multiple reference points.

[0075] The data labeled DMRG in Figure 4 illustrates the energy error when dynamic correlation is absent, where the variational QCT circuit acts minimally, and the static correlation generated by the pre-entangled MPS circuit completely determines the energy approximation. Figure 4 also shows the results of second-order N-electron valence state perturbation theory (NEVPT2) applied in addition to the multi-reference wavefunction from DMRG. The energy error of DMRG-QCT at one electron, labeled QCT-S in Figure 4, shows the energy reduction when the QCT circuit contains only variational parameters for one-electron excitations. It should be noted that unitary coupling cluster ansatz containing only one-electron excitations is not typically considered in the literature. This is due to Thouless's theorem

[54] , which states that a cluster of one-electron excitations cannot reduce the energy of a single-reference wavefunction. The energy reduction by constructing dynamic correlation in addition to the static MPS quantum circuit is a unique feature of QCT-S.

[0076] DMRG-QCT with one-electron and two-electron excitations, called "QCT-SD," can find states with an error less than the chemical accuracy for H2O and BeH2. The energy error of NEVPT2 is small for Figure 4(a, b), but this error is not sufficient to achieve the chemical accuracy for BeH2 and P4 systems. Furthermore, even in Figure 4(a, b), the energy error of NEVPT2 is not satisfactory in the single reference region. The nonparallelism error (NPE)

[20] , defined as the absolute difference between the maximum and minimum energy errors, is 3.59 mH, 9.93 mH, 16.21 mH, and 1.75 mH for the NEVPT2 method, corresponding to the four plots in Figure 4. Conversely, for the QCT-SD method, the NPEs are 0.30 mH and 1.15 mH, corresponding to Figure 4(a, c). Due to computational and circuit requirements, this disclosure does not describe the DMRG-QCT Ansatz for one-electron and two-electron excitations of N2 and P4 (see Figure 4(b, d)). In contrast, it will be recognized that the GUCC-SD algorithm is computationally unsuitable for all the simulation examples illustrated in this disclosure.

[0077] This disclosure also describes the performance of the QCT ansatz for incomplete static constructions by the DMRG method. Figure 5 illustrates the effect on the performance of the DMRG-QCT ansatz as the coupling dimension of the MPS describing the reference state |ψ0〉 in (1) is changed. Both QCT-S and QCT-SD show some resilience to incomplete MPS constructions by DMRG, and it will be noted that the QCT-SD ansatz maintains the energy error below chemical precision. For significant decreases in coupling dimension D (corresponding to a Hartree-Fock single reference in the limit D→1), QCT does not provide energy within chemical precision. At low coupling dimensions, the CT single reference and CT-SD perform similarly, while at high coupling dimensions, CT-SD comes very close to being accurate. The data for Figure 5 also suggests that adding CT one-electron excitations is preferable to increasing the coupling dimension utilized by DMRG, for example, the CT-S energy at D=6 is already below the maximum active space energy.

[0078] Next, the efficiency of DMRG-QCT will be described in detail. The complexity of the circuit implementing the DMRG-QCT Ansatz and analyzing it in comparison with the GUCC Ansatz will be explained. Furthermore, scaling the number of variational parameters as a function of the number of spin orbits or qubits n will be verified. The number of variational parameters is expected to be the most important factor in determining the cost of the variational quantum eigenvalue solver (both circuit requirements and time complexity). Reducing the number of parameters directly leads to a reduction in depth and the number of basic gates. Furthermore, it also leads to a reduction in the number of iterations required, i.e., energy estimation by the quantum computer and updating of variational parameters by the classical optimizer. Energy estimation by the quantum computer is extremely costly due to the enormous number of Pauli sequences in the chemical Hamiltonian, and therefore, reducing the number of variational iterations leads to a substantial reduction in the execution time of the algorithm.

[0079] Each variational parameter is e of (6). TThis corresponds to one excitation (one or two electrons) in the first-order Trotter-Suzuki approximation, and therefore the number of parameters is equal to the number of excitations. Furthermore, for the QCT Ansatz, the number of electrons in active space or the total number of electrons does not change the number of excitations, and this is also true for the GUCC Ansatz. Figure 6a shows a plot of the scaling of variational parameters by counting the number of excitations in the GUCC and DMRG-QCT Ansatz against the number of spin orbitals. If m is the number of orbitals (i.e., m= n / 2) In GUCC-D, the number of excitations is given by the following:

[0080]

number

[0081] The first (second) term corresponds to two-electron excitation, and in two-electron excitation, the complete action of excitation is one (two) spin channels. The factor of 2 / 3 in the first term takes into account the reduction obtained by enforcing the symmetry of the azimuthal spin. In the case of the DMRG-QCT ansatz, different partitions (c, a, v) are considered by dividing n spin orbitals into core (c) orbitals, active (a) orbitals, and virtual (v) orbitals. Note that for each partition (c, a, v), c = v (i.e., the number of core orbitals is equal to the number of virtual orbitals). As the size of the active space increases, the number of variational parameters decreases (see Fig. 6a (insert)). This decrease is more significant for large n, for example, when a = 0.8n, where a four-fold decrease is achieved. Importantly, this phenomenon is more pronounced for the partition c < a << v, which represents typical MR calculations. For example, for the partition (0.05n, 0.15n, 0.8n), a ten-fold decrease in the number of variational parameters is achieved. Fig. 6a shows a plot of the scaling of the GUCC-S ansatz, which is the upper limit of the scaling of QCT-S. It is clearly seen that the increase in the number of parameters of GUCC-S (or CT-S) is almost negligible compared to the ansatz for two-electron excitation. Therefore, the QCT-S ansatz can be useful in certain multi-reference situations where it can lower the energy without any overhead. It is important to recognize that the minimal basis is used for three out of four multi-reference problems due to computational requirements. Using the minimal basis makes it difficult to strictly utilize the performance of multi-reference techniques for small (usually small) dynamical correlation energies and relatively easy to achieve chemical accuracy. However, no inconsistencies were observed in the performance of DMRG-QCT for all multi-reference problems studied during the development of the embodiments of the present disclosure, and similar performance is expected to be observed when considering beyond the minimal basis.

[0082] In FIGS. 6(b, c), the circuit depth corresponding to the system size with a maximum n = 36 and the cost of implementing excitation / variational parameters as basic gates are shown. For each ansatz, a nearly completely linear scaling is obtained. The pre-factor of the linear scaling is very high, especially with respect to the number of gates, where it is 46. From the scaling of variational parameters, gates, and circuit depth, it is expected that the DMRG-QCT ansatz can obtain a significant cost reduction for the GUC, especially for typical active spaces where c < a << v.

[0083] In FIG. 9A, the resource requirements of the problems considered in FIG. 4 are shown. The number of gates and circuit depth of QCT also include the cost of the MPS state creation circuit. Despite these additional costs, for the molecules considered, a reduction in the total cost metric of 20 - 40% for QCT-SD and 80 - 97% for QCT-S is observed. Note that the relative reduction increases with the size of the system.

[0084] Next, the unitary circuit required to create an MPS of approximately physical dimension d and virtual bond dimension D is described. To handle qubits, it is assumed here that d = 2. First, the sequential unitary (SEQ) algorithm required to construct the MPS is outlined. Then, the effect of unitary freedom in the SEQ description of the MPS is explained.

[0085] Next, the Linear Combination of Unitaries (LCU) algorithm as an alternative to the SEQ approach is described. Various aspects of the SEQ algorithm and the LCU algorithm are explained, and their relative performances are compared.

[0086] In FIG. 13, the second row defines the unitary corresponding to the intermediate tensor of the MPS. Each index has dimension 2, and the color of the matching rows on both sides of each identification is each G [j]Specify the index. Each input of NULL(...) is a vector in a d×D=4-dimensional space, and its output represents the orthogonal base of the zero space of the input vectors. The index G is in the upper right. [j] and the index G in the lower left [j+1] The unitary cascade action obtained by contracting gives a global unitary U, and the action of U on the product state gives an MPS, i.e., |ψ〉=U|00...0〉.

[0087] For a general MPS|ψ〉 where D>d, Ran is U † We realized that it acts as a disentangler. This insight led to an iterative algorithm, which begins by initializing |ψ0〉=|ψ〉, and each iteration consists of compressing the MPS to the joining dimension d and applying a disentangling unitary as follows:

[0088]

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[0089]

number

[0090]

number

[0091]

number

[0092] An important aspect of the SEQ algorithm is the freedom in defining local tensors. [j] The choice of orthonormal groups in zero space used in the definition is not unique. Below, the performance of the SEQ algorithm with different choices of orthonormal groups in each unitary layer for the ground state |ψ〉 of nitrogen dimer (N2) is analyzed. Figure 7(A, b) shows the unitary approximation as a function of the unitary layer.

[0093]

number

[0094] Next, the use of the Unitary Linear Combination (LCU) algorithm is described. This introduces a new method for creating the MPS, which is approximated as follows:

[0095]

number

[0096] [Table 1]

[0097] The LCU algorithm operates iteratively by estimating the residuals of the target MPS and the current approximation (see Algorithm 1 above for implementation). The algorithm begins by compressing |ψ〉 to D=2 and using it to initialize |ψ0〉. It is then possible to find the exact unitary representation of |ψ0〉 such that |ψ0〉=U0|00...0〉 using the method defined in (8). At the beginning of each iteration, the current approximation |ψ i-1 The projection of the target state |ψ> onto > is calculated, that is,

[0098]

number

[0099] Next, from |ψ〉 to |ψ i-1 > proj By subtracting and compressing the resulting MPS to D=d=2, the residual |r i > is calculated. At this time, |ψ> and |ψ i-1 It is important to note that it is also possible to define the residual by taking the difference between |ψ. However, such a definition generally leads to slower convergence of the LCU. i-1 > proj The residuals obtained from this work numerically better when including the features involved in achieving high fidelity in |ψ〉. Next, the variational parameter k i Regarding |ψ〉 and |ψ i-1 > +k i |ri The optimization is performed to maximize the normalized overlap between >. One-parameter optimization is very fast because the fidelity for MPS can be calculated very quickly. Furthermore, without losing any optimality, k i Optimization to >0 is constrained. i Once obtained, a new |ψ i It is possible to set > and the joint dimension is D max If it exceeds a certain limit, it is beneficial to compress it.

[0100] Next, an important issue concerning the circuit implementation of unitary linear combinations is considered. Since unitary linear combinations are not unitary, a non-deterministic implementation is required to realize such operation in quantum devices. Fortunately, the implementation given in

[18] is fitted using the construction of Gray codes [59-61] (see Figure 8). The dashed box in Figure 8 shows the unitaries ordered by those Gray codes.

[0101]

number

[0102]

number

[62] . Using such a construction, the number of controls is linear, and therefore the number of layers D LCUMulti-control unitary gates can be implemented with a logarithmic number of 2-qubit gates (which increase linearly with increasing bond dimensions). While a considerable number of ancilla qubits are required, it is possible to compute quantum chemical problems with NISQ devices having a moderate number of qubits. In Figure 8, the multi-qubit B in the first column has coefficient k i It is initialized with this. The remainder of B is set in the orthogonal subspace to make B unitary. The circuit in Figure 8 is,

[0103]

number

[0104] The cost of the LCU circuitry for the basic gates is determined by the cost of implementing control of the 2-qubit unitary. To implement control of the 2-qubit gates, the corresponding isolength structures (i.e., only the first column of these unitaries, as mentioned above) are also useful. Furthermore, multi-qubit gates B and B in the first column † Since only one is involved, they can be efficiently achieved by using the state creation strategies outlined in

[63] . Worst case O(lgD LCU loglgD LCU ) requires the implementation of B for the CNOT gate and 1-qubit gate. The total cost of implementing the LCU circuit is D LCU The coefficient is linear, but the pre-scaling factor is quite large. If n is the number of qubits, then it is approximately 24nD. LCU CNOT gate and 31nD LUC This requires one qubit gate. In contrast, when implementing a SEQ circuit, the number of CNOTS gates and 1 qubit gates is 2nD each. SEQ and 6nD SEQ It scales as follows. The improved scaling of the SEQ circuit makes the SEQ algorithm more preferable in situations where the desired energy error is achieved when performing quantum chemical simulations.

[0105] Beneficial, the probability of measuring zero with an ancilla qubit for various systems is analyzed. LCU It can be seen that the probability of converging to a reasonable value for is provided in Figure 9. The convergence of the probability can be due to the decay of the LCU coefficient (see Figure 9 (inset)), but the fact that the limiting probability is quite large for the electronic structure problem makes the LCU algorithm particularly useful when applied to construct the ground state of a chemical Hamiltonian. Furthermore, such a method also reduces the need to use amplitude amplification or trivial amplitude amplification, which can incur considerable overhead [64-66].

[0106] Next, we will describe the numerical analysis of the SEQ and LCU algorithms in more detail. An important property of the SEQ algorithm is the presence of plateaus, as also mentioned in

[16] . Similar plateau behavior has been observed in different contexts involving the discovery of purified mixed states

[67] . In each iteration (9), we apply a detangle unitary to increase the Schmidt rank, and therefore the bond dimension of the MPS. The latter is equal to the number of layers D SEQ It increases exponentially with it, and in order to keep it computationally viable, it is given some D max It must be rounded down to D. maxIt is beneficial to analyze the behavior of Schmidt values ​​(with respect to cut-access maximum bond dimension) for the SEQ algorithm without discarding any of them (see Graph (a) in Figures 10A and 10B(I,II)). The prior application of the detangle unitary to the MPS introduces low-weight Schmidt values, and this behavior holds for all different models studied in developing embodiments of this disclosure. It is important to note that the long-term behavior of Schmidt values ​​is quite unique for conventional manys in contrast to chemical systems, as seen in Figures 10A and 10B(I,II)a. Figures 10A and 10B(I,II)c show the multiplicative increase of the bond dimension of the MPS before saturation to a maximum value. One might simply expect to discard the low-weight Schmidt values ​​(introduced by the detangle unitary) without obtaining any results. However, this is not the case, as can be seen in Figures 10A and 10B(I,II)d, |ψ i > to D max The loss caused by compression leads to the appearance of a plateau. The slowing of convergence is more pronounced in the energy error (see Figure 7b), where it flattens well before chemical accuracy is achieved, which greatly contributes to the usefulness of the SEQ algorithm for CT Ansatz.

[0107] The aforementioned LCU is an efficient classical algorithm even when there is no truncation at all. During each iteration of the LCU algorithm, the approximate join dimension of the MPS is |ψ i > increases additively (i.e., |ψ i The join dimension of > is only 2i). This is in contrast to the SEQ algorithm, in which the join dimension is O(2 i ) is expected to be the case. Figures 10A and 10B(I,II)c illustrate the qualitative difference in the increase of the coupling dimension between the SEQ algorithm and the LCU algorithm. Figures 10A and 10B(I,II)b show the |ψ of the LCU algorithm. iThe Schmidt value for > is shown, and here the Schmidt value contains some very unique characteristics. Furthermore, Figures 10A and 10B(I, II)d show the long-term behavior of the LCU algorithm, which continues to increase its fidelity to the target state even for large D values, and the presence of plateaus is not very pronounced.

[0108] In developing embodiments of this disclosure, benchmark performance of the SEQ and LCU algorithms for different chemical and spin systems was implemented. For example, for the DMRG-QCT Ansatz, it was found that for a given MPS creation method to be used in the context of a chemical system, it is important that the method achieves an energy density error below chemical accuracy. The energy error resulting from the unitary approximation of the method becomes the lower bound of the total energy error of the DMRG-QCT Ansatz. Figure 1 shows the behavior of the SEQ and LCU algorithms for fidelity to the true ground state and energy error. For chemical systems (Figure 11(I, II)), multi-reference region data is shown, and for spin problems (Figure 11(III)), the behavior near the critical point is shown. LCU Although the resource overhead for implementing each unitary layer is very high, the LCU algorithm can consistently find energy errors below chemical accuracy. Furthermore, the LCU algorithm achieves low errors even in the case of HAF.

[0109] As a summary and overview of the aforementioned disclosure, a general method is proposed to overcome some of the challenges of variational quantum algorithms. This general method involves two steps: Step 1: The classically discovered trial wave function is created on a quantum computer. Step 2: This trial wave function is then refined using a short variational quantum circuit.

[0110] This general method can be applied in the context of quantum chemistry, where one natural choice is to assign the static and variational parts of a circuit to the static and dynamic correlations of the wave function, respectively. In embodiments of this disclosure, this general method has proven to lead to three types of advantages. (i) Existing Ansatz, such as the GUCC Ansatz, can be extended, which in the embodiments of the present disclosure leads to a 30-80% reduction in the variational parameter, independent of the system size, depending on the relative size of the active space. (ii) This method provides a process for shifting computational loads between classical and quantum processors, for example, switching computations from purely classical computations (where the entire system is in active space) to purely quantum computations (where no pre-computation of the active space is performed). (iii) Importantly, this method opens up new, shallow Ansatz possibilities that have not been considered before. The availability of entangled active-space trial wave functions enables the use of the QCT-S Ansatz, which, for 100 spin orbitals, contains approximately 1 / 1000th the variational parameters of the GUCC Ansatz. This can be a significant advantage in that it enables the simulation of much larger chemical systems on modern NISQ computing devices.

[0111] One important step in the proposed general method is the approximate implementation of MPS on a given quantum computer, e.g., a NISQ-era quantum computer. Thus, a new algorithm for this purpose, namely the LCU algorithm, is provided. The LCU algorithm is compared with known SEQ algorithms from known literature, and in the comparison, the LCU algorithm is found to be more expressive, although it requires a larger constant prefactor in its circuit decomposition. Furthermore, the unitary freedom present in the canonical form of MPS is found to be usable for both disentangler optimization and circuit synthesis, and it is concluded that the latter application is generally more powerful.

[0112] While the embodiments of this disclosure described above provided an arbitrary implementation of a pre-entangler method using DMRG-QCT, it also provides a method that is quite flexible and can be used in plain terms to complement the capabilities of other techniques such as Adapt-VQE and symmetry-preserving Ansatz [68, 69]. Furthermore, this method, including the pre-entangler method, can be advantageously used in the fields of quantum optimization and machine learning.

[0113] Optionally, in embodiments of this disclosure, it is also possible to create an MPS by using a hybrid combination of the SEQ procedure and the LCU procedure. A first way to realize this combination is to modify equation (10) to obtain an Ansatz, which is a set of operators, where each operator itself is a linear combination of unitaries and therefore not necessarily unitary. A second way to realize this combination is a linear combination of successive unitaries of equation (11) (i.e., each unitary in the sum is a product of unitaries). Of these two, the second way can be implemented with a small modification from algorithm 1. In the era of NISQ devices and resources, these two generalized ways can provide a better trade-off between precision and circuit requirements with respect to the creation of tensor states.

[0114] It will be recognized that there are other methods for creating MPS. For example, in equation (70), it has been proposed to optimize the unitary layer of the successive unitary Ansatz by automatic discrimination, which leads to a more optimal approximation. If algorithm 1 is used instead in conjunction with a similar unitary optimization procedure, it is expected that the LCU algorithm will also be greatly improved. However, this will result in an increased classical computational load, and as a result, higher quality states will be obtained in the variational manifold defined by equation (11). Optionally, in embodiments of the present disclosure, a pre-entangler may be used, which constitutes a more general tensor network via a quantum circuit tensor network, as given in

[71] . Optionally, a pre-entangler created by using an adiabatic algorithm

[72] is used in embodiments of the present disclosure. Furthermore, the LCU algorithm described in the present disclosure can be used in other contexts, for example, to create low-energy states of a quantum algorithm based on a time series

[73] .

[0115] While the CT theory was described above in describing embodiments of the present disclosure, other methods exist for reconstructing dynamic correlations from the active space. Furthermore, n-electron valence second-order perturbation theory

[74] or adiabatic connection

[75] may be used optionally in embodiments of the present disclosure.

[0116] Referring next to Figure 12, the steps of the method relating to this disclosure for performing chemical simulations are shown. The method is performed using a hybrid computer mechanism, which includes a combination of a classical computer coupled with a quantum computer, and the hybrid computer mechanism is configured to receive input data and generate corresponding post-processed output data from the input data when in use. The method includes steps 200 to 230. Step 200 involves configuring a classical computer to receive information describing the chemical systems in the input data. Step 210 involves processing information describing the chemical system using a pre-entangler algorithm and a fixed-circuit algorithm to configure a classical computer to generate a quantum ansatz that defines initial values ​​for quantum circuit calculations, and a Hamiltonian that a variational circuit algorithm generates from it. Step 220 involves configuring a quantum computer to compute corresponding quantum circuits and generate quantum computation results using quantum Ansatz and variational circuit algorithms. Step 230 involves configuring a classical computer to process the quantum computation results and generate output data containing information describing the electron orbital simulations of a chemical system.

[0117] Optional, the method is: (i) Assigning core space, virtual space, and molecular orbitals capable of occupying the active space to the active space based on the molecular system, (ii) Approximate the ground state of the Hamiltonian using the MSRG algorithm by generating a matrix product state (MPS) description |ψ0〉 of the ground state for a given bond dimension D, (iii) Find a quantum circuit that creates the MPS description |ψ0〉 on a quantum computer, (iv) Constructing variational quantum circuits that describe dynamic correlations by coupling active orbitals in the core space and active space, (v) From the results of executing the quantum circuit, minimize the ground state energy to generate the output result, This includes configuring a hybrid computer mechanism to perform the following actions.

[0118] Modifications to embodiments of the present disclosure described above are possible without departing from the scope of the present disclosure as defined by the attached claims. Expressions used to describe and claim the present invention, such as “including,” “equipped with,” “incorporate,” “consisting of,” “having,” and “being,” are intended to be interpreted non-exclusively, i.e., allowing items, components, or elements that are not explicitly stated as existing. Singular references should be interpreted as relating to plurals as well. For example, “at least one of” means “one of” in one instance and “multiple” in another. Furthermore, “one or more” should be interpreted similarly.

[0119] The phrases "in one embodiment" and "according to one embodiment" generally mean that the specific features, structures, or characteristics that follow the phrase are included in at least one embodiment of the disclosure, and may be included in two or more embodiments of the disclosure. Importantly, such phrases do not necessarily refer to the same embodiment.

[0120] The terms “computer” or “computation-based device” are used herein to refer to any device having processing capabilities such as executing instructions. Those skilled in the art will recognize that such processing capabilities are incorporated into many different devices, and therefore the terms “computer” and “computation-based device” each include personal computers (PCs), servers, mobile phones (including smartphones), tablet computers, set-top boxes, media players, game consoles, personal digital assistants, wearable computers, and many other devices.

[0121] The methods described herein are, in some examples, performed by machine-readable software on a tangible, non-temporary storage medium, the software being, for example, in the form of a computer program containing computer program code adapted to perform one or more operations of the methods described herein when the program is executed on a computer, the computer program being embodied on a non-temporary, computer-readable medium. The software is suitable for execution on parallel or serial processors so that the operations of the methods are performed in any suitable order or simultaneously.

[0122] This acknowledges that software is a valuable, separately traded commodity. It is intended to include software that runs on or controls “dumb” or standard hardware to perform a desired function. It is also intended to include software that “describes” or defines hardware configurations, such as HDL (Hardware Description Language) software used for designing silicon chips or configuring general-purpose programmable chips to perform a desired function.

[0123] Those skilled in the art will recognize that the storage devices used to store program instructions may optionally be distributed over a network. For example, a remote computer may store an example of a process written as software. A local computer or terminal computer may access the remote computer to download some or all of the software and run the program. Alternatively, the local computer may download some software as needed, or execute some software instructions on the local terminal and some on the remote computer (or computer network). Those skilled in the art will also recognize that, by utilizing prior art known to those skilled in the art, all or some of the software instructions may be executed by dedicated circuits such as digital signal processors (DSPs) or programmable logic arrays.

[0124] As will be apparent to those skilled in the art, the ranges or device values ​​given herein may be extended or modified without loss of the desired effect.

[0125] While the subject matter has been described using terminology specific to its structural features and / or methodological behavior, it should be understood that the subject matter defined in the attached claims is not necessarily limited to the features or behaviors described above. Rather, the specific features or behaviors described above are disclosed as exemplary forms for implementing the claims.

[0126] It will be understood that the benefits and advantages described above may relate to one embodiment or to several embodiments. Embodiments are not limited to those that solve any or all of the problems described, nor to those that possess any or all of the benefits and advantages described. There is no single feature or set of features that is required or essential to every embodiment.

[0127] In particular, conditional words used herein, such as “can,” “may,” “may,” “may,” and “for example,” are generally intended to convey that one embodiment includes certain features, elements, and / or steps, while other embodiments do not, unless otherwise specified or understood differently in the context in which they are used. Therefore, such conditional words are not generally intended to suggest that features, elements, and / or steps are required in any way in one or more embodiments, or that one or more embodiments necessarily include logic for determining, with or without input or instruction from the author, whether those features, elements, and / or steps are included in or should be performed in a particular embodiment. Words such as “equipped with,” “include,” and “have” are synonymous, used inclusively and open-ended, and do not exclude additional elements, features, actions, operations, blocks, etc. Also, the word “or” is used in its inclusive sense (not its exclusive sense), and therefore, for example, when used to connect an enumeration of elements, the word “or” means one, some, or all of the elements in the enumeration. In addition, the articles “a,” “an,” and “the” used in this application and the attached claims should be interpreted as meaning “one or more” or “at least one,” unless otherwise specified.

[0128] Where used herein, the phrase “at least one” in an enumeration of items refers to any combination of those items that contains only one element. For example, “at least one of A, B, or C” is intended to cover A;B;C, A and B;A and C;B and C; and A, B, and C. Conjunctions such as the phrase “at least one of X, Y, and Z” are generally understood, in the context in which they are used, to convey that an item, word, etc., may be at least one of X, Y, or Z, unless otherwise specified. Thus, such conjunctions are not generally intended to suggest that a particular embodiment requires the presence of at least one X, at least one Y, and at least one Z, respectively.

[0129] The operations of the methods described herein may be performed in any preferred order, or simultaneously where appropriate. In addition, individual blocks may be deleted, combined with other blocks, or rearranged in any of the methods, without departing from the scope of the subject matter described herein. Aspects of the examples described above may be combined with aspects of other examples described to form further examples without losing the desired effect.

[0130] It will be understood that the above description is given merely as an example and that various modifications may be made by those skilled in the art. The above detailed description, examples, and data provide a complete description of the structure and use of the exemplary embodiments. Although various embodiments have been described above with a certain degree of detail or by reference to one or more individual embodiments, those skilled in the art can make numerous modifications to the disclosed embodiments without departing from the scope of this specification. Addendum: List of references related to quantum computing [1] F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, R. Barends, R. Biswas, S. Boixo, F. G. Brandao, D. A. Buell, et al., Quantum supremacy using a programmable superconducting processor, Nature 574, 505 (2019). [2] A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'brien, A variational eigenvalue solver on a photonic quantum processor, Nature communications 5, 1 (2014). [3] B. F. Schier, J. Tura, and J. I. Cirac, Adiabatic spectroscopy and a variational quantum adiabatic algorithm, arXiv preprint arXiv:2103.01226 (2021). [4] B. Bauer, D. Wecker, A. J. Millis, M. B. Hastings, and M. Troyer, Hybrid quantum-classical approach to correlated materials, Physical Review X 6, 031045 (2016). [5] K. M. Nakanishi, K. Fujii, and S. Todo, Sequential minimal optimization for quantum-classical hybrid algorithms, Physical Review Research 2, 043158 (2020). [6] S. McArdle, X. Yuan, and S. Benjamin, Error-mitigated digital quantum simulation, Physical review letters 122, 180501 (2019). [7] M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, et al., Variational quantum algorithms, Nature Reviews Physics 3, 625 (2021). [8] J. R. McClean, J. Romero, R. Babbush, and A. Aspuru-Guzik, The theory of variational hybrid quantumclassical algorithms, New Journal of Physics 18, 023023 (2016). [9] J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nature communications 9, 1 (2018).

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Claims

1. A method for configuring a hybrid computer mechanism to perform chemical simulations, wherein the hybrid computer mechanism includes a combination of a classical computer coupled to a quantum computer, and the hybrid computer mechanism is configured to receive input data and generate corresponding processed output data from the input data when in use, and the method is (a) Configuring the classical computer to receive information describing the chemical system in the input data, (b) Configuring the classical computer to process the information describing the chemical system using a pre-entangler to generate a fixed circuit describing the static correlation of the wave functions describing the chemical system, and to generate a variational circuit describing the dynamic correlation of the wave functions using quantum Ansatz, (c) Configuring the quantum computer to execute quantum circuits corresponding to the fixed circuit and the variational circuit and generate quantum computation results, (d) Configuring the classical computer to process the quantum computation results and generate output data that includes information describing the electron orbital simulation of the chemical system, A method that includes this.

2. The method according to claim 1, comprising configuring the pre-entangler to function as a parameter-free pre-entangler.

3. The method according to claim 1, comprising constructing the pre-entangler using a Matrix Product States (MPS) algorithm.

4. The method according to claim 3, comprising generating a matrix product state (MPS) based on a unitary linear combination describing the chemical system.

5. The method according to claim 3, comprising configuring the hybrid computer mechanism to generate matrix product states (MPS) using a density matrix renormalization group (DMRG) algorithm in order to capture the complete active space (CAS) for one or more nonlinear transition metal complexes contained in the chemical system.

6. The method according to claim 3, comprising configuring the hybrid computer mechanism to generate matrix product states (MPS) by using an MPS algorithm based on sequential generation using ancilla qubits.

7. The method according to claim 1, comprising using the quantum circuit to find the ground state of the Hamiltonian of the chemical system.

8. The method according to claim 1, comprising configuring the variational circuit as a variational quantum eigenvalue solver based on one or more canonical transformations, wherein the method comprises configuring the hybrid computer mechanism to generate a density matrix renormalization group (DMRG) algorithm using the classical computer to construct static correlations in a wave function describing the chemical system, the density matrix renormalization group (DMRG) algorithm being used to generate the corresponding fixed portion of the quantum circuit.

9. (i) The operation of configuring the classical computer to process the information describing the chemical system, and assigning core space, virtual space, and molecular orbitals capable of occupying the active space to the active space based on the chemical system, (ii) The classical computer is configured to approximate the static correlation of the Hamiltonian of the chemical system by using the DMRG algorithm as the pre-entangler, and a matrix product state (MPS) description of the ground state for a given coupling dimension D is provided |ψ ０ The operation of generating > and (iii) The MPS description on the quantum computer |ψ ０ The operation of generating a quantum circuit that creates > (iv) The operation of constructing a variational quantum circuit that describes dynamic correlation by coupling orbitals in the core space, active space and virtual space, (v) An operation to minimize the ground state energy and generate an output result from the results of executing the quantum circuit, The method according to claim 1, comprising configuring the hybrid computer mechanism to perform the following.

10. A hybrid computer system configured to perform chemical simulations, wherein the hybrid computer system includes a combination of a classical computer coupled to a quantum computer, and the hybrid computer system is configured to receive input data and generate corresponding processed output data from the input data when in use, and the computer system is (a) Configured to receive information describing the chemical system in the input data, (b) The system is configured to process the information describing the chemical system using a pre-entangler to generate a fixed circuit describing the static correlation of the wave functions describing the chemical system, and to generate a variational circuit describing the dynamic correlation of the wave functions using quantum Ansatz, (c) A quantum circuit corresponding to the fixed circuit and the variational circuit is configured to execute and generate a quantum computation result, (d) A hybrid computer mechanism configured to process the quantum computation results and generate output data containing information describing the electron orbital simulation of the chemical system.

11. The hybrid computer mechanism according to claim 10, wherein the pre-entangler is configured to function as a parameter-free pre-entangler.

12. The hybrid computer mechanism according to claim 10, wherein the pre-entangler is configured to use a matrix multiplication state (MPS) algorithm.

13. The hybrid computer mechanism according to claim 12, wherein the hybrid computer mechanism is configured to generate matrix product states (MPS) using a density matrix renormalization group (DMRG) algorithm in order to capture the fully active space (CAS) for one or more nonlinear transition metal complexes contained in the chemical system.

14. The hybrid computer mechanism according to claim 10, wherein the hybrid computer mechanism is configured to generate matrix product states (MPS) by using an MPS algorithm based on sequential generation using ancilla qubits.

15. The hybrid computer mechanism according to claim 10, wherein the hybrid computer mechanism is configured to use the quantum circuit to find the ground state of the Hamiltonian of the chemical system.

16. The hybrid computer mechanism according to claim 9, wherein the hybrid computer mechanism is configured to include the variational circuit as a variational quantum eigenvalue solver based on one or more canonical transformations, and the hybrid computer mechanism is configured to use the classical computer to generate a density matrix renormalization group (DMRG) algorithm to construct static correlations in wave functions describing the chemical system, and the density matrix renormalization group (DMRG) algorithm is used to generate the corresponding fixed portion of the quantum circuit.

17. The aforementioned hybrid computer mechanism, (i) Assigning core space, virtual space, and molecular orbitals capable of occupying the active space to the active space based on the chemical system, (ii) Approximate the ground state of the Hamiltonian by using the DMRG algorithm as the pre-entangler, and describe the matrix product state (MPS) of the ground state for a given coupling dimension D |ψ ０ To generate > and (iii) The MPS description on the quantum computer |ψ ０ Finding a quantum circuit that creates > (iv) Constructing a variational quantum circuit that describes dynamic correlation by coupling active orbitals in the core space and active space, (v) Based on the results of executing the quantum circuit, minimize the ground state energy to generate an output result, A hybrid computer mechanism according to claim 9, configured to perform the following:

18. A non-temporary computer-readable storage medium comprising a unique computer-readable instruction executable by data processing hardware, wherein the unique computer-readable instruction, when executed using the data processing hardware, implements the method according to any one of claims 1 to 9.

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