Hybrid Quantum-Classical Calculation Simulation of the Department of Chemistry

Abstract

A chemical system is simulated using a hybrid quantum-classical computing system. The classical component of the system determines fermionic constraint information regarding an active space electron Hamiltonian defined in the space of two or more active orbitals of the chemical system, replaces the fermionic constraint information to a qubit basis to generate qubit constraint information regarding the active space electron Hamiltonian, provides the qubit constraint information to the quantum component of the system, receives a quantum-measured value corresponding to an expected value of a quantum operator acting on the quantum state of the qubits of the quantum component, and represents an expected value of a quantum operator acting on an eigenstate of the active space electron Hamiltonian, and utilizes the measured value to approximate an expected value of a quantum operator acting on an eigenstate of the overall electron Hamiltonian to generate a model of the chemical system representing structural properties and / or chemical interaction properties of the chemical system.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims the benefit of U.S. Application No. 63 / 344,592, filed May 20, 2022, the entire content of which is incorporated herein by reference.

[0002] This disclosure relates to simulating chemical systems. Exemplary embodiments relate to using hybrid quantum - classical computing to simulate chemical systems.

Background Art

[0003] A given chemical system, including but not limited to atoms, molecules, ions, periodic solids, periodic surface slabs, or combinations thereof, consists of one or more atomic nuclei and at least one electron. The quantum state of the electron is represented by the electron's wave function, which, conveniently, is expressed as a linear combination of Slater determinants made from molecular (or crystal) orbitals.

Summary of the Invention

Problems to be Solved by the Invention

[0004] As the number of electrons in an atom and / or the number of atoms in a molecule, periodic solid, and / or periodic surface slab increases, the computational complexity and processing cost of modeling such a system increase significantly. Through dedicated efforts, ingenuity, and innovation, many of the deficiencies in modeling and / or simulating such systems have been solved by developing strategies structured according to embodiments of the present invention, many examples of which are described in detail herein.

Means for Solving the Problems

[0005] Various embodiments provide a method, system, apparatus, computer program product, etc. for simulating chemical systems. Exemplary embodiments can simulate chemical systems such as atoms, molecules, periodic solids, periodic surface slabs, and / or combinations thereof more accurately than conventional methods by simulating a series of electronic states more comprehensively and accurately without creating computationally difficult tasks for computing hardware.

[0006] In various embodiments, hybrid quantum-classical computing techniques are used to accurately and efficiently model and / or simulate chemical systems. For example, in various embodiments, a first level of chemical system simulation is used to identify and / or determine an approximation to the electronic state of a chemical system, particularly to generate molecular orbitals, by, for example, Hartree-Fock theory where the electron wavefunction is defined by a single Slater determinant. In various systems, more accurate approximations may be constructed such that the orbitals can be rotated and / or separated into active and inactive orbitals, and the electron wavefunction is defined by a linear combination of Slater determinants constructed by different occupancies of the active orbitals. Inactive orbitals include core orbitals and virtual orbitals.

[0007] Fermion constraint information regarding the active orbitals is transformed into a qubit basis corresponding to the qubits of the quantum computing component. For example, in various embodiments, the fermion constraint information comprises an active space electron Hamiltonian represented in second quantization, i.e., via the occupancy of a subset of the active orbitals. In one exemplary embodiment, the quantum computing component is used to process information regarding the active space Hamiltonian in the qubit basis to determine a qubit representation of the properties of the eigenstates of the active space electron Hamiltonian.

[0008] Next, the qubit representation of the properties of the eigenstates of the active space Hamiltonian is replaced with the classical representation of the properties of the eigenstates of the active space Hamiltonian. For example, a measurement operation is performed on a plurality of qubits of a quantum computing component, and a measurement value corresponding to the expected value of a quantum operator acting on at least a portion of the plurality of qubits is then determined. Next, using the classical representation of the properties of the eigenstates of the active space Hamiltonian, an approximation to the properties of the eigenstates of the overall electronic Hamiltonian of the system, such as the expected value of a quantum operator acting on such a state, is classically determined, completing the simulation of the chemical system and determining how the chemical system behaves in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), determining the structural properties of the chemical system, and so on.

[0009] According to a first aspect, a method for simulating a chemical system using a hybrid quantum-classical computing system is provided. The method includes determining, by a classical computing component of the hybrid quantum-classical computing system, fermionic constraint information regarding an active-space electronic Hamiltonian defined in a space of two or more active orbitals; replacing, by the classical computing component, the fermionic constraint information regarding the active-space electronic Hamiltonian with a qubit basis to generate qubit constraint information regarding the active-space electronic Hamiltonian; providing, by the classical computing component, the qubit constraint information regarding the active-space electronic Hamiltonian to a quantum computing component of the hybrid quantum-classical computing system; receiving, by the classical computing component, a measurement value corresponding to an expected value of a quantum operator acting on a quantum state of at least a portion of a plurality of qubits of the quantum computing component and representing an expected value of the quantum operator acting on an eigenstate of the active-space electronic Hamiltonian; and generating, by the classical computing component, an approximation to an expected value of a quantum operator acting on an eigenstate of the overall electronic Hamiltonian to generate a model of the chemical system representing at least one of a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system, using the measurement value representing the expected value of the quantum operator acting on the eigenstate of the active-space electronic Hamiltonian.

[0010] In one exemplary embodiment, the fermionic constraint information regarding the active-space electronic Hamiltonian defined in a space of two or more active orbitals comprises an effective fermionic Hamiltonian, and the qubit constraint information regarding the active-space electronic Hamiltonian defined in a space of two or more active orbitals comprises a replaced version of the fermionic Hamiltonian in the qubit basis.

[0011] In one exemplary embodiment, the measurement value comprises at least one of an expected value of the active-space Hamiltonian or at least one reduced density matrix (RDM).

[0012] In one exemplary embodiment, at least one RDM comprises at least one of a one-particle RDM (1-RDM), a two-particle RDM (2-RDM), a three-particle RDM (3-RDM), or a four-particle RDM (4-RDM).

[0013] In one exemplary embodiment, the method further comprises determining an estimate of the 4-RDM based at least in part on at least one of the 1-RDM, 2-RDM, or 3-RDM by classical computing components.

[0014] In one exemplary embodiment, the step of utilizing a measurement representing an expected value of a quantum operator acting on an eigenstate of an active space electronic Hamiltonian to produce an approximation of the expected value of a quantum operator acting on an eigenstate of the overall electronic Hamiltonian comprises performing a quadratic N-electron valence state perturbation theory calculation.

[0015] In one exemplary embodiment, one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0016] In one exemplary embodiment, the method further comprises performing state preparation of a plurality of qubits based at least in part on qubit constraint information regarding an active space Hamiltonian defined in a space of two or more active orbitals by a quantum computing component, and performing one or more measurement operations to determine a measurement value based on the quantum state of at least a portion of the plurality of qubits by the quantum computing component.

[0017] In one exemplary embodiment, the method further comprises identifying a plurality of orbitals of a chemical system and partitioning the plurality of orbitals into two or more active orbitals and one or more inactive orbitals by classical computing components.

[0018] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0019] In one exemplary embodiment, the method further comprises causing, by a classical computing component, at least one of (a) displaying a graphical representation of at least a portion of a model of a chemical system, or (b) generating a file comprising one or more parameters of a model of a chemical system and storing it in classical memory.

[0020] In one exemplary embodiment, one or more parameters of a model of a chemical system include at least one of structural properties of the chemical system, chemical interaction properties of the chemical system, and reaction properties of the chemical system.

[0021] According to another aspect, a hybrid quantum-classical computing system configured to simulate a chemical system is provided. In one exemplary embodiment, the hybrid quantum-classical computing system includes a classical computing component and a quantum computing component. The hybrid quantum-classical computing component is configured to use the classical computing component to determine fermionic constraint information regarding an active-space electronic Hamiltonian defined in the space of two or more active orbitals of the chemical system, to generate qubit constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals by replacing the fermionic constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals with a qubit basis, to provide the qubit constraint information regarding the active-space electronic Hamiltonian to the quantum computing component of the hybrid quantum-classical computing system, to receive a measurement value corresponding to the expected value of a quantum operator acting on at least a portion of the quantum states of a plurality of qubits of the quantum computing component and representing the expected value of the quantum operator acting on the eigenstates of the active-space electronic Hamiltonian, and to generate an approximation to the expected value of the quantum operator acting on the eigenstates of the overall electronic Hamiltonian to generate a model of the chemical system representing at least one of the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system, using the measurement value representing the expected value of the quantum operator acting on the eigenstates of the active-space electronic Hamiltonian.

[0022] In one exemplary embodiment, the fermionic constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals comprises an effective fermionic Hamiltonian, and the qubit constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals comprises a replaced version of the effective fermionic Hamiltonian with a qubit basis.

[0023] In one exemplary embodiment, the measurement value comprises the expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0024] In one exemplary embodiment, the at least one RDM comprises at least one of a one-particle RDM (1-RDM), a two-particle RDM (2-RDM), a three-particle RDM (3-RDM), or a four-particle RDM (4-RDM).

[0025] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a classical computing component to determine an estimate of the 4-RDM based at least in part on at least one of the 1-RDM, 2-RDM, or 3-RDM.

[0026] In one exemplary embodiment, the step of utilizing a measurement value representing the expected value of a quantum operator acting on an eigenstate of an active space electronic Hamiltonian to produce an approximation of the expected value of a quantum operator acting on an eigenstate of the total electronic Hamiltonian comprises performing a second-order N-electron valence state perturbation theory calculation.

[0027] In one exemplary embodiment, the one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0028] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a quantum computing component to perform state preparation of a plurality of qubits based at least in part on qubit constraint information regarding an active space Hamiltonian defined in a space of two or more active orbitals, and to perform one or more measurement operations to determine a measurement value based on the quantum state of at least a portion of the plurality of qubits.

[0029] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a classical computing component to identify and optionally rotate a plurality of orbits of a chemical system, and to classify the plurality of orbits into two or more active orbits and one or more inactive orbits.

[0030] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0031] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a classical computing component to cause at least one of (a) display of a graphical representation of at least a portion of a model of a chemical system, or (b) generation of a file comprising one or more parameters of a model of a chemical system and storage thereof in classical memory.

[0032] In one exemplary embodiment, the one or more parameters of a model of a chemical system include at least one of the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system.

[0033] According to another aspect, a computer program product is provided that includes at least one non-transitory computer-readable medium storing computer-readable instructions. When the computer-readable instructions are executed by a hybrid quantum-classical computing system comprising classical computing components and quantum computing components, the hybrid quantum-classical computing system is caused to use the classical computing components to determine fermionic constraint information regarding an active space electronic Hamiltonian defined in the space of two or more active orbitals of a chemical system, replace the fermionic constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals with qubit constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals in order to generate qubit constraint information regarding the active space electronic Hamiltonian, provide the qubit constraint information regarding the active space electronic Hamiltonian to the quantum computing components of the hybrid quantum-classical computing system, receive a measurement value corresponding to an expected value of a quantum operator acting on at least a portion of a plurality of qubits of the quantum computing components and representing an expected value of the quantum operator acting on an eigenstate of the active space electronic Hamiltonian, and utilize the measurement value representing the expected value of the quantum operator acting on the eigenstate of the active space electronic Hamiltonian to produce an approximation to the expected value of the quantum operator acting on the eigenstate of the overall electronic Hamiltonian, in order to generate a model of the chemical system representing at least one of the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system.

[0034] In one exemplary embodiment, the fermionic constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals comprises an effective fermionic Hamiltonian, and the qubit constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals comprises a replaced version of the fermionic Hamiltonian in the qubit basis.

[0035] In one exemplary embodiment, the measured value comprises an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0036] In one exemplary embodiment, the at least one RDM comprises at least one of a one-particle RDM (1-RDM), a two-particle RDM (2-RDM), a three-particle RDM (3-RDM), or a four-particle RDM (4-RDM).

[0037] In one exemplary embodiment, the computer-readable instructions, when executed by a hybrid quantum-classical computing system, further configure the hybrid quantum-classical computing system to use a classical computing component to determine an estimate of the 4-RDM based at least in part on at least one of the 1-RDM, 2-RDM, or 3-RDM.

[0038] In one exemplary embodiment, the step of utilizing a measured value representing an expected value of a quantum operator acting on an eigenstate of an active space electronic Hamiltonian to produce an approximation to the expected value of the quantum operator acting on an eigenstate of the total electronic Hamiltonian comprises performing a second-order N-electron valence state perturbation theory calculation.

[0039] In one exemplary embodiment, the one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0040] In one exemplary embodiment, the computer-readable instructions, when executed by a hybrid quantum-classical computing system, further configure the hybrid quantum-classical computing system to use a quantum computing component to perform state preparation of a plurality of qubits based at least in part on qubit constraint information regarding an active space Hamiltonian defined in the space of two or more active orbitals, and to perform one or more measurement operations to determine a measured value based on the quantum state of at least a portion of the plurality of qubits.

[0041] In one exemplary embodiment, when the computer-readable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is further configured to cause a classical computing component to be used to identify a plurality of orbits of a chemical system and to partition the plurality of orbits into two or more active orbits and one or more inactive orbits.

[0042] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0043] In one exemplary embodiment, when the computer-readable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is further configured to cause a classical computing component to be used to cause at least one of (a) display of a graphical representation of at least a portion of a model of a chemical system or (b) generation of a file comprising one or more parameters of a model of a chemical system and storage in classical memory.

[0044] In one exemplary embodiment, one or more parameters of a model of a chemical system include at least one of a structural characteristic of the chemical system, a chemical interaction characteristic of the chemical system, or a reaction characteristic of the chemical system.

[0045] According to another aspect, a hybrid quantum-classical computing system is provided. The hybrid quantum-classical computing system includes a classical computing component configured to determine at least an inactive portion of a chemical system model, where the inactive portion of the chemical system model represents one or more inactive orbitals of the chemical system. The hybrid quantum-classical computing system further includes a quantum computing component configured to determine at least an active portion of a chemical system model, where the active portion of the chemical system model is defined in the space of two or more active orbitals to provide qubit constraint information corresponding to an active space electronic Hamiltonian in the space of a plurality of qubits of the quantum computing component, and is determined based on replacing fermionic constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals with qubit basis and implementing a quantum circuit using a plurality of qubits based at least in part on the qubit constraint information, and represents characteristics of the active orbitals of the chemical system.

[0046] In one exemplary embodiment, the fermionic constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals uses a spinless representation of the two or more active orbitals.

[0047] In one exemplary embodiment, the quantum computing component is configured to use an ansatz that is a symmetry-adapted singlet unitary coupled-cluster singles and doubles (UCCSD) ansatz.

[0048] In one exemplary embodiment, the classical computing component is configured to use a cumulant expansion to generate at least one approximation of at least one multi-particle reduced density matrix (RDM).

[0049] In one exemplary embodiment, the classical computing component is configured to generate a four-particle reduced density matrix (4-RDM) from at least one of a one-particle reduced density matrix (1-RDM), a two-particle reduced density matrix (2-RDM), or a three-particle reduced density matrix (3-RDM) measured by the quantum computing component.

[0050] In one exemplary embodiment, the classical computing component is configured to calculate the NEVPT2 energy based at least in part on a measurement result indicating an RDM value, the measurement result being obtained as part of performing a quantum circuit.

[0051] In one exemplary embodiment, the hybrid quantum-classical computing system is configured to define an active space corresponding to at least two active orbitals and a basis function system corresponding to a chemical system, construct an active space electronic Hamiltonian defined in the active space, define a corresponding ansatz representing two or more active orbitals of the chemical system, and determine parameters of the chemical system generated from the active space electronic Hamiltonian and provided together with the ansatz as initial quantum computing parameters by using a VQE method applied to a quantum circuit. In various embodiments, the defined basis function system is a function format used to represent orbits (e.g., Gaussian-type atomic orbitals, Wannier functions, plane waves, etc.).

[0052] According to another aspect, a method performed by a hybrid quantum-classical computing system for generating a model of a chemical system is provided. The hybrid quantum-classical computing system includes a classical computing component coupled to a quantum computing component. In one exemplary embodiment, the method includes representing an overall electronic Hamiltonian and an active space electronic Hamiltonian of a chemical system in the classical computing component, and representing an active space wave function and at least one active space reduced density matrix (RDM) of the chemical system in the quantum computing component based at least in part on replacing the active space electronic Hamiltonian with respect to a qubit basis of a plurality of qubits of the quantum computing component. The classical computing component uses at least one active space RDM to determine an approximation of at least one additional RDM representing at least one of a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system.

[0053] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to use spinless formulations of at least one active space reduced density matrix (RDM) and at least one additional RDM when calculating properties of a chemical system by using quantum computing components.

[0054] In one exemplary embodiment, the method includes configuring quantum computing components to use an ansatz that is symmetry-adapted singlet unitary coupled cluster with singles and doubles (UCCSD).

[0055] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to use a cumulant expansion to generate an approximation of at least one additional RDM.

[0056] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to generate 4-RDM from 1-RDM, 2-RDM, and 3-RDM.

[0057] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to calculate NEVPT2 energy using quantum-measured RDM.

[0058] In one exemplary embodiment, the method includes defining an active space corresponding to at least two active orbitals and a basis function system corresponding to a chemical system, constructing an active space electronic Hamiltonian defined in the active space, defining a corresponding ansatz representing two or more active orbitals of the chemical system, and determining parameters of the chemical system generated from the active space electronic Hamiltonian and provided together with the ansatz as initial quantum computing parameters by using a variational quantum eigensolver (VQE) method applied to a quantum circuit, thereby configuring a hybrid quantum-classical computing system.

[0059] According to another aspect, a machine-readable data storage medium is provided that comprises specific instructions executable on data processing hardware. When executed by the data processing hardware, the instructions cause the classical computing component of the hybrid quantum-classical computing system to represent the overall electronic Hamiltonian and the active space Hamiltonian of the chemical system in the classical computing component, and based at least in part on the replacement of the active space electronic Hamiltonian with the qubit basis of a plurality of qubits of the quantum computing component, cause the quantum computing component to represent the active space wavefunction of the chemical system and at least one active space reduced density matrix (RDM) of the chemical system. The classical computing component uses at least one active space RDM to determine an approximation of at least one additional RDM that represents at least one of the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system.

[0060] Since the present invention has been described in general terms, reference is now made to the accompanying drawings, which are not necessarily drawn to scale.

Brief Description of the Drawings

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[0062] Here, the present invention will be described more fully hereinafter with reference to the accompanying drawings, in which some, but not all, embodiments of the invention are shown. In fact, the invention may be embodied in many different forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will satisfy applicable legal requirements. The term "or" (also denoted as " / ") is used herein in the sense of both alternatives and conjunctions unless otherwise indicated. The terms "exemplary" and "exemplifying" are used as examples without indicating a quality level. The terms "generally", "substantially", and "approximately" refer to within manufacturing and / or production tolerances and / or within the measurement capabilities of a user, unless otherwise indicated. Throughout, like numbers refer to like elements.

[0063] Various embodiments provide a method, system, apparatus, computer program product, etc. for simulating a chemical system. Exemplary embodiments can simulate atoms, molecules, solids, periodic atomic systems, etc. more accurately than conventional methods by simulating their orbits, specifically their active orbits, and more comprehensively and accurately without creating computationally difficult tasks for computing hardware. For example, various embodiments provide a method, system, apparatus, computer program product, etc. for generating a model of a chemical system that represents at least one of the structural characteristics of the chemical system, the chemical interaction characteristics of the chemical system, or the reaction characteristics of the chemical system.

[0064] In various embodiments, hybrid quantum-classical computing techniques are used to accurately and efficiently model and / or simulate a chemical system. For example, in various embodiments, a first level of simulation of the chemical system is used to identify and / or determine an approximation to the electronic state of the chemical system, particularly to generate molecular orbits, by means of the Hartree-Fock theory, such that the wave function of an electron is defined by a single Slater determinant. In various systems, a more accurate approximation may be constructed such that the orbits can be rotated and divided into active and inactive orbits, and the wave function of the electron is defined by a linear combination of Slater determinants constructed by different occupations of the active orbits. Inactive orbits include core orbits and virtual orbits.

[0065] In various embodiments, based on the structural and / or interaction characteristics of the chemical system being investigated, evaluated, modeled, etc., the orbits can be divided into active and inactive orbits. For example, an active space comprising and / or consisting of two or more active orbits is defined, and an inactive space comprising and / or consisting of one or more inactive orbits is defined. One or more inactive orbits include core orbits and virtual orbits.

[0066] Fermion constraint information regarding an active space electronic Hamiltonian defined in the space of two or more active orbitals is determined and replaced and / or transformed into qubit bases corresponding to qubits of a quantum computing component. In various embodiments, the qubit bases are determined by and / or dependent on the type of qubits used by the quantum component of the hybrid quantum-classical computing system being used. For example, the quantum component may use photons, electrons, atomic nuclei, neutral atoms, ions, Josephson junctions, quantum dots, topological anions, and / or other quantum particles and / or systems as qubits. The qubit constraint information determined by replacing and / or transforming the fermion constraint information into qubit bases depends on the qubit bases corresponding to the particular qubits used by the quantum component. For example, in various embodiments, the fermion constraint information comprises an active space electronic Hamiltonian regarding the Hilbert space of a chemical system and / or an operator in the active space of a chemical system as defined by two or more active orbitals. The qubit constraint information comprises an active space electronic Hamiltonian regarding an operator in the Hilbert space of the qubits of the quantum computing component.

[0067] In one exemplary embodiment, using quantum computing components, qubit constraint information is processed to determine and / or generate a qubit representation of the characteristics of the eigenstates of the active space electronic Hamiltonian. For example, a quantum circuit is determined and executed to perform state preparation of a plurality of qubits of the quantum component such that the quantum states of the plurality of qubits are prepared according to the active space electronic Hamiltonian to represent one or more eigenstates (e.g., active orbital wave functions) and / or expectation values of the active space electronic Hamiltonian. In one exemplary embodiment, the prepared state of the qubits provides a qubit representation of the characteristics of the eigenstates of the active space electronic Hamiltonian. In one exemplary embodiment, a measurement operation is performed by the quantum computing component to extract the qubit representation of the characteristics of the eigenstates of the active space electronic Hamiltonian. For example, the measurement operation is performed on a plurality of qubits of the quantum computing component, and a measurement value corresponding to the expectation value of a quantum operator acting on at least a portion of the plurality of qubits is then determined.

[0068] The qubit representation of the characteristics of the eigenstates of the active space Hamiltonian is then replaced with a classical representation of the characteristics of the eigenstates of the active space Hamiltonian. For example, the measurement values corresponding to the characteristics of the eigenstates of the active space Hamiltonian are determined based on the results of the measurement operations performed on the qubits.

[0069] For example, then, classically determining an approximation of the characteristics of the eigenstates of the overall electronic Hamiltonian of the system, such as the expectation value of a quantum operator acting on such states, completing a simulation of a chemical system, determining how a chemical system behaves in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), determining the structural characteristics of a chemical system, etc., the classical representation of the characteristics of the eigenstates of the active space Hamiltonian is utilized.

[0070] As used herein, a classical component or classical computer is a computing entity that uses semiconductor-based computing techniques and hardware. A quantum component or quantum computing component uses the quantum states of quantum particles (referred to as qubits) to perform calculations.

[0071] To simulate chemical modules and determine the manner of interaction with other molecules, conventional classical computer software products are known that can be executed on classical computing hardware, such as classical non-quantum computing components. Such computer software products are configured to calculate the properties of the electronic states of a given atom, molecule, or solid, where the electronic states are represented as single-electron configurations (Slater determinants) as a first category of calculations, and the computer software products are then configured to calculate the properties of these states, which are represented as electron configurations (Slater determinants) obtained by exciting (raising) one or more electrons from occupied electronic states to unoccupied electronic states as a second category of calculations.

[0072] A real technical problem encountered in practice is that the computing resources required to implement the second category of calculations can be difficult. In some situations, the amount of computing resources required can become unmanageable. As a result, approximations are often used conventionally when performing calculations related to the aforementioned second category. In various scenarios, these approximations are not accurate enough to provide the structural and / or interaction properties of atoms or molecules for considering and / or predicting real-world observations of atoms or molecules and / or their interactions.

[0073] Quantum computing components are expected to provide a system that can perform complex calculations in a short time frame with low memory requirements. However, currently operating quantum computing components tend to include a relatively small number of qubits (e.g., less than 100 qubits) and tend to be relatively noisy. As a result, there are further technical problems in that currently operating quantum computing components do not even provide sufficient computing resources to perform a full simulation of a chemical system or even a simulation of the excited state of a chemical system.

[0074] Various embodiments provide technical solutions to these technical problems. For example, in various embodiments, (quantum) measured values for a Hamiltonian defined in the space of occupation of active orbitals are determined using the quantum component of a hybrid quantum-classical computing system. The static (i.e., non-dynamic) correlation energy arising from the entanglement of active orbitals has a large impact on the structural, interaction, and / or reaction characteristics of interest for a chemical system and requires higher computational power for determination than the dynamic correlation energy arising from excitation to non-active virtual orbitals. However, the minimum number of active orbitals required for a satisfactory accurate model of a chemical system tends to be in the range from 2 to 100 orbitals.

[0075] Thus, by limiting the problems transmitted to the quantum component to the active orbitals, a more accurate determination of the structural and / or interaction characteristics of the structure of interest for the chemical system can be obtained, and the computing power of the quantum component is used efficiently and effectively. Moreover, instead of simply using the quantum component to generate a qubit representation of the characteristics of the eigenstates of the overall electronic Hamiltonian, by using the quantum component to generate a qubit representation of the characteristics of the eigenstates of the active space Hamiltonian, the accuracy and efficiency of the model of the chemical system are further improved. Accordingly, various embodiments provide an improvement in the technical field of chemical system simulations by providing a computationally tractable and more accurate simulation of the structural characteristics, interaction characteristics, and / or reaction characteristics of a chemical system.

[0076] For example, in various embodiments, for a given chemical system, an active space with two or more active orbitals and a basis function system for the chemical system are defined. A fermionic Hamiltonian for the active space is determined using the defined basis function system. Next, state preparation of the qubits of the quantum computing component is performed such that the quantum state of the qubits represents the characteristics of the eigenstates of the active space electronic Hamiltonian of the chemical system. A measurement operation is performed such that at least a one-particle reduced density matrix, a two-particle reduced density matrix, and a three-particle reduced density matrix (1-RDM, 2-RDM, and 3-RDM) are determined through quantum measurement and / or measurement of the quantum state of the qubits of the quantum computing component. In various embodiments, a four-particle reduced density matrix (4-RDM) can be determined through quantum measurement and / or measurement of the quantum state of the qubits of the quantum computing component or through cumulant expansion. The classical computing component uses at least one active space RDM to determine an approximation of at least one additional RDM and / or NEVPT2 energy that represents at least one of the structural characteristics, chemical interaction characteristics, or reaction characteristics of the chemical system.

[0077] Exemplary Hybrid Quantum-Classical Computing System FIG. 1 provides a block diagram of an exemplary hybrid quantum-classical computing system 100 according to various embodiments. In various embodiments, the hybrid quantum-classical computing system 100 includes classical components such as classical computing component 110 and quantum components such as quantum computing component 130.

[0078] The quantum computing component 130 includes a controller 132, qubits 134, a qubit operation component 136, and a sensor 138. The controller 132 is configured to control the operation of the qubit operation element 136 to cause a desired operation (e.g., the evolution of a controlled quantum state) of the qubits 134. The controller 132 is further configured to control the operation of a sensor 138 configured to monitor, measure, and / or acquire measurement results corresponding to the operation of the qubit operation component and to acquire measurement results indicating the respective quantum states of the respective qubits 134.

[0079] For example, in various embodiments, the qubit operation component 136 includes a voltage / current source, a laser source, a magnetic field source (e.g., an electromagnet and / or a permanent magnet), and / or other hardware components configured for use in confining qubits and / or manipulating the quantum states of qubits. For example, in various embodiments, the sensor 138 includes a photodetector, a voltage / current sensor, a temperature sensor, a pressure sensor, and / or other sensors that can be used to determine the quantum state of a qubit and / or monitor one or more operations of the qubit operation component 136.

[0080] In various embodiments, classical computing component 110 communicates with controller 132 of quantum computing component 130 via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication. For example, classical computing component 110 provides qubit constraint information to quantum computing component 130 (e.g., its controller 132), and corresponds to the expected value of a quantum operator acting on the quantum state of at least a portion of a plurality of qubits of the quantum computing component, and represents a measurement value of the expected value of a quantum operator acting on the eigenstate of the active space electronic Hamiltonian provided by quantum computing component 130 (e.g., its controller 132), and receives it via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication between classical computing component 110 and quantum computing component 130. For example, quantum computing component 130 receives qubit constraint information provided by classical computing component 110, and corresponds to the expected value of a quantum operator acting on the quantum state of at least a portion of a plurality of qubits of the quantum computing component, and provides a measurement value representing the expected value of a quantum operator acting on the eigenstate of the active space electronic Hamiltonian for reception by classical computing component 110 via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication between classical computing component 110 and quantum computing component 130.

[0081] Exemplary Operation of a Hybrid Quantum-Classical Computing System In various embodiments, the hybrid quantum-classical computing system 100 is used to simulate a chemical system. For example, in various embodiments, the hybrid quantum-classical computing system 100 is used to generate a model of a chemical system that represents one or more structural properties of the chemical system, one or more chemical interaction properties of the chemical system, one or more reaction properties of the chemical system, and the like. In various embodiments, the model, a portion thereof, and / or its graphical representation are displayed via a display (e.g., of the classical computing component 110) and stored in a file that can be used as an input to other simulations or models that use the interactions, structural properties, and / or reaction properties of the chemical system, such as for performing one or more functions thereof, and / or provided directly as an input thereto.

[0082] In various embodiments, the classical computing component 110 obtains information corresponding to the chemical system. For example, user input (e.g., received via a user input interface of the classical computing component 110) can provide access to, select, and / or elicit information corresponding to the chemical system. In one exemplary embodiment, the information corresponding to the chemical system can be the chemical formula of the chemical system (H, H2O, NH4 + etc.) and / or other designations of the chemical system. In one exemplary embodiment, the information corresponding to the chemical system includes nuclear information for each atomic nucleus of the chemical system (e.g., the number of protons and neutrons present in each atomic nucleus), the number of electrons in the chemical system, the nuclear Cartesian coordinates, and / or any other information used to define the chemical system.

[0083] In various embodiments, obtaining information corresponding to a chemical system triggers and / or causes classical computing component 110 to determine and / or generate a model of the chemical system that represents one or more structural characteristics of the chemical system, one or more chemical interaction characteristics of the chemical system, one or more reaction characteristics of the chemical system, and the like. For example, classical computing component 110 may determine and / or identify the active orbitals of a chemical system and provide information corresponding to the active orbitals to quantum computing component 130. Quantum computing component 130 may use the information corresponding to the active orbitals to determine one or more measurement values based on the qubit representation of the characteristics of the active orbitals. For example, in various embodiments, the one or more measurement values comprise at least one of the expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM). For example, in various embodiments, the one or more measurement values represent the expected value of a quantum operator acting on the eigenstate of the active space electronic Hamiltonian.

[0084] Considering that the number of active orbitals is limited (e.g., generally less than 10), currently operating quantum computing components (e.g., tend to be noisy and have less than 100 qubits in operation) are capable of accurately determining measurement values. Classical computing component 110 may determine determined values corresponding to various inactive orbitals (e.g., core orbitals and / or virtual orbitals). Classical computing component 110 may then utilize the measurement values and determined values to determine the structural characteristics, interaction characteristics, and / or other characteristics of the chemical system. For example, the classical computing component may determine an approximation of the characteristics of the eigenstate of the overall electronic Hamiltonian of the system, such as the expected value of a quantum operator acting on such a state, complete a simulation of the chemical system, determine how the chemical system behaves in one or more interactions (e.g., with other chemical systems and / or with electromagnetic radiation), determine the structural characteristics of the chemical system, and the like, using the measurement values and determined values.

[0085] In accordance with various embodiments, FIG. 2 provides a flowchart of various processes, procedures, operations, etc. implemented by classical computing component 110, and FIG. 3 provides a flowchart of various processes, procedures, operations, etc. implemented by quantum computing component 130. In various embodiments, steps / operations 302-312 are implemented between the implementation of step / operation 212 and the implementation of step / operation 214. In the illustrated embodiment, step / operation 216 is implemented after step / operation 214, but in various other embodiments, step / operation 216 may be implemented before step / operation 212 or step / operation 214.

[0086] Starting at step / operation 202 of FIG. 2, classical computing component 110 determines and / or identifies an approximation to the electronic state of a chemical system. The approximation to the electronic state of a chemical system is determined and / or identified by generating and / or determining an approximation to each wave function corresponding to the electronic state. For example, in one exemplary embodiment, classical computing component 110 uses a quantum many-body approximation to generate an approximation to the wave function and energy of the electronic state of a chemical system. For example, each wave function corresponds to one of the electronic states of the chemical system.

[0087] For example, in various embodiments, the classical computing component 110 performs a first level of simulation of a chemical system to identify and / or determine an approximation to the chemical system's orbitals. For example, the classical computing component 110 may use a mean-field approximation method such as Hartree-Fock theory, in which the wavefunction of an electron is defined by a single Slater determinant, to generate, among other things, molecular orbitals. In various embodiments, the classical computing component 110 constructs a more accurate approximation such that the orbitals can be rotated and divided into active and inactive orbitals, and the wavefunction of the electron is defined by a linear combination of Slater determinants constructed by different occupations of the active orbitals. Inactive orbitals include core orbitals and virtual orbitals. However, as will be understood by those skilled in the art, the generated and / or determined approximations to the wavefunction and energy are first approximations that are not accurate enough to provide a valid model of the chemical system alone.

[0088] In step / operation 204, the classical computing component 110 may transform each orbital of the chemical system. For example, the classical computing component 110 may determine the localization of each orbital. For example, the wavefunction may be spatially and / or energetically localized based at least in part on the structural and / or chemical interaction characteristics of interest. For example, if a particular bond in the chemical system is of particular interest, one or more appropriate orbitals may be localized in the region of that particular bond. In various embodiments, the transformation of the orbitals is performed by performing a rotation of the corresponding wavefunction to a desired coordinate system and the like.

[0089] In step / operation 206, the classical computing component 110 divides the orbitals of the chemical system into active and inactive orbitals (including, for example, core orbitals, virtual orbitals, etc.). For example, the classical computing component 110 may process the associated generated and / or determined wavefunction and / or energy and then identify and / or select the active orbitals.

[0090] The active orbitals define the active space of the Hilbert space of the chemical system, and the inactive orbitals define the inactive space of the Hilbert space of the chemical system. In other words, the active space comprises and / or consists of the active orbitals, and the inactive space comprises and / or consists of the inactive orbitals.

[0091] In various embodiments, the core orbitals are orbitals of the chemical system that are occupied by two electrons in a reference mean-field (Hartree-Fock) wave function and are not selected as active orbitals, for example, because their interaction with other active orbitals can be ignored. In various embodiments, the virtual orbitals comprise orbitals that are not occupied in a reference mean-field (Hartree-Fock) wave function and are not selected as active orbitals.

[0092] In various embodiments, the active orbitals are identified and / or selected based on user input (e.g., received via the user input device of the classical computing component 110). In various embodiments, the active orbitals are identified and / or selected based at least in part on the structural properties, chemical interaction properties, and / or reaction properties that the model of the chemical system is to represent. In various embodiments, the active orbitals include and / or consist of the selection of occupied orbitals in an approximation to an orbit determined as part of step / operation 202 (e.g., the reference Hartree-Fock wave function of the chemical system), and the selection of unoccupied orbitals in an approximation to an electronic state determined as part of step / operation 202.

[0093] In various embodiments, two or more orbitals are selected and / or specified as active orbitals. For example, the active space is defined based on two or more active orbitals. In various embodiments, two to six orbitals are selected and / or specified as active orbitals. In various embodiments, up to 100 orbitals are selected and / or specified as active orbitals. In various embodiments, the number and / or the maximum number of orbitals selected and / or specified as active orbitals are determined based on the number of qubits 134 of the quantum computing component 130 of the hybrid quantum-classical computing system 100.

[0094] In one exemplary embodiment, the partitioning of the orbitals into active and inactive orbitals is performed automatically by the classical computing component 110 (e.g., based on the execution of computer-readable instructions without interaction with a human user). In one exemplary embodiment, the partitioning of the orbitals into active and inactive orbitals is performed through user interaction with the classical computing component (e.g., based on user input received via one or more user input devices of the classical computing component 110).

[0095] In step / operation 208, classical computing component 110 determines fermionic constraint information regarding the active space. In various embodiments, the fermionic constraint information comprises an effective fermionic Hamiltonian of the active space. In one exemplary embodiment, the fermionic constraint information comprises an active space electronic Hamiltonian defined in the space of two or more active orbitals (e.g., defined in the active space). In one exemplary embodiment, the fermionic constraint information is a description of the energy and / or wavefunction of electrons in the active orbitals. For example, in one exemplary embodiment, the fermionic constraint information comprises an operator configured to operate on the wavefunction corresponding to the active orbitals to provide energy information corresponding to the active orbitals and / or a wavefunction on which the operator acts. For example, in one exemplary embodiment, the fermionic constraint information comprises a Hamiltonian of the active orbitals. In various embodiments, the fermionic constraint information corresponds to an active space defined by two or more active orbitals. For example, the fermionic constraint information does not correspond to an inactive space defined by one or more inactive orbitals.

[0096] In various embodiments, the fermionic constraint information is determined using procedures known as complete active space configuration interaction (CAS-CI) or selected active space configuration interaction, which correspond to all configuration interaction (CFI) calculations restricted to two or more active orbitals. For example, the wavefunction is represented as a linear combination of all or a subset of the configurations obtained by exciting electrons within the active space, where the inner shell orbitals remain fully occupied and the virtual orbitals remain empty. For example, for a chemical system having two active orbitals |A> and |B>, the wavefunction is represented in the form a|A> + b|B>, where |a 2 + b 2 | = 1.

[0097] In one exemplary embodiment, since the fermionic constraint information is determined using the multi-configuration self-consistent field (MC-SCF) technique, the wave function is represented as a linear combination of all or a selected set of configurations obtained by exciting electrons within the active space, where the inner shell orbitals remain fully occupied and the virtual orbitals are optimized to minimize the active space configuration interaction (CI) energy.

[0098] In various embodiments, the fermionic constraint information is determined using a multi-reference technique that modifies and / or adds dynamical correlation to the determination of the active space (AS) electron wave function. For example, in one exemplary embodiment, the fermionic constraint information is determined using a multi-reference configuration interaction (MR-CI) technique such that the wave function has a linear combination of electron configurations constructed by applying excitation operators to the AS wave function.

[0099] In one exemplary embodiment, the fermionic constraint information is determined using a multi-reference many-body perturbation theory (MR-MBPT) technique. For example, perturbation theory techniques such as the Moller-Plesset method (e.g., second-order Moller-Plesset method) can be applied to the CAS Hamiltonian to determine the fermionic constraint information.

[0100] In one exemplary embodiment, the second-order N-electron valence state perturbation theory (NEVPT2) technique is used to determine the fermionic constraint information. For example, a two-electron Dyall Hamiltonian can be used as a starting point for applying excitation operators to determine the configurations to include in the electron wave function.

[0101] In one exemplary embodiment, multi-reference coupled cluster theory (MR-CC) is used to determine the fermionic constraint information.

[0102] In various embodiments, determining the fermionic constraint information comprises determining an active space electronic Hamiltonian. In various embodiments, the active space electronic Hamiltonian is determined and / or defined based at least in part on a one-electron effective Hamiltonian for the active orbitals, the determined two-electron integrals, and the nuclear repulsion energy for the chemical system, which are determined as part of steps / operations 202 and 204 in various embodiments. For example, an effective one-electron Hamiltonian and transformed two-electron integrals in a molecular orbital basis function system are generated and used to define the active space electronic Hamiltonian.

[0103] In step / operation 210, classical computing component 110 generates qubit constraint information regarding the active orbitals by converting and / or replacing the fermionic constraint information to / with a qubit basis. The qubit basis is determined based on the quantum computing component 130 that is to be used to determine measurements corresponding to the active orbitals. For example, the qubit basis for a quantum computing component 130 that uses ion trap qubits is different from the qubit basis for a quantum computing component 130 that uses Josephson junction qubits.

[0104] In one exemplary embodiment, the qubit constraint information comprises an active space electronic Hamiltonian that is mapped, replaced, and / or converted to a qubit basis to provide a qubit Hamiltonian that encodes the spatial and energy constraints of the active space electronic Hamiltonian. For example, classical computing component 110 replaces, maps, and / or converts the fermionic constraint information regarding the active space electronic Hamiltonian to a qubit basis to generate qubit constraint information regarding the active space electronic Hamiltonian.

[0105] In various embodiments, the qubit basis corresponds to qubit operators that can be implemented for the qubits of the quantum computing component 130. Thus, mapping, replacing, and / or transforming the fermionic constraint information into qubit constraint information comprises replacing or mapping the fermionic operators of the active space electronic Hamiltonian of the fermionic constraint information to the qubit operators of the qubit basis. In various embodiments, Jordan-Wigner, Bravyi-Kitaev, Z2-symmetries, low-density parity-check (LDPC), segment, CI-matrix, degree-D, optimal-degree, and / or other mappings or encodings for transforming fermionic constraint information into qubit constraint information.

[0106] In various embodiments, the qubit constraint information comprises ansatz information. For example, the ansatz information can be used to formulate an expression of a wave function mapped and / or replaced to the qubit basis. For example, in various embodiments, the ansatz can be a predicted functional form of the wave function corresponding to the active orbitals. In one exemplary embodiment, the ansatz is a symmetry-adapted singlet unitary coupled-cluster singles and doubles (UCCSD) ansatz.

[0107] In step / operation 212, the classical computing component 110 provides the qubit constraint information to the quantum computing component. For example, the classical computing component 110 can transmit or otherwise communicate the qubit constraint information such that the controller 132 of the quantum computing component 130 receives the qubit constraint information regarding the active space electronic Hamiltonian.

[0108] As detailed with respect to FIG. 3, the quantum computing component 130 may use qubit constraint information to generate a qubit representation of the properties of the eigenstates of the active space electronic Hamiltonian (e.g., through the implementation of a quantum circuit and / or algorithm). For example, a qubit representation of the active orbitals and / or the wave functions of the eigenstates of the active space electronic Hamiltonian may be generated through the execution of a quantum circuit and / or algorithm. In various embodiments, quantum state preparation is performed using, for example, the variational quantum eigenvalue solver (VQE) method, variational quantum deflation, quantum subspace expansion, imaginary time evolution, variational quantum phase estimation, quantum phase estimation, or quantum bitization. For example, in one exemplary embodiment, quantum state preparation is performed using the VQE algorithm using the unitary coupled cluster ansatz.

[0109] Subsequently, various measurements may be performed on the qubit representation to generate measurements corresponding to the active orbitals. For example, a measurement operation may be performed on a plurality of qubits 134 of the quantum computing component 130, and a measurement value corresponding to the expected value of a quantum operator acting on at least a portion of the plurality of qubits is then determined. In various embodiments, the measurement values comprise, for example, at least one expected value of the active space electronic Hamiltonian, one or more of the spinless (i.e., spin-traced) one-particle, two-particle, three-particle, and four-particle reduced density matrices (RDMs). In various embodiments, the measurement values are measured and / or determined from the qubit measurement results using, for example, operator averaging, partial tomography of the quantum state, superposition quantum tomography, etc. For example, in one exemplary embodiment, the measurement values are measured and / or determined from the qubit measurement results using the operator averaging method using measurement reduction techniques.

[0110] For example, the quantum computing component 130 is configured to generate and / or measure an expression of an eigenstate of an active space electronic Hamiltonian of an active space defined by two or more active orbits in a chemical system. For example, in one exemplary embodiment, the quantum computing component 130 is configured to measure one or more RDMs (e.g., one-particle RDM (1-RDM), two-particle RDM (2-RDM), three-particle RDM (3-RDM), and / or four-particle RDM (4-RDM)). Moreover, using the generated and / or measured expression of the active orbits to generate measurement results of one or more RDMs results in a more accurate determination of the one or more RDMs than conventional approximations for the one or more RDMs, thereby improving the quantitative accuracy of simulations of chemical systems.

[0111] In step / operation 214, the classical computing component 110 receives a measurement value. For example, in various embodiments, the classical computing component 110 receives a measurement value corresponding to an expected value of a quantum operator acting on the quantum state of at least a portion of a plurality of qubits of the quantum computing component, and representing the expected value of a quantum operator acting on an eigenstate of the active space electronic Hamiltonian. For example, since the quantum computing component 130 can provide a measurement value, the classical computing component 110 receives the measurement value.

[0112] In various embodiments, the measurement value received by the classical computing component 110 includes the expected value of a quantum operator acting on an eigenstate of the active space electronic Hamiltonian, a spinless (i.e., spin-traced) one-particle RDM, a two-particle RDM, a three-particle RDM, a four-particle RDM, and the like. In various embodiments, the classical computing component 110 generates an n-RDM operator based on the measurement values corresponding to the 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM.

[0113] In step / operation 216, classical computing component 110 determines a decision value corresponding to an orbital. For example, in various embodiments, classical computing component 110 may correspond to inactive orbitals (e.g., inner shell orbitals and / or virtual orbitals) and / or determine various decision values representing an inactive space defined by one or more inactive orbitals. For example, the classical computing component is configured to generate and / or determine a representation of the basis and / or inner shell orbitals of a chemical system. For example, in various embodiments, classical computing component 110 may use various methods such as MR-MBPT, NEVPT2, quadratic complete active space perturbation theory (CASPT2), MR-CC, MR-CI, etc. to determine one or more decision values corresponding to the spatial distribution and / or energy of one or more inactive orbitals (e.g., inner shell orbitals and / or virtual orbitals).

[0114] In various embodiments, classical computing component 110 may determine a 4-particle RDM (4-RDM). For example, based on quantum computing component 130 and / or the properties of a chemical system, quantum computing component 130 may not have sufficient computational resources to enable the measurement of 4-RDM for an active space defined by two or more active orbitals. In such cases, classical computing component 110 may determine 4-RDM using, for example, cumulant expansion techniques. For example, in various embodiments, 4-RDM is determined and / or approximated using a spinless cumulant expansion based at least in part on 1-RDM, 2-RDM, and / or 3-RDM. This results in a significant reduction in the computational resources (e.g., processing time / capability, memory requirements) required to generate an accurate model of a chemical system.

[0115] In step / operation 218, classical computing component 110 utilizes (quantumly) measured values and (classically) determined values to generate a model of the chemical system that represents at least one of the structural properties, chemical interaction properties, or reaction properties of the chemical system. In various embodiments, classical computing component 110 produces an approximation to the expected value of a quantum operator acting on an eigenstate of the total electronic Hamiltonian to generate a model of the chemical system that represents at least one of the structural properties, chemical interaction properties, or reaction properties of the chemical system, using measured values that represent the expected value of a quantum operator acting on an eigenstate of the active space electronic Hamiltonian. For example, an expected value for the active space electronic Hamiltonian or at least one of the at least one RDMs is used to generate a model of the chemical system.

[0116] For example, classical computing component 110 may use determined and measured values to perform a strongly contracted NEVPT2 calculation to determine corrections to the energies and / or wavefunctions of the orbitals determined and / or identified in step / operation 202. In one exemplary embodiment, a spinless formulation of the strongly contracted NEVPT2 technique is used to determine approximate energies of the orbitals and / or corrections to the wavefunctions determined and / or identified in step / operation 202 using measured values (e.g., expected values for the active space electronic Hamiltonian, 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM). The corrections may then be applied to the energies and / or wavefunctions of the orbitals to generate a model of the chemical system that represents the structural properties, chemical interaction properties, reaction properties, etc. of the chemical system.

[0117] In various embodiments, the structural properties of the chemical system characterize and / or provide information regarding the structure of the chemical system. For example, the structural properties may indicate the shape of the chemical system, the order and / or spatial distribution of atoms or groups of atoms of the components in the chemical system, the properties of the various bonds in the chemical system, the relative nuclear positions in the chemical system, etc.

[0118] In various embodiments, the chemical interaction characteristics of a chemical system characterize and / or provide information regarding how the chemical system interacts with one or more other chemical systems of the same or different types. For example, the chemical interaction characteristics of a chemical system can provide information regarding how the chemical system interacts with other chemical systems of the same type / chemical formula or of a different type / chemical formula than the chemical system.

[0119] For example, the structural and / or chemical interaction characteristics can be a dissociation curve, binding energy, reaction energy, reaction barrier, binding energy, absorption energy, etc.

[0120] In various embodiments, the reaction characteristics of a chemical system characterize and / or provide information regarding how the chemical system interacts with electromagnetic radiation. For example, the reaction characteristics of a chemical system can be an excitation energy, singlet-triplet gap, photodissociation energy, photoionization energy, absorption cross section, permittivity, dielectric function, oscillator strength, etc.

[0121] In step / operation 220, the classical computing component 110 provides at least a portion of a model of the chemical system that represents the structural characteristics, chemical interaction characteristics, and / or reaction characteristics of the chemical system. In various embodiments, providing at least a portion of a model of the chemical system includes displaying, storing, transmitting (e.g., via one or more wired and / or wireless networks), providing, etc., a call response (e.g., an application program interface (API) call response).

[0122] For example, in one exemplary embodiment, the classical computing component 110 causes a display (e.g., display 516 shown in FIG. 5 and / or another display) to display a representation of a chemical system model. For example, the graphics processing unit (GPU) of the classical computing component 110 can generate a graphical representation of at least a portion of a chemical system model that provides, for example, visualization of the structural properties, chemical interaction properties, and / or reaction properties of the chemical system. The classical computing component 110 can then cause the graphical representation of at least a portion of the chemical system model to be displayed via the display for review and / or browsing by a human user.

[0123] In another example, the classical computing component 110 can generate a file comprising at least a portion of a chemical system model and store it (e.g., in memories 522, 524). For example, the file can comprise the modified energy and / or wave function of the chemical system's orbitals, structural properties, chemical interaction properties, reaction properties, chemical formulas, and the like. The file can then be provided as input for one or more functions and / or calculations performed thereby to one or more programs, applications, modules, etc. operating on the classical computing component 110 or another computing entity. For example, a file storing and / or encoding at least a portion of a chemical system model can be used by various programs, applications, modules, etc. for generating a graphical representation and / or visualization and / or a portion thereof of the chemical system, performing a simulation that includes chemical system interactions with one or more other chemical systems (same or different chemical formulas), performing a simulation of a bulk material comprising the chemical system, performing a simulation that includes chemical system interactions with one or more biological systems, and the like.

[0124] FIG. 3 provides a flowchart showing various processes, procedures, operations, etc. performed by the quantum component of the hybrid quantum-classical computing system 100 to generate and / or provide a model of a chemical system representing the structural characteristics of the chemical system, the chemical interaction characteristics of the chemical system, the reaction characteristics of the chemical system, and the like.

[0125] Starting at step / operation 302, the controller 132 of the quantum computing component 130 receives qubit constraint information. For example, the qubit constraint information is a mapping and / or replacement of fermionic constraint information to the qubit basis corresponding to the quantum computing component 130. For example, the qubit constraint information includes a replaced version of the active space electronic Hamiltonian defined in the space of two or more active orbitals in the qubit basis of the quantum computing component 130.

[0126] In various embodiments, the controller 132 receives the qubit constraint information via the communication interface 420 (see FIG. 4). For example, the classical computing component 110 may provide the qubit constraint information such that the quantum computing component 130 receives the qubit constraint information.

[0127] In step / operation 304, the controller 132 of the quantum computing component generates and / or determines an executable queue of commands for preparing the states of a plurality of qubits 134 based on qubit constraint information. For example, the quantum circuit and / or algorithm is defined, determined, generated, and / or compiled to perform state preparation of the plurality of qubits 134 such that the quantum state of the qubits 134 represents the wave function and / or energy of the active orbitals after the implementation of the quantum circuit and / or algorithm. For example, the quantum circuit and / or algorithm is defined, determined, generated, and / or compiled to perform state preparation of the plurality of qubits 134 such that the quantum state of the qubits 134 represents the eigenstate of the active space electronic Hamiltonian after the implementation of the quantum circuit and / or algorithm. For example, the occupancy of N active orbitals (fermion modes) is mapped to N (or a number close to N) qubits 134 via the quantum circuit and / or algorithm.

[0128] For example, the quantum circuit and / or algorithm can include an ordered combination of single-qubit gates and multi-qubit gates implemented on specific qubits 134 such that the quantum state of the qubits represents the wave function and / or energy of the active orbitals of a chemical system and / or represents the eigenstate of the active space electronic Hamiltonian. The ordered combination of single-qubit gates and multi-qubit gates is determined based on qubit constraint information. In one exemplary embodiment, the quantum circuit and / or algorithm is defined, determined, generated, and / or compiled using a VQE algorithm using a unitary coupled cluster ansatz. In various embodiments, various other ansätze can be used.

[0129] In various embodiments, measurement reduction techniques are used to partition the quantum circuit and / or algorithm into a swap set to reduce the number of measurements required.

[0130] In step / operation 306, the controller 132 executes an executable queue to perform state preparation of the qubit 134. For example, the controller 132 executes the executable queue to cause the qubit operation component 136 to perform an ordered combination of single-qubit gates and two or more qubit gates, so as to represent in the quantum state of the qubit 134 the wave function and / or energy of the active orbitals of the chemical system and / or the eigenstates of the active space electron Hamiltonian.

[0131] In step / operation 308, the controller 132 causes a measurement operation to be performed to determine the quantum state of the qubit 134. For example, the controller 132 controls the operation of the qubit operation component 136 and monitors the signal received from the sensor 138 to determine the respective quantum states of the qubit 134. In one exemplary embodiment, a symmetry check is performed (e.g., by the controller 132 and / or the classical computing component 110) to determine which elements are decaying and thus need not be measured. For example, in one exemplary scenario, an active electron number equal to 2 causes the 3-RDM and 4-RDM to decay (e.g., become substantially equal to 0). Thus, in such an example, computational resources can be saved by determining that the 3-RDM and 4-RDM need not be measured. In another scenario, the symmetry of the active space Hamiltonian can cause some matrix elements of the 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM to decay (e.g., become substantially equal to 0). Thus, in such an example, computational resources can be saved by determining that the said matrix elements of the 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM need not be measured.

[0132] In step / operation 310, the controller 132 determines a measurement value corresponding to the active orbit based on the result of the measurement operation (e.g., the measured quantum state of the quantum bit 134). For example, in various embodiments, the measurement value includes the expected value of the active space Hamiltonian, the spinless (i.e., spin-traced) one-particle reduced density matrix (RDM), two-particle reduced density matrix (RDM), three-particle reduced density matrix (RDM), and four-particle reduced density matrix (RDM). For example, in various embodiments, the measurement value corresponds to the expected value of a quantum operator acting on the quantum state of at least a portion of a plurality of quantum bits of the quantum computing component 130, and / or represents the expected value of a quantum operator acting on the eigenstate of the active space electronic Hamiltonian. In various embodiments, the measurement value is measured and / or determined from the quantum bit measurement result using operator averaging, partial tomography of the quantum state, superposition quantum tomography, etc. For example, in one exemplary embodiment, the measurement value is measured and / or determined from the quantum bit measurement result using an operator averaging method using a measurement reduction technique.

[0133] In step / operation 312, the controller 132 causes the quantum computing component 130 to provide the measurement value (e.g., via the communication interface 420). For example, the quantum computing component 130 provides the measurement value such that the classical computing component 110 receives the measurement value and determines and / or generates a model of the chemical system based at least in part thereon. For example, the quantum computing component 130 may provide the measurement value received by the classical computing component 110 via one or more wired and / or wireless networks 120, direct wired and / or wireless communication, etc.

[0134] As shown in FIG. 3, the controller 132 determines a measurement value based on the result of a measurement operation and provides the measurement value received by the classical computing component 110. In one exemplary embodiment, the controller 132 provides the result of the measurement operation received by the classical computing component 110, and the classical computing component 110 determines the measurement value based on the result of the measurement operation.

[0135] Technical Advantages Conventional classical computer software products are known that can be executed on classical computing hardware, e.g., on classical non-quantum computing components, to simulate chemical systems and determine the manner of interaction with other molecules, electromagnetic fields, and electromagnetic radiation. Such computer software products calculate an approximation to the electronic state of a chemical system, for example, by Hartree-Fock theory such that the wave function of an electron is defined by a single Slater determinant, or by density functional theory such that the electron density is calculated by a single Slater determinant, and then, as a second category of calculations to account for electron correlation effects, calculate other approximations to the electronic state of the system, including single-reference approximations, active space approximations, and multi-reference (multi-configuration) approximations.

[0136] A real-world technical problem encountered in practice is that the computational resources required to perform the second category of calculations can be very difficult. In some situations, the amount of computational resources required can become unmanageable. As a result, approximations are often used when performing calculations related to the second category described above. In various scenarios, these approximations are not accurate enough to provide the structural and / or interaction characteristics of atoms or molecules to account for and / or predict real-world observations of atoms or molecules and / or their interactions.

[0137] Quantum computing components are expected to provide systems that can perform complex calculations in a short time frame. However, currently operating quantum computing components tend to include a relatively small number of qubits (e.g., less than 100 qubits) and tend to be relatively noisy. As a result, there are further technical problems in that currently operating quantum computing components do not even provide sufficient computational resources to perform a full simulation of a chemical system or even a simulation of the excited states of a chemical system.

[0138] Various embodiments provide technical solutions to these technical problems. For example, in various embodiments, measurements for model active space Hamiltonian orbits are determined using the quantum component of a hybrid quantum-classical computing system. Many chemical systems, called multi-reference systems, cannot be adequately modeled by a single-reference wave function such that only one Slater determinant (electron configuration), called the reference determinant, has large coefficients in the configuration interaction expansion. Usually, the electronic structure of such systems is generally considered to have all orbits active and is calculated by the full configuration interaction method that includes all Slater determinants obtained by the excitation of electrons to virtual orbits, or is considered to have a subset of orbits and electrons active and is modeled by a multi-reference method such that it is constructed as a linear combination of Slater determinants obtained by all possible occupancies of active electrons in active orbits. Subsequently, to enable the calculation of the excitation of electrons to virtual orbits outside the active space and the dynamic correlation energy, the multi-reference wave function is further improved by the application of multi-reference configuration interaction, multi-reference perturbation theory, or multi-reference coupled cluster methods. Therefore, the determination of the reference wave function is equivalent to the calculation of full configuration interaction on the active space. Due to the computational cost of determining the coefficients of the reference wave function on a classical computer (related to the number of active electrons and active orbits), classical implementations of multi-reference methods are usually limited to an active space consisting of up to about 20 electrons in 20 orbits. However, subsequent calculations of the dynamic correlation energy can be efficiently performed classically (i.e., in polynomial time), especially by configuration interaction or perturbation theory. Quantum implementations of full configuration interaction simulations require the mapping of all orbits to a quantum bit register. However, hybrid quantum-classical implementations of multi-reference methods can be constructed by limiting the problems passed to the quantum component to active electrons and active orbits. Therefore, instead of applying the computational power of the quantum computing component to the entire electronic structure problem consisting of sub-problems with classically efficient strategies, it can be used only for the classically difficult part of the electronic structure problem, which can be an advantage over classical algorithms.

[0139] For example, various embodiments are configured to provide an improved model of a chemical system that improves the operation of programs, applications, and / or modules that use a model of the chemical system to perform various tasks (such as simulating chemical interactions, bulk material properties of materials including chemical systems, interactions of chemical systems with biological systems, interactions of materials with electromagnetic fields and / or electromagnetic waves, etc.). Moreover, various embodiments provide improvements beyond the capabilities of classical computers through the use of hybrid quantum-classical computing systems that utilize the currently available computing power of currently functioning quantum computing components to generate measurements corresponding to the active orbitals of a chemical system of interest. This use of quantum computing power assists and / or extends the capabilities of the computing system to generate an accurate representation of the chemical system while overcoming technical issues related to the relatively small number of qubits available in currently functioning quantum computing components. Accordingly, various embodiments provide a practical application that provides the functionality of an improved computer system that results in improved modeling of chemical systems.

[0140] For example, an exemplary embodiment is used to determine the dissociation curve of a dilithium molecule (Li2). Such a simulation is a prototype multi-reference problem, which cannot be well described by mean-field methods or general single-reference correlation methods (such as second-order Moller-Plesset (MP2) method or coupled cluster singles and doubles (CCSD) method). In the calculations shown, the correlation-consistent polarized valence only triple-zeta (cc-pVTZ) basis function system is advantageously used. The NEVPT2 calculation is performed using an active space consisting of 4 electrons out of 6 active space orbitals (12 spin orbitals), which can be optimized using the complete active space self-consistent field (CASSCF) technique. In VQE-NEVPT2, 12 spin orbitals can be mapped to 12 qubits via the Jordan-Wigner mapping. The ansatz used is preferably symmetry-adapted singlet UCCSD. FIGS. 6A and 6B provide a graphical representation of a model of a chemical system and its comparison with a previously determined Li2 dissociation curve. For example, FIG. 6A shows the deviation of the Li2 dissociation curve determined according to an exemplary embodiment from the conventional CAS-NEVPT2 results, and FIG. 6B shows the Li2 dissociation curve determined according to an exemplary embodiment together with that determined using the conventional CAS-NEVPT2 results. Thus, as shown by FIGS. 6A and 6B, various embodiments provide the structural properties, chemical interaction properties, and / or reaction properties of a chemical system that are consistent with existing results for simple systems and achieve more efficient use of computational resources than conventional techniques.

[0141] Exemplary controller In various embodiments, the hybrid quantum-classical computing system 100 includes a quantum computing component 130. The quantum computing component 130 is configured to perform various quantum computations and / or operations via the execution of one or more quantum circuits and / or algorithms. In various embodiments, the quantum computing component 130 is configured to control the operation of one or more components of the quantum computing component 130 (e.g., qubit manipulation elements 136, sensors 138), receive sensor signals indicative of measurement results captured by the sensors 138, and / or communicate with the classical computing component 110.

[0142] As shown in FIG. 4, in various embodiments, the controller 132 may include various controller elements, including a processing element 405, a memory 410, a driver controller element 415, a communication interface 420, an analog-to-digital converter element 425, and the like. For example, the processing element 405 may include one or more processing devices such as a complex programmable logic device (CPLD), a microprocessor, a coprocessing entity, an application-specific instruction set processor (ASIP), an integrated circuit, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices, and / or circuits. The term circuit may refer to a purely hardware embodiment or a combination of hardware and a computer program product. In one exemplary embodiment, the processing element 405 of the controller 132 is a clock and / or communicates with a clock.

[0143] For example, the memory 410 may include non-transitory memory such as volatile and / or non-volatile memory storage, such as one or more of a hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, and the like. In various embodiments, the memory 410 may store a queue of commands (e.g., an executable queue) to be executed to enable the execution of quantum algorithms and / or circuits, a qubit record corresponding to the qubits of the quantum computing component (e.g., in a qubit record data store, qubit record database, qubit record table, etc.), a calibration table, computer program code (e.g., in one or more computer languages, a dedicated controller language, etc.). In one exemplary embodiment, the execution of at least a portion of the computer program code stored in the memory 510 (e.g., by the processing element 405) causes the controller 132 to control the operation of one or more qubit operation elements 136, process sensor signals indicative of measurement results captured by the sensor 138, and / or communicate with the classical computing component 110 of the hybrid quantum-classical computing system 100 to perform one or more of the steps, operations, processes, procedures, etc. described herein.

[0144] In various embodiments, the driver controller element 410 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 410 may comprise a driver and / or a driver controller. For example, the driver controller may be configured to cause one or more corresponding drivers to be operated according to executable instructions, commands, etc. scheduled (e.g., by the processing element 405) and executed by the controller 132. In various embodiments, the driver controller element 415 may enable the controller 30 to operate various ones of the qubit operation elements 136 and / or the sensors 138. In various embodiments, the driver may comprise a laser driver configured to operate one or more lasers, a driver for controlling the operation of one or more voltage / current sources to cause the generation and provision of one or more voltage signals and / or current signals, and / or various other drivers configured to control the operation of each qubit operation element 136 of the quantum computing component 130.

[0145] In various embodiments, the controller 132 comprises means for communicating and / or receiving signals from one or more sensors (e.g., photodetectors, voltage / current sensors, temperature sensors, pressure sensors, and / or other sensors). For example, the controller 132 may comprise one or more analog-to-digital converter elements 425 configured to receive signals from one or more sensors.

[0146] In various embodiments, the controller 132 comprises a communication interface 420 for interfacing and / or communicating with the classical computing component 110 of the hybrid quantum-classical computing system 100. For example, the controller 132 may receive quantum bit constraint information, executable instructions, command sets, etc. from the classical computing component 110, and provide to the classical computing component 110 the output received from (e.g., via the sensor 138) and / or the result of processing the output from the quantum computing component 130 for determining measurement values corresponding to the active orbitals. In various embodiments, the classical computing component 110 and the controller 132 may communicate directly via a wired connection and / or a wireless connection, and / or via one or more wired and / or wireless networks 120.

[0147] Exemplary classical computing component FIG. 5 provides an exemplary schematic diagram representing an exemplary computing entity 10 that may be used with embodiments of the present invention. In various embodiments, the classical computing component 110 is configured to interface with the quantum computing component 130. For example, the classical computing component 110 is configured to interface with the quantum computing component 130 to enable an efficient and accurate modeling of a chemical system through direct modeling of the state of the active orbitals using the quantum computing component 130. For example, the classical computing component 110 may be configured to communicate with the quantum computing component 130 to enable a user (e.g., a human user or a program operating on the classical computing component 110) to provide an input to the quantum computing component 130, receive, display, analyze, etc. the output from the quantum computing component 130.

[0148] As shown in FIG. 5, classical computing component 110 may include an antenna 512, a transmitter 504 (e.g., wireless), a receiver 506 (e.g., wireless), and a processing element 508 that respectively provide signals to and receive signals from a transmitter 504 and a receiver 506. The signals provided to and received from the transmitter 504 and the receiver 506 respectively may include signaling information / data in accordance with the interface specifications of the applicable wireless system to communicate with various entities such as a controller 132, other classical computing components 110, etc. In this regard, the classical computing component 110 may be capable of operating using one or more air interface specifications, communication protocols, modulation types, and access types.

[0149] For example, the classical computing component 110 may be configured to receive and / or provide communications using a wired data transmission protocol, such as fiber distributed data interface (FDDI), digital subscriber line (DSL), Ethernet, asynchronous transfer mode (ATM), frame relay, data over cable service interface specification (DOCSIS), or any other wired transmission protocol.Similarly, the classical computing component 110 may be configured to communicate via a wireless external communication network using any of a variety of protocols, such as general packet radio service (GPRS), Universal Mobile Telecommunications System (UMTS), Code Division Multiple Access 2000 (CDMA2000), CDMA2000 1X (1xRTT), Wideband Code Division Multiple Access (WCDMA (registered trademark)), Global System for Mobile Communications (GSM), Enhanced Data rates for GSM Evolution (EDGE), Time Division-Synchronous Code Division Multiple Access (TD-SCDMA), Long Term Evolution (LTE (registered trademark)), Evolved Universal Terrestrial Radio Access Network (E-UTRAN), Evolution-Data Optimized (EVDO), High Speed Packet Access (HSPA), High-Speed Downlink Packet Access (HSDPA), IEEE 802.11 (Wi-Fi (registered trademark)), Wi-Fi Direct, 802.16 (WiMAX (registered trademark)), ultra wideband (UWB), infrared (IR) protocol, near field communication (NFC) protocol, Wibree, Bluetooth protocol, wireless universal serial bus (USB) protocol, and / or any other wireless protocol.The classical computing component 110 may use such protocols and standards to communicate using, for example, Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), HyperText Markup Language (HTML), and the like.

[0150] Through these communication standards and protocols, classical computing component 110 can communicate with various other entities using concepts such as Unstructured Supplementary Service information / data (USSD), Short Message Service (SMS), Multimedia Messaging Service (MMS), Dual-Tone Multi-Frequency Signaling (DTMF), and / or Subscriber Identity Module Dialer (SIM dialer). Classical computing component 110 can also download changes, add-ons, and updates to, for example, its firmware, software (including executable instructions, applications, program modules), and operating system.

[0151] In various embodiments, classical computing component 110 may comprise a network interface 520 for interfacing with and / or communicating with, for example, controller 132. For example, classical computing component 110 may provide qubit constraint information, executable instructions, instruction sets, etc. for reception by controller 132, and / or may comprise a network interface 520 for receiving outputs (such as measurements corresponding to active orbits) and / or results processed from the outputs provided by quantum computing component 130. In various embodiments, classical computing component 110 and controller 132 may communicate directly via wired and / or wireless connections, and / or via one or more wired and / or wireless networks 120.

[0152] In various embodiments, processing element 508 may comprise one or more processing devices such as a Complex Programmable Logic Device (CPLD), a microprocessor, a coprocessing entity, an Application Specific Instruction Set Processor (ASIP), an integrated circuit, an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a hardware accelerator, a Graphics Processing Unit (GPU), a Central Processing Unit (CPU), other processing devices and / or circuitry. The term circuitry may refer to an entirely hardware embodiment or a combination of hardware and a computer program product.

[0153] The classical computing component 110 may also comprise a user interface device having one or more user input / output interfaces (e.g., a display 516 and / or a speaker / speaker driver coupled to the processing element 508, and a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 508). For example, the user output interface is configured to cause the display or audible presentation of information / data and to interact therewith via one or more user input interfaces, and to be interchangeably executed on the computing entity 10 and / or accessible via the computing entity 10, and to provide an application, browser, user interface, interface, dashboard, screen, web page, page, and / or similar terms used herein. The user input interface may comprise any of a number of devices that enable the computing entity 10 to receive data, such as a keypad 518 (hard or soft), a touch display, a mouse, a voice / speech or motion interface, a scanner, a reader, or other input device. In embodiments including the keypad 518, the keypad 518 may include (or cause the display of) conventional numbers (0-9) and associated keys (#, *), and other keys used to operate the classical computing component 110, and may include a set of keys that can be driven to provide a full set of alphabetic keys or a full set of alphanumeric keys. In addition to providing input, the user input interface may be used to enable or disable certain functions, such as a screen saver and / or sleep mode. Through such input, the classical computing component 110 can collect information / data, user interaction / input, etc.

[0154] The classical computing component 110 may also include volatile storage or memory 522 and / or non-volatile storage or memory 524, which may be integrated and / or removable. For example, non-volatile memory may be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. Volatile memory may be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. Volatile and non-volatile storage or memory can store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, bytecode, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functions of the classical computing component 110.

[0155] In any of the above aspects, various features may be implemented in hardware or as software modules executed on one or more processors / computers.

[0156] The present invention also provides a computer program or a computer program product comprising instructions which, when executed by a computer (or a hybrid quantum-classical computer), cause the computer to perform any of the methods / method steps described herein, and a non-transitory computer-readable medium comprising instructions which, when executed by a computer (or a hybrid quantum-classical computer), cause the computer to perform any of the methods / method steps described herein. The computer program embodying the present invention may be stored in a non-transitory computer-readable medium or may be in the form of a signal such as, for example, a downloadable data signal provided from an Internet website, or in any other form.

[0157] For example, the present disclosure extends to a computer program comprising executable instructions, which, when executed by a hybrid quantum-classical computing system, cause the hybrid quantum-classical computing system to determine, by a classical computing component of the hybrid quantum-classical computing system, fermionic constraint information regarding an active-space electronic Hamiltonian defined in an active space of two or more active orbitals of a chemical system, cause the classical computing component to replace the fermionic constraint information regarding the active-space electronic Hamiltonian with qubit basis to generate qubit constraint information regarding the active-space electronic Hamiltonian, cause the classical computing component to provide the qubit constraint information regarding the active-space electronic Hamiltonian to a quantum computing component of the hybrid quantum-classical computing system, cause the classical computing component to receive a measurement value corresponding to an expected value of a quantum operator acting on a quantum state of at least a portion of a plurality of qubits of the quantum computing component and representing an expected value of a quantum operator acting on an eigenstate of the active-space electronic Hamiltonian, and cause the classical computing component to generate an approximation to an expected value of a quantum operator acting on an eigenstate of the overall electronic Hamiltonian to utilize the measurement value representing the expected value of the quantum operator acting on the eigenstate of the active-space electronic Hamiltonian to generate a model of the chemical system representing at least one of a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system.

[0158] As a further example, the present disclosure extends to a computer program comprising executable instructions that, when executed by a hybrid quantum-classical computing system, cause the hybrid quantum-classical computing system to: (i) represent the overall electronic Hamiltonian and the active space electronic Hamiltonian of a chemical system in a classical computing component; and (ii) represent an active space wavefunction and at least one active space reduced density matrix (RDM) of the chemical system in a quantum computing component, based at least in part on replacing the active space electronic Hamiltonian with respect to the qubit basis of a plurality of qubits of the quantum computing component, wherein the classical computing component uses at least one active space RDM to determine an approximation of at least one additional RDM representing at least one of the structural properties, chemical interaction properties, or reaction properties of the chemical system.

[0159] Conclusion Many modifications and other embodiments of the invention set forth herein will come to mind to those skilled in the art to which the invention pertains having the benefit of the teachings presented in the foregoing description and the related drawings. Therefore, the invention is not to be limited to the specific embodiments disclosed, and it is intended that modifications and other embodiments be included within the scope of the appended claims. Although specific terms are employed herein, they are used in a generic and descriptive sense only and not for purposes of limitation.

Description of the Reference Numerals

[0160] 10 Computing entity 100 Hybrid quantum-classical computing system 110 Classical computing component 120 Wireless network 130 Quantum computing component 132 Controller 134 Qubit 136 Qubit operation element 138 Sensor 405 Processing element 410 Memory 415 Driver controller element 420 Communication interface 425 Analog-to-digital converter 504 Transmitter 506 Receiver 508 Processing element 512 Antenna 516 Display 518 Keypad 520 Network interface 522 Volatile memory 524 Non-volatile memory

Claims

1. A method for simulating a chemical system using a hybrid quantum-classical computing system, comprising: determining, by a classical computing component of the hybrid quantum-classical computing system, fermionic constraint information regarding an active-space electronic Hamiltonian defined in an active space of two or more active orbitals of the chemical system; replacing, by the classical computing component, the fermionic constraint information regarding the active-space electronic Hamiltonian with a qubit basis in order to generate qubit constraint information regarding the active-space electronic Hamiltonian; providing, by the classical computing component, the qubit constraint information regarding the active-space electronic Hamiltonian to a quantum computing component of the hybrid quantum-classical computing system; receiving, by the classical computing component, a measurement value that (a) corresponds to an expected value of a quantum operator acting on quantum states of at least a portion of a plurality of qubits of the quantum computing component and (b) represents the expected value of the quantum operator acting on an eigenstate of the active-space electronic Hamiltonian; utilizing, by the classical computing component, the measurement value representing the expected value of the quantum operator acting on the eigenstate of the active-space electronic Hamiltonian to produce an approximation of an expected value of a quantum operator acting on an eigenstate of an overall electronic Hamiltonian, and generating a model of the chemical system representing at least one of a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system; A method comprising the above steps.

2. The method according to claim 1, wherein the fermionic constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals comprises an effective fermionic Hamiltonian, and the qubit constraint information regarding the active-space electronic Hamiltonian defined in the space of two or more active orbitals comprises a replaced version of the fermionic Hamiltonian in the qubit basis.

3. The method according to claim 1 or 2, wherein the measurement value comprises at least one of an expected value of the active-space Hamiltonian or at least one reduced density matrix (RDM).

4. The method according to claim 3, wherein the at least one RDM comprises at least one of a one-particle RDM (1-RDM), a two-particle RDM (2-RDM), a three-particle RDM (3-RDM), or a four-particle RDM (4-RDM).

5. The method according to claim 4, further comprising the step of determining an estimation of the 4-RDM by the classical computing component.

6. The method according to any one of claims 1 to 5, wherein the step of utilizing the measurement values to produce an approximation of an expected value of a quantum operator acting on an eigenstate of the overall electronic Hamiltonian comprises performing a second-order N-electron valence state perturbation theory calculation.

7. The method according to any one of claims 1 to 6, wherein the one or more inactive orbitals comprise one or more inner shell orbitals or virtual orbitals.

8. The step of performing state preparation of a plurality of qubits by the quantum computing component based at least in part on the quantum bit constraint information regarding the active space electronic Hamiltonian, and The step of performing one or more measurement operations by the quantum computing component to determine the measurement values based on quantum states of at least a portion of the plurality of qubits The method according to any one of claims 1 to 7, further comprising.

9. The step of identifying a plurality of orbitals of the chemical system by the classical computing component, and The step of partitioning the plurality of orbitals into the two or more active orbitals and the one or more inactive orbitals The method according to any one of claims 1 to 8, further comprising.

10. The method according to any one of claims 1 to 9, wherein the quantum computing component is configured to use a maximum of 100 qubits to perform a quantum circuit.

11. The method according to any one of claims 1 to 10, wherein the classical computing component further causes at least one of (a) display of a graphical representation of at least a portion of the model of the chemical system, or (b) generation of a file comprising one or more parameters of the model of the chemical system and storage in classical memory.

12. A classical computing component, and A quantum computing component Comprising A hybrid quantum-classical computing system configured to implement the method according to any one of claims 1 to 11.

13. A computer program product comprising at least one non-transitory computer-readable medium storing computer-readable instructions, wherein when the computer-readable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is configured to implement the method according to any one of claims 1 to 11.

14. A classical computing component configured to determine at least an inactive part of a model of a chemical system, wherein the inactive part of the model of the chemical system represents at least one or more inactive orbitals of the chemical system, and A quantum computing component configured to determine at least an active part of the model of the chemical system, wherein the active part of the model of the chemical system provides quantum bit constraint information corresponding to the active space electronic Hamiltonian, and the fermionic constraint information corresponding to the active space electronic Hamiltonian defined in the space of the two or more active orbitals is replaced with quantum bit basis, and is determined based on implementing a quantum circuit based on at least a part of the quantum bit constraint information, and represents attributes of two or more active orbitals of the chemical system, and A hybrid quantum-classical computing system comprising the same.

15. The hybrid quantum-classical computing system according to claim 14, wherein the fermionic constraint information corresponding to the active space electronic Hamiltonian defined in the space of the two or more active orbitals uses a spinless representation of the active orbitals.

16. The hybrid quantum-classical computing system according to claim 14 or 15, wherein the quantum computing component is configured to use an ansatz that is a symmetry-adapted singlet unitary coupled-cluster singles and doubles (UCCSD) ansatz.

17. The hybrid quantum-classical computing system according to any one of claims 14 to 16, wherein the classical computing component is configured to use a cumulant expansion to generate at least one approximation of at least one multi-particle RDM.

18. The hybrid quantum-classical computing system according to any one of claims 14 to 17, wherein the classical computing component is configured to generate a four-particle reduced density matrix (4-RDM) from at least one of a one-particle RDM (1-RDM), a two-particle RDM (2-RDM), or a three-particle RDM (3-RDM) measured by the quantum computing component.

19. The hybrid quantum-classical computing system according to any one of claims 14 to 18, wherein the classical computing component is configured to calculate NEVPT2 energy based at least in part on a measurement result indicating an RDM value, and the measurement result is obtained as part of performing the quantum circuit.

20. The hybrid quantum-classical computing system, (i) defining an active space and a basis function system corresponding to the chemical system; (ii) constructing a corresponding Hamiltonian representing the chemical system; (iii) defining a corresponding ansatz representing the chemical system; (iv) determining parameters of the chemical system by using the VQE method applied to a quantum circuit generated from the active space electronic Hamiltonian and provided together with the ansatz as initial quantum computing parameters. The hybrid quantum-classical computing system according to any one of claims 14 to 19, wherein the hybrid quantum-classical computing system is configured to perform the above steps.

21. A method performed by a hybrid quantum-classical computing system to generate a model of a chemical system, the hybrid quantum-classical computing system comprising a classical computing component coupled to a quantum computing component, the method comprising: (i) representing, in the classical computing component, the overall electronic Hamiltonian and the active space electronic Hamiltonian of the chemical system; (ii) representing, in the quantum computing component, the active space wave function of the chemical system and at least one active space reduced density matrix (RDM) of the chemical system, based at least in part on replacing the active space electronic Hamiltonian with a qubit basis of a plurality of qubits of the quantum computing component. including A method in which the classical computing component uses the at least one active space RDM to determine at least one additional approximation of the RDM that represents at least one of the structural characteristics, chemical interaction characteristics, or reaction characteristics of the chemical system.

22. The method according to claim 21, comprising the step of configuring the hybrid quantum-classical computing system to use a spinless formulation of the at least one active space RDM and the at least one additional RDM when calculating the characteristics of the chemical system by using the quantum computing component.

23. The method according to claim 21 or 22, comprising the step of configuring the quantum computing component to use an ansatz that is symmetry-adapted single-reference coupled cluster doubles (UCCSD).

24. The method according to any one of claims 21 to 23, comprising the step of configuring the hybrid quantum-classical computing system to use a cumulant expansion to generate the approximation of the at least one additional RDM.

25. The method according to any one of claims 21 to 24, comprising the step of configuring the hybrid quantum-classical computing system to generate 1-RDM, 2-RDM, 3-RDM to 4-RDM.

26. The method according to any one of claims 21 to 25, comprising the step of configuring the hybrid quantum-classical computing system to calculate the NEVPT2 energy using the quantum-measured RDM.

27. The method (i) defining an active space and a basis function system corresponding to the chemical system; (ii) constructing a corresponding Hamiltonian representing the chemical system; (iii) defining a corresponding ansatz representing the chemical system; (iv) determining the parameters of the chemical system by using the variational quantum eigensolver (VQE) method applied to a quantum circuit generated from the active space electronic Hamiltonian and provided together with the ansatz as initial quantum computing parameters The method according to any one of claims 21 to 26, comprising the step of configuring the hybrid quantum-classical computing system to perform the above operations.

28. A machine-readable data storage medium comprising specific instructions executable on data processing hardware, wherein when the instructions are executed by the data processing hardware, the method according to any one of claims 21 to 27 is implemented.

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