Hybrid Quantum-Classical Computational Simulation of the Chemistry Department

Abstract

A chemical system is simulated using a hybrid quantum-classical computing system. The classical component of the system evaluates a class selection metric based on the structure of the chemical system, determines whether the class selection metric meets one or more class selection criteria, and in response to the determination that the class selection metric meets the class selection criteria, provides qubit constraint information to the quantum component of the system, receives a quantum-measured value corresponding to the expected value of a quantum operator acting on the quantum state of the qubits of the quantum component and representing the expected value of the quantum operator acting on the eigenstate of the active space electronic Hamiltonian, and utilizes the measured value to approximate 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 the structural and / or chemical interaction characteristics of the chemical system.

Description

Technical Field

[0001] Cross - reference to Related Applications This application is a continuation - in - part of U.S. Application No. 17 / 931,616, filed on September 13, 2022, and claims the priority of U.S. Application No. 63 / 344,592, filed on 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 electrons is represented by the electron wave function, which, conveniently, is expressed as a linear combination of Slater determinants made up of 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 noted efforts, ingenuity, and innovation, many of the deficiencies in modeling and / or simulating such systems have been solved by developing strategies structured in accordance with 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 more comprehensively and accurately simulating a series of electronic states 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 simulation of a chemical system 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 in which an electron wave function 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 wave function 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.

[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 electronic Hamiltonian represented in second quantization, i.e., via the occupation 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 electronic Hamiltonian.

[0008] Next, the qubit representation of the properties of the active space Hamiltonian is replaced with the classical representation of the properties 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, a classical determination is made of 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 states, to complete a simulation of the chemical system and to determine how the chemical system will behave in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), to determine the structural properties of the chemical system, and so on.

[0009] In various embodiments, the chemical system is evaluated to determine whether the chemical system is a good candidate for using a hybrid quantum-classical approximation to generate a model of the chemical system. For example, in one exemplary embodiment, class selection metrics are evaluated by a classical computing component to determine whether the class selection metrics meet one or more class selection criteria. In various embodiments, when the class selection metrics do not meet the class selection criteria, a notification is provided and / or a model of the chemical system is generated using a classical approximation. In various embodiments, when the class selection metrics meet the class selection criteria, a model of the chemical system is generated using a hybrid approximation. In various embodiments, the hybrid approximation used is selected based on an evaluation of type selection metrics and type selection criteria.

[0010] 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.

[0011] In an 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.

[0012] In an 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).

[0013] 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).

[0014] In one exemplary embodiment, the method further comprises determining an estimate of the 4-RDM by a classical computing component based at least in part on at least one of the 1-RDM, 2-RDM, or 3-RDM.

[0015] 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 second-order N-electron valence state perturbation theory calculation.

[0016] In one exemplary embodiment, one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0017] In one exemplary embodiment, the method further comprises performing state preparation of a plurality of qubits by a quantum computing component 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 performing one or more measurement operations by the quantum computing component to determine a measurement value based on the quantum state of at least a portion of the plurality of qubits.

[0018] In one exemplary embodiment, the method further comprises identifying a plurality of orbitals of a chemical system by a classical computing component, and partitioning the plurality of orbitals into two or more active orbitals and one or more inactive orbitals.

[0019] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0020] 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.

[0021] 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, or reaction properties of the chemical system.

[0022] 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 comprises 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 by utilizing the measurement value representing the expected value of the quantum operator acting on the eigenstates of the active space electronic Hamiltonian.

[0023] 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.

[0024] In one exemplary embodiment, the measured value comprises the expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0025] 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).

[0026] 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.

[0027] In one exemplary embodiment, the step of utilizing a measured value representing the 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 a quantum operator acting on an eigenstate of the total electronic Hamiltonian comprises performing a second-order N-electron valence state perturbation theory calculation or an AC0 calculation.

[0028] In one exemplary embodiment, the one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0029] In one exemplary embodiment, the hybrid quantum-classical computing system performs state preparation of a plurality of qubits using a quantum computing component 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 performs 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.

[0030] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a classical computing component to identify and optionally rotate multiple orbits of a chemical system, and to classify the multiple orbits into two or more active orbits and one or more inactive orbits.

[0031] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0032] 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) displaying a graphical representation of at least a portion of a model of a chemical system, or (b) generating and storing in classical memory a file comprising one or more parameters of a model of a chemical system.

[0033] In one exemplary embodiment, the one or more parameters of the model of the chemical system include 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.

[0034] According to another aspect, there is provided a computer program product comprising 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 an expected value of the quantum operator acting on an eigenstate of the overall electronic Hamiltonian and generate a model of the chemical system representing 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.

[0035] In an 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.

[0036] 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).

[0037] 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).

[0038] In one exemplary embodiment, when executed by a hybrid quantum-classical computing system, the computer-readable instructions 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.

[0039] 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 electron 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.

[0040] In one exemplary embodiment, the one or more inactive orbitals comprise core orbitals and virtual orbitals.

[0041] In one exemplary embodiment, when executed by a hybrid quantum-classical computing system, the computer-readable instructions 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 measurement value based on the quantum state of at least a portion of the plurality of qubits.

[0042] 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.

[0043] In one exemplary embodiment, the quantum computing component is configured to use up to 100 qubits to implement a quantum circuit.

[0044] 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 thereof in classical memory.

[0045] In one exemplary embodiment, the one or more parameters of the model of the chemical system include 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.

[0046] 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 model of a chemical system, where the inactive portion of the model of the chemical system 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 model of the chemical system, where the active portion of the model of the chemical system is defined in a space of two or more active orbitals to provide qubit constraint information corresponding to an active space electronic Hamiltonian in a space of a plurality of qubits of the quantum computing component, replace fermionic constraint information regarding the active space electronic Hamiltonian defined in the space of two or more active orbitals with qubit basis, and perform a quantum circuit based at least in part on the qubit constraint information using the plurality of qubits, and represents characteristics of active orbitals of the chemical system determined thereby.

[0047] 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.

[0048] 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.

[0049] 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).

[0050] 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.

[0051] In one exemplary embodiment, the classical computing component is configured to calculate the NEVPT2 or AC0 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.

[0052] 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 orbitals (e.g., Gaussian-type atomic orbitals, Wannier functions, plane waves, etc.).

[0053] According to another aspect, a method is provided that is performed by a hybrid quantum-classical computing system to generate a model of a chemical system. 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, in the classical computing component, the total electronic Hamiltonian and the active space electronic Hamiltonian of the chemical system, and representing, in the quantum computing component, the active space wave function and at least one active space reduced density matrix (RDM) of the chemical system based at least in part on a replacement of the active space electronic Hamiltonian with 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 the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system.

[0054] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to use spinless formulations of at least one active space RDM and at least one additional RDM when calculating properties of a chemical system by using quantum computing components.

[0055] In one exemplary embodiment, the method includes configuring quantum computing components to use an ansatz that is symmetry-adapted singlet UCCSD.

[0056] 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.

[0057] 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.

[0058] In one exemplary embodiment, the method includes configuring a hybrid quantum-classical computing system to calculate NEVPT2 or AC0 energy using quantum-measured RDM.

[0059] 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 VQE method applied to a quantum circuit, so as to configure a hybrid quantum-classical computing system.

[0060] 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 to represent the active space wavefunction of the chemical system 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 the replacement of the active space electronic Hamiltonian with the 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 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.

[0061] According to another aspect, a method for simulating a chemical system using a hybrid quantum-classical computing system is provided. In one exemplary embodiment, the method includes obtaining an indication of the chemical system by a classical computing component of the hybrid quantum-classical computing system; evaluating a class selection metric by the classical computing component based at least in part on the structure of the chemical system; determining by the classical computing component whether the class selection metric meets one or more class selection criteria; and in response to a determination that the class selection metric does not meet one or more class selection criteria, performing by the classical computing component at least one of: (a) providing a notification that the class selection criteria are not met by the chemical system, or (b) performing a classical approximation to generate a model of the 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. The method further includes, in response to a determination that the class selection metric meets one or more class selection criteria, providing by the classical computing component qubit constraint information regarding an active space electronic Hamiltonian for the chemical system 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 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 utilizing the measurement value by the classical computing component to generate a model of the 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.

[0062] In one exemplary embodiment, the step of evaluating a class selection metric comprises performing a multireference diagnosis of the chemical system to determine a multireference diagnostic number corresponding to the chemical system, and determining whether the class selection metric meets one or more class selection criteria, the step of determining whether the multireference diagnostic number corresponding to the chemical system is greater than a threshold intensity.

[0063] In one exemplary embodiment, the step of performing a multireference diagnosis of the chemical system comprises determining a classical approximation of the multireference wavefunction of the chemical system and determining the degree of electronic correlation of the chemical system based at least in part on the classical approximation of the multireference wavefunction.

[0064] 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 the chemical system, or (b) generating a file comprising one or more parameters of the model of the chemical system and storing it in classical memory.

[0065] In one exemplary embodiment, the method further comprises, in response to a determination that one or more class selection criteria are met, evaluating a type selection metric by a classical computing component based on one or more of (a) at least a portion of the structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input, and selecting a hybrid approximation based on one or more type selection criteria and the type selection metric, the step of using the hybrid approximation by the classical computing component to generate a model of the chemical system using measurements.

[0066] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of active electrons of the chemical system, the number of active orbitals of the chemical system, or one or more symmetries of the chemical system.

[0067] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of qubits of the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

[0068] In one exemplary embodiment, the hybrid approximation is one of a quadratic N-electron valence perturbation theory (NEVPT2) approximation or an AC0 approximation.

[0069] In one exemplary embodiment, the measurement value measured by the quantum computing component is determined based on the hybrid approximation.

[0070] In one exemplary embodiment, the measurement value comprises at least one of an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0071] 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).

[0072] In one exemplary embodiment, the method further comprises generating qubit constraint information, and the step of generating qubit constraint information comprises determining, by a classical computing component, fermionic constraint information regarding an active space electronic Hamiltonian defined in an active space of two or more active orbitals of a chemical system, and replacing, by the classical computing component, the fermionic constraint information regarding the active space electronic Hamiltonian with qubit basis to generate qubit constraint information regarding the active space electronic Hamiltonian.

[0073] In one exemplary embodiment, fermionic constraint information regarding an active space electronic Hamiltonian defined in the active space of two or more active orbitals of a chemical system is implemented as part of evaluating a class selection metric.

[0074] In one exemplary embodiment, the method further comprises: performing, by a quantum computing component, state preparation of a plurality of qubits based at least in part on qubit constraint information regarding an active space electronic Hamiltonian; and performing, by the quantum computing component, 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.

[0075] 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 comprises a classical computing component and a quantum computing component. The hybrid quantum-classical computing system is configured to use the classical computing component to obtain an indication of the chemical system, evaluate a class selection metric based at least in part on the structure of the chemical system, determine whether the class selection metric meets one or more class selection criteria, and in response to a determination that the class selection metric does not meet one or more class selection criteria, perform at least one of: (a) providing a notification that the class selection criteria are not met by the chemical system, or (b) performing a classical approximation to generate a model of the 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. The hybrid quantum-classical computing system is further configured to, in response to a determination that the class selection metric meets one or more class selection criteria, use the classical computing component to provide qubit constraint information regarding an active space electronic Hamiltonian for the chemical system to the quantum computing component of the hybrid quantum-classical computing system, receive a measurement value that corresponds to an 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 that represents an expected value of the quantum operator acting on an eigenstate of the active space electronic Hamiltonian, and utilize the measurement value to generate a model of the 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.

[0076] In one exemplary embodiment, evaluating the class selection metric comprises performing a multi-reference diagnosis of the chemical system to determine a multi-reference diagnosis number corresponding to the chemical system, and determining whether the class selection metric meets one or more class selection criteria comprises determining whether the multi-reference diagnosis number corresponding to the chemical system is greater than a threshold intensity.

[0077] In one exemplary embodiment, performing a chemical multi-reference diagnosis comprises determining a classical approximation of a chemical multi-reference wavefunction and determining a degree of electronic correlation of the chemical system based at least in part on the classical approximation of the multi-reference wavefunction.

[0078] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use classical computing components to cause at least one of (a) display of a graphical representation of at least a portion of a 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.

[0079] In one exemplary embodiment, the hybrid quantum-classical computing system, in response to a determination that one or more class selection criteria are met, uses classical computing components to evaluate a type selection metric based on one or more of (a) at least a portion of the structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input, and selects a hybrid approximation based on the one or more type selection criteria and the type selection metric, wherein the classical computing component uses the hybrid approximation to generate a model of the chemical system using measurements.

[0080] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of active electrons of the chemical system, the number of active orbitals of the chemical system, or one or more symmetries of the chemical system.

[0081] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of qubits of the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

[0082] In one exemplary embodiment, the hybrid approximation is one of a second-order N-electron valence perturbation theory (NEVPT2) approximation or an AC0 approximation.

[0083] In one exemplary embodiment, the measurement value measured by the quantum computing component is determined based on the hybrid approximation.

[0084] In one exemplary embodiment, the measurement value comprises at least one of an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0085] 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).

[0086] In one exemplary embodiment, the hybrid quantum-classical computing system is further configured to use a classical computing component to generate qubit constraint information, and generating the qubit constraint information comprises determining fermionic constraint information regarding an active space electronic Hamiltonian defined in an active space of two or more active orbitals of a chemical system, and replacing the fermionic constraint information regarding the active space electronic Hamiltonian with respect to a qubit basis to generate qubit constraint information regarding the active space electronic Hamiltonian.

[0087] In one exemplary embodiment, the fermionic constraint information regarding the active space electronic Hamiltonian defined in an active space of two or more active orbitals of a chemical system is implemented as part of an evaluation of a class selection metric.

[0088] In one exemplary embodiment, a hybrid quantum-classical computing system is further configured to use a classical computing component to perform state preparation of a plurality of qubits based at least in part on qubit constraint information regarding an active space electronic Hamiltonian, and to perform one or more measurement operations by a quantum computing component to determine measurement values based on the quantum states of at least a portion of the plurality of qubits.

[0089] 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 obtain an indication of a chemical system, evaluate a class selection metric based at least in part on the structure of the chemical system, determine whether the class selection metric meets one or more class selection criteria, and in response to a determination that the class selection metric does not meet one or more class selection criteria, perform at least one of (a) providing a notification that the class selection criteria are not met by the chemical system, or (b) performing a classical approximation to generate a model of the 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. When executed by the data processing hardware, the instructions further cause the classical computing component to, in response to a determination that the class selection metric meets one or more class selection criteria, provide qubit constraint information regarding the active space electronic Hamiltonian for the chemical system to the quantum computing component of the hybrid quantum-classical computing system, receive a measurement value that corresponds to an expected value of a quantum operator acting on at least a portion of the plurality of qubits of the quantum computing component and that represents an expected value of the quantum operator acting on an eigenstate of the active space electronic Hamiltonian, and utilize the measurement value to generate a model of the 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.

[0090] According to yet another aspect, a method for simulating a chemical system using a hybrid quantum-classical computing system is provided. In one exemplary embodiment, the method includes obtaining an indication of the chemical system by a classical computing component of the hybrid quantum-classical computing system, and by the classical computing component, evaluating a selection metric based on one or more of (a) at least a portion of the atomic structure of the chemical system, (b) information about a quantum computing component of the hybrid quantum-classical computing system, or (c) user input, selecting a hybrid approximation based on one or more type selection criteria and the selection metric, providing, by the classical computing component, qubit constraint information regarding an active space electronic Hamiltonian for the chemical system 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 at least a portion of the quantum states 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 using, by the classical computing component, the measurement value and the hybrid approximation to generate a model of the chemical system representing 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.

[0091] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of active electrons of the chemical system, the number of active orbitals of the chemical system, or one or more symmetries of the chemical system.

[0092] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of qubits of the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

[0093] In one exemplary embodiment, the hybrid approximation is one of a second-order N-electron valence perturbation theory (NEVPT2) approximation or an AC0 approximation.

[0094] In one exemplary embodiment, a measurement value measured by a quantum computing component is determined based on a hybrid approximation.

[0095] In one exemplary embodiment, the measurement value comprises at least one of an expected value of an active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0096] 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 comprises a classical computing component and a quantum computing component. The hybrid quantum-classical computing system uses the classical computing component to obtain an indication of the chemical system and evaluates a selection metric based on one or more of (a) at least a portion of the atomic structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input, selects a hybrid approximation based on one or more type selection criteria and the selection metric, provides quantum bit constraint information regarding an active space electronic Hamiltonian for the chemical system to the quantum computing component of the hybrid quantum-classical computing system, receives 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 quantum bits 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 utilizes the measurement value and the hybrid approximation to generate a model of the chemical system representing at least one of a structural characteristic of the chemical system, a chemical interaction characteristic of the chemical system, or a reaction characteristic.

[0097] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of active electrons in the chemical system, the number of active orbitals in the chemical system, or one or more symmetries of the chemical system.

[0098] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on the number of qubits in the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

[0099] In one exemplary embodiment, the hybrid approximation is one of a quadratic N-electron valence state perturbation theory (NEVPT2) approximation or an AC0 approximation.

[0100] In one exemplary embodiment, the measurement value measured by the quantum computing component is determined based on the hybrid approximation.

[0101] In one exemplary embodiment, the measurement value comprises at least one of an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

[0102] According to another aspect, there is provided a machine-readable data storage medium comprising 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 obtain chemical labels of a chemical system, and to evaluate a selection metric based on one or more of (a) at least a portion of the atomic structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input, select a hybrid approximation based on one or more type selection criteria and the selection metric, provide qubit constraint information regarding the active space electronic Hamiltonian for the chemical system to the quantum computing component of the hybrid quantum-classical computing system, receive 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 an expected value of a quantum operator acting on an eigenstate of the active space electronic Hamiltonian, and utilize the measurement value and the hybrid approximation to generate a model of the chemical system representing at least one of the structural characteristics, chemical interaction characteristics, or reaction characteristics of the chemical system.

[0103] The present invention has been described in general terms, and reference is now made to the accompanying drawings, which are not necessarily drawn to scale. BRIEF DESCRIPTION OF THE DRAWINGS

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DETAILED DESCRIPTION OF THE INVENTION

[0105] Reference will now be made in detail to the accompanying drawings, which show, by way of illustration, some, but not all embodiments of the present invention. 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 its alternative and conjunctive sense, unless otherwise indicated. The terms "exemplary" and "exemplifying" are used as examples without indicating a quality level. The terms "generally", "substantially", and "approximately" refer, unless otherwise indicated, within manufacturing and / or production tolerances, and / or within the measurement capabilities of the user. Throughout, like numbers refer to like elements.

[0106] Various embodiments provide a method, system, apparatus, computer program product, etc. for simulating a chemical system. Exemplary embodiments provide a method, system, apparatus, computer program product, etc. for simulating a chemical system that 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 generating 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.

[0107] 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, an approximation to the electronic state of a chemical system is identified and / or determined, and in particular molecular orbitals are generated, by Hartree-Fock theory, such that, for example, the wavefunction of an electron is defined by a single Slater determinant. In various systems, a more accurate approximation may be constructed such that the orbitals can be rotated and partitioned 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.

[0108] In various embodiments, based on the structural and / or interaction characteristics of a chemical system being investigated, evaluated, modeled, etc., the orbitals can be divided into active and inactive orbitals. For example, an active space is defined that comprises and / or consists of two or more active orbitals, and an inactive space is defined that comprises and / or consists of one or more inactive orbitals. One or more inactive orbitals include core orbitals and virtual orbitals.

[0109] 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 the 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 operators in the Hilbert space of a chemical system and / or 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 operators in the Hilbert space of the qubits of the quantum computing component.

[0110] In one exemplary embodiment, using quantum computing components, qubit constraint information is processed to determine and / or generate a qubit representation of the properties 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 wavefunctions) and / or expectation values of the active space electronic Hamiltonian. In one exemplary embodiment, the prepared state of the qubit provides a qubit representation of the properties 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 properties 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.

[0111] The qubit representation of the properties of the eigenstates of the active space Hamiltonian is then replaced with a classical representation of the properties of the eigenstates of the active space Hamiltonian. For example, a measurement value corresponding to the properties of the eigenstates of the active space Hamiltonian is determined based on the results of the measurement operation performed on the qubits.

[0112] For example, then, classically determining an approximation of the properties 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 properties of a chemical system, etc., the classical representation of the properties of the eigenstates of the active space Hamiltonian is utilized.

[0113] 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 state of quantum particles (referred to as qubits) to perform computations.

[0114] In various embodiments, prior to generating a model, a chemical system is evaluated to determine whether the chemical system is a good candidate for using a hybrid quantum-classical approximation to generate a model of the chemical system. For example, in one exemplary embodiment, a class selection metric is evaluated by a classical computing component to determine whether the class selection metric meets one or more class selection criteria. For example, whether the class selection metric meets the class selection criteria is used by the classical computing component to determine which class of approximation (e.g., hybrid approximation or classical approximation) to use when generating a model of the chemical system. In various embodiments, when the class selection metric does not meet the class selection criteria, a notification is provided and / or a model of the chemical system is generated using a classical approximation. In various embodiments, when the class selection metric meets the class selection criteria, a model of the chemical system is generated using a hybrid approximation. For example, in various embodiments, when a multi-reference diagnostic number corresponding to the chemical system (but not limited to, such as T1 diagnosis, or D1 diagnosis) meets (e.g., is greater than or equal to) a threshold of the class selection criteria, it is determined that the class selection metric meets one or more class selection criteria and a hybrid approximation is used to generate a model of the chemical system. In another example, in various embodiments, when a multi-reference diagnostic number corresponding to the chemical system does not meet (i.e., is less than) a threshold of the class selection criteria, it is determined that the class selection metric does not meet one or more class selection criteria and a hybrid approximation is not used to generate a model of the chemical system.

[0115] In various embodiments, the type of hybrid approximation used is selected based on an evaluation of type selection metrics and type selection criteria. For example, in various embodiments, the type selection metrics are determined based on one or more of at least a portion of the atomic structure of a chemical system, information about the quantum computing component of a hybrid quantum-classical computing system, user input, and the like. For example, a hybrid quantum-classical computing system may be configured to generate a model of a chemical system using two or more hybrid approximations. The classical computing component of the hybrid quantum-classical computing system may select which of the two or more hybrid approximations to use to generate a model of the chemical system based on comparing the type selection metrics to the type selection criteria. In one exemplary embodiment, the two or more hybrid approximations include second-order N-electron valence state perturbation theory (NEVPT2) and / or AC (AC0) with a first-order expansion of the adiabatic connection (AC) integrand at a coupling constant equal to zero.

[0116] Conventional classical computer software products are known that can be executed on classical computing hardware, such as classical non-quantum computing components, to simulate a chemical module and determine the manner of interaction with other molecules. Such computer software products are configured to calculate the properties of the electronic state of a given atom, molecule, or solid, where the electronic state is represented as a single-electron configuration (Slater determinant) as a first category of calculation, and the computer software product is then configured to calculate the properties of the electronic state, where these states are represented as electron configurations (Slater determinants) obtained by exciting (promoting) one or more electrons from occupied electronic states to unoccupied electronic states as a second category of calculation.

[0117] The practical and existing technical problem encountered in practice is that the computing resources required to implement the calculations of the second category 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 characteristics of atoms or molecules to account for and / or predict real-world observations of atoms or molecules and / or their interactions.

[0118] Quantum computing components are expected to provide a system that can perform complex calculations with low memory requirements within 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 is a further technical problem that currently operating quantum computing components do not even provide sufficient computing resources to perform a simulation of a complete chemical system or even a simulation of the excited state of a chemical system.

[0119] 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 occupancy 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 significant 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 inactive 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.

[0120] Accordingly, by limiting the problems transmitted to the quantum component to the active orbitals, a more accurate determination of the structural and / or interaction properties 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 properties of the eigenstates of the overall electronic Hamiltonian, the accuracy and efficiency of the model of the chemical system are further improved by using the quantum component to generate a qubit representation of the properties of the eigenstates of the active space Hamiltonian. Accordingly, various embodiments provide an improvement in the technical field of chemical system simulations by providing computationally tractable and more accurate simulations of the structural properties, interaction properties, and / or reaction properties of the chemical system.

[0121] 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 properties of the eigenstates of the active space electronic Hamiltonian of the chemical system. A measurement operation is performed such that at least the one-particle reduced density matrix, two-particle reduced density matrix, and 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, the 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 at least one additional RDM and / or an approximation of NEVPT2 or AC0 energy 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.

[0122] In addition, in various embodiments, prior to using quantum computing resources, a check is performed to determine whether the chemical system is a good candidate for the determination of a hybrid quantum-classical approximation model. For example, a class selection metric is determined based on the structural properties of the chemical system and compared to class selection criteria to determine whether the chemical system is a good candidate for the determination of a hybrid quantum-classical approximation model. For example, when the class selection metric meets the class selection criteria, using a quantum computing component in the determination of the chemical system's model is expected to result in more accurate and / or computationally efficient results. When the class selection metric does not meet the class selection criteria, using a quantum computing component in the determination of the chemical system's model is not expected to be beneficial, so quantum computing resources may not be used to determine the chemical system's model. This provides the advantage of ensuring that (limited) quantum computing resources (e.g., the quantum computing component of a hybrid quantum-classical computing system) are used efficiently and effectively, improving the performance of the hybrid quantum-classical computing system.

[0123] Moreover, in various embodiments, the hybrid quantum-classical computing system is configured to select a hybrid approximation to be used in generating a model of a chemical system. For example, the hybrid quantum-classical computing system is configured to use two or more hybrid approximations in generating a model of a chemical system. The classical computing component may evaluate a type selection metric and compare the type selection metric to an approximation selection criterion to select a hybrid approximation to be used in generating a model of the chemical system. In various embodiments, the type selection metric is determined based on one or more of at least a portion of the atomic structure of the chemical system, information about the quantum computing component of the hybrid quantum-classical computing system, user input, etc. Thus, a hybrid approximation that efficiently and effectively uses (limited) quantum computing resources (e.g., the quantum computing component of the hybrid quantum-classical computing system) may be selected for use. This feature of various embodiments results in an improvement in the performance of the hybrid quantum-classical computing system and an improvement in the user experience.

[0124] 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 a classical computing component 110 and quantum components such as a quantum computing component 130.

[0125] The quantum computing component 130 includes a controller 132, qubits 134, qubit operation elements 136, and sensors 138. The controller 132 is configured to control the operation of the qubit operation elements 136 to cause a desired operation of the qubits 134 (e.g., the evolution of a controlled quantum state). The controller 132 is further configured to control the operation of the sensors 138, which are configured to monitor, measure, and / or acquire measurement results corresponding to the operation of the qubit operation components and acquire measurement results indicating the respective quantum states of the respective qubits 134.

[0126] For example, in various embodiments, the qubit operation elements 136 include 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 to be used in confining qubits and / or manipulating the quantum states of qubits. For example, in various embodiments, the sensors 138 include 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 the operation of one or more of the qubit operation elements 136.

[0127] 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 is configured to receive 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 is configured to receive qubit constraint information provided by classical computing component 110, and 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, 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.

[0128] 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.

[0129] FIG. 2 provides a flowchart of various processes, procedures, operations, etc. performed by the classical computing component 110, for example, to generate and provide a model of a chemical system. In various embodiments, starting from step / operation 202, the classical computing component 110 obtains information corresponding to, indicative of, and / or specifying the chemical system. For example, user input (e.g., received via the 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.

[0130] 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 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. 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 measurements based on the qubit representation of the properties of the active orbitals. For example, in various embodiments, the one or more measurements 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 measurements represent the expected value of a quantum operator acting on the eigenstate of the active space electronic Hamiltonian.

[0131] 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) can accurately determine measurements. 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 measurements and determined values to determine the structural, interaction, and / or other properties of the chemical system. For example, the classical computing component may determine an approximation of the properties 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 properties of the chemical system, and the like, using the measurements and determined values.

[0132] However, considering the limitations of currently operating quantum computing components, using a hybrid approximation when determining and / or generating a chemical system model does not always result in advantages in terms of the accuracy of the results and / or the use of computational resources. For example, currently operating quantum computing components may not have a sufficient number of qubits to use a hybrid approximation to generate and / or determine a model of a chemical system having a large number of active orbitals and / or a large number of electrons that can occupy the active orbitals. Thus, in various embodiments, a determination is made as to which class of approximation to use to generate the model. In various embodiments, the class of approximation configured and / or programmed to be performed by a hybrid quantum-classical computing component includes a hybrid approximation and, in some embodiments, a classical approximation. In various embodiments, the hybrid approximation utilizes one or more measurements generated through the operation of the quantum computing component of the hybrid quantum-classical computing system, and the classical approximation is performed by the classical computing component without any other value inputs determined based on the measurements or the operation of the quantum computing component.

[0133] For example, in various embodiments, in step / operation 204, the classical computing component 110 evaluates and / or determines a class selection metric for a chemical system. In various embodiments, the class selection metric is evaluated and / or determined based at least in part on the structure and / or properties of the chemical system. For example, the class selection metric is determined based on the relative positions of one or more nuclei of the chemical system, the number of electrons of the chemical system, the symmetry of the chemical system, and the like.

[0134] In various embodiments, evaluating a class selection metric comprises performing a multi-reference diagnosis of a chemical system to determine a multi-reference diagnostic number corresponding to the chemical system. For example, in one exemplary embodiment, performing a multi-reference diagnosis of a chemical system comprises determining a classical approximation of the wavefunction of the chemical system and determining a degree or metric of electronic correlation (including, but not limited to, T1 diagnosis or D1 diagnosis, etc.) of the chemical system based at least in part on the classical approximation of the wavefunction.

[0135] In one exemplary embodiment, a class selection metric includes one or more of a multi-reference diagnostic number of a chemical system, a degree or metric of electronic correlation of the chemical system, a number of active orbitals of the chemical system, a number of active electrons of the chemical system, one or more symmetries of the chemical system, etc.

[0136] In step / operation 206, classical computing component 110 determines whether the class selection criteria are satisfied by the class selection metric. In one exemplary embodiment, the class selection criteria include one or more thresholds and / or ranges each related to a respective metric of the class selection metric. To determine whether the class selection criteria are satisfied by the class selection metric, each metric of the class selection metric is compared with the respective thresholds and / or ranges to determine whether the respective thresholds and / or ranges are satisfied by the respective metrics. For example, in one exemplary embodiment, if it is determined that the multi-reference diagnostic number and / or the strength of electronic correlation are each above their respective threshold strengths, it is determined that the class selection metric satisfies the class selection criteria. If it is determined that the multi-reference diagnostic number and / or the strength of electronic correlation are each below their respective threshold strengths, it is determined that the class selection metric does not satisfy the class selection criteria. For example, in one exemplary embodiment, the multi-reference diagnostic number is a T1 diagnosis and the respective threshold strength is 0.02. Various other multi-reference diagnostic numbers and their respective threshold strengths may be used in various other embodiments, as appropriate for this application.

[0137] In one exemplary embodiment, one or more class selection criteria comprise a single criterion (e.g., a single threshold or range requirement). In various embodiments, one or more class selection criteria include multiple criteria and / or use a combination of metrics (e.g., a function of the values of the class selection metrics) to determine whether one or more class selection criteria are satisfied by a class selection metric. In one exemplary embodiment, at least one of one or more class selection criteria (e.g., a threshold and / or its range) is determined and / or set based on one or more characteristics and / or functionalities of the quantum computing component 130 (e.g., the number of qubits, qubit connectivity, etc.).

[0138] In step / operation 206, if it is determined that one or more class selection metrics do not satisfy one or more class selection criteria, the process proceeds to step / operation 208. In various embodiments, in step / operation 208, the classical computing component 110 determines a model of the chemical system using classical approximation. For example, the classical computing component 110 may generate a model of the chemical system using one or more of coupled cluster singles and doubles (CCSD), coupled cluster singles doubles (triples) (CCSD(T)), second-order Moller-Plesset (MP2), or Perdew-Burke-Ernzerhof (PBE) methods.

[0139] In various embodiments, step / operation 208 may include, in addition to and / or instead of using classical approximation to generate a model of the chemical system, providing a notification that the chemical system is not a good candidate for using a hybrid approximation when determining a model for the chemical system. For example, the notification may be provided through a user output device (e.g., a display or speaker) of the classical computing component 110 or through a communication interface (e.g., email, text message, voicemail, push notification, etc.) of the classical computing component 110. For example, the notification is configured to notify the user that the chemical system is not a good candidate for using a hybrid approximation when determining a model for the chemical system. In one exemplary embodiment, the notification is configured to notify the user that the chemical system is not a good candidate for using a hybrid approximation when determining a model for the chemical system using the available quantum computing component 130 of the hybrid quantum-classical computing system.

[0140] In step / operation 206, when it is determined that one or more class selection metrics satisfy one or more class selection criteria, the process proceeds to step / operation 210. In step / operation 210, the classical computing component 110 evaluates and / or determines a type selection metric. In various embodiments, the type selection metric is evaluated and / or determined based on one or more of at least a portion of the structure of the chemical system, information about the quantum computing component of the hybrid quantum-classical computing system, user input, and the like.

[0141] For example, in various embodiments, the second selection criterion is evaluated based at least in part on the number of active electrons of the chemical system, the number of active orbitals of the chemical system, or one or more symmetries of the chemical system.

[0142] In one exemplary embodiment, the second selection criterion is evaluated based at least in part on, for example, the number of qubits of the quantum computing component 130, the available runtime of the quantum computing component 130, the noise profile of one or more functions of the quantum computing component 130, and the like.

[0143] In various embodiments, the type selection metric is determined based on user input (e.g., received via a user input device of the classical computing component 110). For example, the user may provide input indicating that a particular hybrid approximation should be used, such as to generate a model of a chemical system or to provide a preference ranking of available hybrid approximations (e.g., indicating which user preference of hybrid approximations should be used if the hybrid approximation is appropriate and / or available).

[0144] In various embodiments, at least a portion of the type selection metric is evaluated and / or determined as part of the evaluation and / or determination of the class selection metric.

[0145] In step / operation 212, the classical computing component 110 selects a hybrid approximation based on the type selection criteria and the type selection metric. For example, the type selection criteria, when evaluated based on the type selection metric, provides a set of logic that selects and / or provides a selection of a hybrid approximation from among groups of two or more hybrid approximations that the hybrid quantum-classical computing system 100 is configured and / or programmed to implement. For example, in one exemplary embodiment, the hybrid quantum-classical computing system 100 is configured and / or programmed to generate a model of a chemical system using each selected one of NEVPT2, AC0, and / or one or more other hybrid approximations.

[0146] In one exemplary embodiment, the type selection criterion is configured to cause a selection of a hybrid approximation indicated by a second selection metric corresponding to user input indicating a hybrid approximation. In another exemplary embodiment, the type selection criterion is based on an expected amount of computational resources required to generate a measurement (e.g., through operation of the quantum computing component 130) for use in generating a model using the hybrid approximation and the availability of computational resources of the quantum computing component 130, and is configured to cause a selection of the hybrid approximation. For example, the classical computing component 110 may evaluate one or more functions based on the value of the type selection metric and use the obtained values of the one or more functions to select a hybrid approximation.

[0147] When the classical computing component 110 selects a hybrid approximation, the hybrid quantum-classical computing system 100 begins to generate a model of the chemical system using the selected hybrid approximation.

[0148] In step / operation 214, the classical computing component 110 generates qubit constraint information for the chemical system. In various embodiments, the qubit constraint information provides information necessary to generate a quantum circuit or program encoding information regarding the active space of the chemical system. For example, in various embodiments, the qubit constraint information provides information necessary to generate a quantum circuit or program encoding the active space electronic Hamiltonian. For example, in various embodiments, the qubit constraint information includes a replaced version of the active space electronic Hamiltonian defined within the space of two or more active orbitals in the qubit basis of the quantum computing component 130. FIG. 3 shows an exemplary process, procedure, and / or operation for generating qubit constraint information according to various embodiments.

[0149] In various embodiments, the qubit constraint information is generated and / or determined in a manner appropriate to the selected hybrid approximation and / or quantum computing component 130. For example, the qubit constraint information provides to the quantum computing component 130 the measurement results of measurements and / or qubits that result in the determination of measurements used by the selected hybrid approximation to generate a model of the chemical system, as well as the information necessary for the quantum computing component 130 to implement a quantum circuit and / or program. In various embodiments, the qubit constraint information provides the measurement results of measurements and / or qubits that result in the determination of measurements used by the selected hybrid approximation to generate a model of the chemical system in a basis appropriate for the qubits of the quantum computing component 130, as well as the information necessary for the quantum computing component 130 to implement a quantum circuit and / or program.

[0150] In various embodiments, generating the qubit constraint information includes determining a first-level approximation of the energy and / or wavefunction of the orbitals (and / or active space orbitals) of the chemical system. In one exemplary embodiment, at least a portion of the information used to generate the qubit constraint information is determined in step / operation 204 (e.g., evaluation of the class selection metric) and / or step / operation 210 (e.g., evaluation of the type selection metric). In various embodiments, generating the qubit constraint information includes converting and / or replacing information corresponding to the first-level approximation of the orbital energy and / or wavefunction to a qubit basis corresponding to the qubits of the quantum computing component 130.

[0151] In step / operation 216, the classical computing component 110 provides the qubit constraint information to the quantum computing component. For example, the classical computing component 110 may 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.

[0152] As detailed with respect to FIG. 4, 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 performance 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.

[0153] Subsequently, various measurements may be performed on the qubit representation to generate measurements corresponding to the active orbitals. For example, the measurement operation may be performed on a plurality of qubits 134 of the quantum computing component 130, and a measurement 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 measurements include, 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 measurements and / or the measurements determined are determined based on a selected hybrid approximation. In various embodiments, the measurements 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 measurements are measured and / or determined from the qubit measurement results using the operator averaging method using a measurement reduction technique.

[0154] 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 orbitals 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 orbitals 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 the simulation of the chemical system.

[0155] In step / operation 218, 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 an 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.

[0156] In various embodiments, the measurement values received by the classical computing component 110 include an 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, two-particle RDM, three-particle RDM, and four-particle RDM, etc. In one exemplary embodiment, the measurement values include a spinless (i.e., spin-traced) 1-RDM and 2-RDM. 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.

[0157] In step / operation 220, classical computing component 110 uses the selected hybrid approximation and measurements to generate a model of the chemical system. For example, classical computing component 110 uses the selected hybrid approximation and measurements to generate a model of the chemical system 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.

[0158] In various embodiments, classical computing component 110 determines a determinant value corresponding to an orbital. For example, in various embodiments, classical computing component 110 can determine various determinant values corresponding to inactive orbitals (e.g., core orbitals and / or virtual orbitals) and / or 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 core orbitals of the chemical system. For example, in various embodiments, classical computing component 110 can use various methods such as MR-MBPT, NEVPT2, AC0, quadratic complete active space perturbation theory (CASPT2), MR-CC, MR-CI, etc. to determine one or more determinant values corresponding to the spatial distribution and / or energy of one or more inactive orbitals (e.g., core orbitals and / or virtual orbitals).

[0159] In various embodiments, classical computing component 110 may determine a four-particle reduced density matrix (4-RDM). For example, based on quantum computing component 130 and / or the properties of the chemical system, quantum computing component 130 may not have sufficient computational resources to enable measurement of the 4-RDM for an active space defined by two or more active orbitals. In such cases, classical computing component 110 may determine the 4-RDM using, for example, cumulant expansion techniques. For example, in various embodiments, the 4-RDM is determined and / or approximated using a spinless cumulant expansion based at least in part on the 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 the chemical system. In various embodiments, the selected hybrid approximation may require only the 1-RDM and 2-RDM, and in such embodiments, the measurements and / or determined values may include the 1-RDM and 2-RDM but may not include the 3-RDM and / or 4-RDM. For example, the determined values determined by classical computing component 110 may be determined and / or controlled by the selected hybrid approximation and the information required by the selected hybrid approximation to generate a model of the chemical system.

[0160] Based on the selected hybrid approximation, classical computing component 110 utilizes (quantumly) measured values and (classically) determined values to generate a model of a 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 a 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.

[0161] In one exemplary embodiment, hybrid quantum-classical computing system 100 is configured and / or programmed to generate a model of a chemical system using a strongly contracted NEVPT2 calculation. For example, in one exemplary embodiment, the selected hybrid approximation is selected from a group of hybrid approximations that includes a strongly contracted NEVPT2 approximation. 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 214. In one exemplary embodiment, a spinless formulation of the strongly contracted NEVPT2 technique is used with measured values (e.g., the expected value of the active space electronic Hamiltonian, 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM) to determine corrections to the approximate energies and / or wavefunctions of the orbitals determined and / or identified in step / operation 214. 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.

[0162] In one exemplary embodiment, the hybrid quantum-classical computing system 100 is configured and / or programmed to generate a model of a chemical system using an AC technique (AC0) involving a first-order expansion of an adiabatic connection (AC) integrand at a coupling constant equal to 0. For example, in one exemplary embodiment, a selected hybrid approximation is selected from a group of hybrid approximations that includes the AC0 approximation. For example, the classical computing component 110 may use determined values and measured values to perform an AC0 calculation to determine corrections to the energy and / or wave function of the orbitals determined and / or specified in step / operation 214. In one exemplary embodiment, the AC0 technique is used to determine corrections to the approximate energy and / or wave function of the orbitals determined and / or specified in step / operation 214 using measured values (e.g., the expected value of the active space electronic Hamiltonian, the 1-RDM, and / or the 2-RDM). The corrections may then be applied to the energy and / or wave function of the orbitals to generate a model of the chemical system that represents structural characteristics of the chemical system, chemical interaction characteristics of the chemical system, reaction characteristics of the chemical system, and the like.

[0163] In various embodiments, the structural characteristics of a chemical system characterize and / or provide information about the structure of the chemical system. For example, the structural characteristics 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 characteristics of the various bonds in the chemical system, the relative nuclear positions in the chemical system, and the like.

[0164] In various embodiments, the chemical interaction characteristics of a chemical system characterize and / or provide information about 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 the chemical system may provide information about 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.

[0165] For example, the structural properties and / or chemical interaction properties can be a dissociation curve, binding energy, reaction energy, reaction barrier, binding energy, absorption energy, and the like.

[0166] In various embodiments, the reaction properties of a chemical system characterize and / or provide information regarding how the chemical system interacts with electromagnetic radiation. For example, the reaction properties of a chemical system can be an excitation energy, singlet-triplet gap, photodissociation energy, photoionization energy, absorption cross section, permittivity, dielectric function, oscillator strength, and the like.

[0167] In step / operation 222, the classical computing component 110 provides at least a portion of a model of the chemical system that represents the structural properties, chemical interaction properties, and / or reaction properties 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, and the like, a call response (e.g., an application program interface (API) call response).

[0168] For example, in one exemplary embodiment, the classical computing component 110 causes a display (e.g., the display 616 shown in FIG. 6 and / or another display) to display a representation of the model of the chemical system. For example, the graphics processing unit (GPU) of the classical computing component 110 can generate a graphical representation of at least a portion of the model of the chemical system that provides, for example, a 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 model of the chemical system to be displayed via the display for review and / or browsing by a human user.

[0169] In another example, the classical computing component 110 may generate and store (e.g., in memories 622, 624) a file comprising at least a portion of a chemical model. For example, the file may comprise modified energies and / or wave functions of chemical orbits, structural properties, chemical interaction properties, reaction properties, chemical formulas, etc. of the chemical system. The file may 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 model may be used by various programs, applications, modules, etc. to generate a graphical representation and / or visualization and / or a portion thereof of the chemical system, perform a simulation including chemical interactions of the chemical system with one or more other chemical systems (same or different chemical formulas), perform a simulation of a bulk material including the chemical system, perform a simulation including chemical interactions of the chemical system with one or more biological systems, etc.

[0170] FIG. 3 provides a flowchart showing various processes, procedures, operations, etc. performed by the classical computing component 110 to perform classical preprocessing to generate qubit constraint information. For example, in various embodiments, the classical computing component 110 may perform the steps, processes, procedures, operations, etc. shown in FIG. 3 to generate qubit constraint information. For example, in various embodiments, the processes, procedures, operations, etc. shown in FIG. 3 may be performed as part of step / operation 214.

[0171] Starting at step / operation 302 of FIG. 3, classical computing component 110 determines and / or specifies an approximation to the electronic state of a chemical system. The approximation to the electronic state of a chemical system is determined and / or specified 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 approximations of 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 a chemical system.

[0172] For example, in various embodiments, classical computing component 110 performs a first level of simulation of a chemical system to specify and / or determine an approximation to the orbitals of the chemical system. For example, classical computing component 110 uses a mean-field approximation method such as Hartree-Fock theory, where the wave function of an electron is defined by a single Slater determinant, to generate, among other things, molecular orbitals. In various embodiments, 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 wave function 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 appreciated by those skilled in the art, the generated and / or determined approximations to the wave function and energy are first approximations that are not accurate enough to provide a valid model of the chemical system alone.

[0173] In various embodiments, the performance of step / operation 302 is performed as part of evaluating and / or determining a class selection metric in step / operation 204 and / or evaluating and / or determining a type selection metric in step / operation 210. In such embodiments, information regarding the orbitals of a chemical system can be accessed from memory (e.g., cache) during the generation of quantum bit constraint information.

[0174] In step / operation 304, classical computing component 110 may transform each orbital of the chemical system. For example, classical computing component 110 may determine the localization of each orbital. For example, a wave function 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 of 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 wave function to a desired coordinate system and the like.

[0175] In step / operation 306, classical computing component 110 classifies the orbitals of the chemical system into active orbitals and inactive orbitals (including, for example, inner shell orbitals, virtual orbitals, etc.). For example, classical computing component 110 may process the associated generated and / or determined wave functions and / or energies and then identify and / or select the active orbitals.

[0176] 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 scheme 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.

[0177] In various embodiments, an inner shell orbital is an orbital of the chemical system that is occupied by two electrons in a reference mean field (Hartree-Fock) wave function and is not selected as an active orbital, for example, because its interaction with other active orbitals can be ignored. In various embodiments, a virtual orbital comprises an orbital that is not occupied in a reference mean field (Hartree-Fock) wave function and is not selected as an active orbital.

[0178] In various embodiments, the active orbitals are identified and / or selected based on user input (e.g., received via a 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 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 302 (e.g., a reference Hartree - Fock wavefunction of the chemical system), and the selection of unoccupied orbitals in an approximation to an electronic state determined as part of step / operation 302.

[0179] In various embodiments, two or more orbitals are selected and / or identified as active orbitals. For example, an active space is defined based on two or more active orbitals. In various embodiments, two to six orbitals are selected and / or identified as active orbitals. In various embodiments, up to 100 orbitals are selected and / or identified as active orbitals. In various embodiments, the number and / or maximum number of orbitals selected and / or identified as active orbitals is determined based on the number of qubits 134 of the quantum computing component 130 of the hybrid quantum - classical computing system 100.

[0180] In one exemplary embodiment, the partitioning of 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 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).

[0181] In step / operation 308, 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 energies and / or wave functions of electrons in the active orbitals. For example, in one exemplary embodiment, the fermionic constraint information comprises an operator configured to operate on the wave functions corresponding to the active orbitals to provide energy information corresponding to the active orbitals and / or a wave function upon which an operator has acted. 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.

[0182] 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 wave function is represented as a linear combination of all or a subset of the configurations obtained by exciting electrons within the active space, where the core orbitals remain fully occupied and the virtual orbitals remain empty. For example, for a chemical system having two active orbitals |A> and |B>, the wave function is represented in the form a|A> + b|B>, where |a 2 + b 2 | = 1.

[0183] In one exemplary embodiment, since the fermionic constraint information is determined using the multi-configuration self-consistent field (MC-SCF) technique, the wavefunction is represented as a linear combination of all or a selected subset of the configurations obtained by exciting electrons within the active space, where the core orbitals remain fully occupied and the virtual orbitals are optimized to minimize the active space configuration interaction (CI) energy.

[0184] 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 wavefunction. For example, in one exemplary embodiment, the fermionic constraint information is determined using a multi-reference configuration interaction (MR-CI) technique such that the wavefunction has a linear combination of electronic configurations constructed by applying excitation operators to the AS wavefunction.

[0185] 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.

[0186] In one exemplary embodiment, the second-order N-electron valence 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 to determine the configurations for inclusion and / or use in the wavefunction of the electrons that are at least partially included and / or used to determine the fermionic constraint information by applying excitation operators.

[0187] In one exemplary embodiment, multi-reference coupled cluster theory (MR-CC) is used to determine the fermionic constraint information.

[0188] In one exemplary embodiment, to determine fermionic constraint information, an AC technique (AC0) involving a first-order expansion of an adiabatic connection (AC) integrand at a coupling constant equal to zero is used.

[0189] In various embodiments, determining 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 active orbitals, determined two-electron integrals, and nuclear repulsion energy for the chemical system, which are determined as part of steps / operations 302 and 304 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.

[0190] In step / operation 310, 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 using ion trap qubits is different from the qubit basis for a quantum computing component 130 using Josephson junction qubits.

[0191] 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 encoding spatial and energy constraints of the active space electronic Hamiltonian. For example, classical computing component 110 replaces, maps, and / or converts fermionic constraint information regarding the active space electronic Hamiltonian to a qubit basis to generate qubit constraint information regarding the active space electronic Hamiltonian.

[0192] 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 fermionic constraint information into qubit constraint information comprises replacing or mapping fermionic operators of the active space electronic Hamiltonian of the fermionic constraint information to 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 converting fermionic constraint information into qubit constraint information.

[0193] 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 a 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.

[0194] FIG. 4 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 that represents structural properties of the chemical system, chemical interaction properties of the chemical system, reaction properties of the chemical system, and the like. In various embodiments, steps / operations 402-412 are performed during the performance of steps / operations 216 and 218.

[0195] Starting at step / operation 402, 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 a 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 orbits in the qubit basis of the quantum computing component 130.

[0196] In various embodiments, the controller 132 receives qubit constraint information via a communication interface 520 (see FIG. 5). For example, the classical computing component 110 may provide qubit constraint information so that the quantum computing component 130 receives the qubit constraint information.

[0197] In step / operation 404, the controller 132 of the quantum computing component generates and / or determines an executable queue of commands for performing state preparation of a plurality of qubits 134 based on the 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 orbit after 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 implementation of the quantum circuit and / or algorithm. For example, the occupancy of N active orbits (fermion modes) is mapped to N (or a number close to N) qubits 134 via the quantum circuit and / or algorithm.

[0198] For example, a quantum circuit and / or an algorithm may include an ordered combination of single-qubit gates and multi-qubit gates performed on a particular qubit 134 such that the quantum state of the qubit represents the wave function and / or energy of an active orbital of a chemical system and / or represents an eigenstate of an 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 may be used.

[0199] In various embodiments, measurement reduction techniques are used to reduce the number of measurements required and to partition the quantum circuit and / or algorithm into exchange sets.

[0200] Continuing with FIG. 4, in step / operation 406, 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 manipulation element 136 to perform an ordered combination of single-qubit gates and two or more qubit gates to cause the quantum state of the qubit 134 to represent the wave function and / or energy of an active orbital of a chemical system and / or an eigenstate of an active space electronic Hamiltonian.

[0201] In step / operation 408, 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 manipulation element 136 and monitors the signal received from the sensor 138 to determine the respective quantum states of the qubits 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 do not need to be measured. For example, in one exemplary scenario, the number of active electrons equal to 2 causes the 3-RDM and 4-RDM to decay (e.g., be made substantially equal to 0). Thus, in such an example, computational resources can be saved by determining that the 3-RDM and 4-RDM do not need to 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., be made 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 do not need to be measured.

[0202] In various embodiments, the state preparation performed in step / operation 406 and the measurement operation performed in step / operation 408 are determined based on a selected hybrid approximation. For example, in one exemplary embodiment, when the selected hybrid approximation is NEVPT2, measurement results corresponding to one or more matrix elements of each of the 1-RDM, 2-RDM, 3-RDM, and / or 4-RDM are determined, and when the selected hybrid approximation is AC0, measurement results corresponding to one or more matrix elements of each of the 1-RDM, 2-RDM (but not corresponding to matrix elements corresponding to the 3-RDM and / or 4-RDM) are determined.

[0203] In step / operation 410, 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 values include 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 states of at least a portion of the plurality of quantum bits of the quantum computing component 130 and / or represents the expected value of a quantum operator acting on the eigenstates of the active space electronic Hamiltonian. In various embodiments, the measurement value is measured and / or determined from the quantum bit measurement results 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 results using an operator averaging method using a measurement reduction technique.

[0204] In step / operation 412, the controller 132 causes the quantum computing component 130 to provide the measurement value (e.g., via the communication interface 520). 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.

[0205] As shown in FIG. 4, 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 a measurement value based on the result of the measurement operation.

[0206] Technical Advantages Conventional classical computer software products are known that can be executed on classical computing hardware, for example, 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 where the wave function of an electron is defined by a single Slater determinant, or by density functional theory where 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.

[0207] A real 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 be 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.

[0208] 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 additional technical problems in that currently operating quantum computing components do not even provide sufficient computational resources to perform simulations of complete chemical systems or just simulations of the excited states of chemical systems.

[0209] 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 a large coefficient in the configuration interaction expansion. Usually, the electronic structure of such systems is generally considered to have all orbits active, and is modeled by the full configuration interaction method, which includes all Slater determinants obtained by the excitation of electrons to virtual orbits, or by the multi-reference method, where a subset of orbits and electrons is considered active and the multi-configuration reference wave function is constructed as a linear combination of Slater determinants obtained by all possible occupations of active electrons in the 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-configuration reference wave function is further improved by the application of multi-reference configuration interaction, multi-reference perturbation theory, or multi-reference coupled cluster methods. Thus, 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 (with respect to the number of active electrons and active orbits), classical implementations of the multi-reference method 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, a hybrid quantum-classical implementation of the multi-reference method can be constructed by limiting the problem passed to the quantum component to active electrons and active orbits. Thus, instead of applying the computational power of the quantum computing component to the entire electronic structure problem, which consists of subproblems 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.

[0210] 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 a hybrid quantum-classical computing system that utilizes 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 aids 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 practical applications that provide the functionality of an improved computer system that results in improved modeling of chemical systems.

[0211] In addition, in various embodiments, prior to using quantum computing resources, a check is performed to determine whether the chemical system is a good candidate for the determination of a hybrid quantum-classical approximation model. For example, a class selection metric is determined based on the structural properties of the chemical system and compared to class selection criteria to determine whether the chemical system is a good candidate for the determination of a hybrid quantum-classical approximation model. For example, when the class selection metric meets the class selection criteria, the use of a quantum computing component in the determination of the model of the chemical system is expected to result in more accurate and / or computationally efficient results. When the class selection metric does not meet the class selection criteria, the use of a quantum computing component in the determination of the model of the chemical system is not expected to provide an advantage, so quantum computing resources may not be used to determine the model of the chemical system. This provides the advantage of ensuring that (limited) quantum computing resources (e.g., the quantum computing component of a hybrid quantum-classical computing system) are used efficiently and effectively, and as a result, improves the performance of the hybrid quantum-classical computing system.

[0212] Moreover, in various embodiments, the hybrid quantum-classical computing system is configured to select a hybrid approximation to be used in generating a model of a chemical system. For example, the hybrid quantum-classical computing system is configured to use two or more hybrid approximations in generating a model of a chemical system. The classical computing component may evaluate a type selection metric and compare the type selection metric to an approximation selection criterion to select a hybrid approximation to be used in generating a model of the chemical system. In various embodiments, the type selection metric is determined based on one or more of at least a portion of the atomic structure of the chemical system, information about the quantum computing component of the hybrid quantum-classical computing system, user input, etc. Thus, a hybrid approximation that efficiently and effectively uses (limited) quantum computing resources (e.g., the quantum computing component of the hybrid quantum-classical computing system) may be selected for use. This feature of various embodiments results in an improvement in the performance of the hybrid quantum-classical computing system and an improvement in the user experience.

[0213] 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 common 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. 7A and 7B provide a graphical representation of a model of a chemical system and its comparison with a previously determined Li2 dissociation curve. For example, FIG. 7A shows the deviation of the Li2 dissociation curve determined according to an exemplary embodiment from the conventional CAS-NEVPT2 results, and FIG. 7B 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. 7A and 7B, various embodiments provide the structural characteristics, chemical interaction characteristics, and / or reaction characteristics of a chemical system that are consistent with existing results for simple systems and achieve more efficient use of computational resources than conventional techniques.

[0214] Another exemplary embodiment is used to determine the dissociation curve of a dihydrogen molecule (H2). FIG. 8 shows three determined and / or generated H2 dissociation curves determined using the NEVPT2 hybrid approximation, the VQE-AC0 hybrid approximation, and the classical full configuration interaction (FCI) approximation. Various embodiments provide the advantage that a user can double-check a first hybrid approximation using a second (or additional) hybrid approximation for confirmation of model predictions. As shown in FIG. 8, various embodiments provide 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.

[0215] Exemplary controller In various embodiments, the hybrid quantum-classical computing system 100 comprises 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.

[0216] As shown in FIG. 5, in various embodiments, the controller 132 may include various controller elements, including a processing element 505, a memory 510, a driver controller element 515, a communication interface 520, an analog-to-digital converter element 525, and the like. For example, the processing element 505 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 505 of the controller 132 is a clock and / or communicates with a clock.

[0217] For example, the memory 510 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, etc. In various embodiments, the memory 510 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 components (e.g., in a qubit record data store, a qubit record database, a 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 505) causes the controller 132 to control the operation of one or more qubit manipulation elements 136, process sensor signals indicative of measurement results captured by the sensor 138, and / or communicate with the classical computing components 110 of the hybrid quantum-classical computing system 100 to perform one or more of the steps, operations, processes, procedures, etc. described herein.

[0218] In various embodiments, the driver controller element 510 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 510 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 operate in accordance with executable instructions, commands, etc. scheduled (e.g., by the processing element 505) and executed by the controller 132. In various embodiments, the driver controller element 515 may enable the controller 132 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 respective qubit operation elements 136 of the quantum computing component 130.

[0219] 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 525 configured to receive signals from one or more sensors.

[0220] In various embodiments, the controller 132 comprises a communication interface 520 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.

[0221] Exemplary classical computing component FIG. 6 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 input to the quantum computing component 130, receive, display, analyze, etc. the output from the quantum computing component 130.

[0222] As shown in FIG. 6, classical computing component 110 may include an antenna 612, a transmitter 604 (e.g., wireless), a receiver 606 (e.g., wireless), and a processing element 608 that respectively provide signals to and receive signals from a transmitter 604 and a receiver 606. The signals provided to and received from the transmitter 604 and the receiver 606 respectively may include signaling information / data according to the interface specifications of the applicable wireless system to communicate with various entities such as a controller 132 and other classical computing components 110. In this regard, classical computing component 110 may be capable of operating using one or more air interface specifications, communication protocols, modulation types, and access types.

[0223] For example, 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 can be configured to communicate via a wireless external communication network using any of various 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.Classical computing component 110 may use such protocols and specifications 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), etc.

[0224] Via these communication standards and protocols, the 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). The 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.

[0225] In various embodiments, the classical computing component 110 may comprise a network interface 620 for interfacing with and / or communicating with, for example, the controller 132. For example, the classical computing component 110 may provide qubit constraint information, executable instructions, instruction sets, etc. for reception by the controller 132, and / or may comprise a network interface 620 for receiving processed outputs and / or results of outputs (such as measurements corresponding to active orbits) provided by the quantum computing component 130. In various embodiments, the classical computing component 110 and the controller 132 may communicate directly via wired and / or wireless connections and / or via one or more wired and / or wireless networks 120.

[0226] In various embodiments, processing element 608 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.

[0227] The classical computing component 110 may also comprise a user interface device comprising one or more user input / output interfaces (e.g., a display 616 and / or a speaker / speaker driver coupled to the processing element 608, and a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 608). For example, the user output interface may be configured to provide an application, browser, user interface, interface, dashboard, screen, web page, page, and / or similar terms used herein that are interchangeably executed on the computing entity 10 and / or accessible via the computing entity 10 to cause the display or audible presentation of information / data and to interact therewith via one or more user input interfaces. 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 618 (hard or soft), a touch display, a mouse, a voice / utterance or motion interface, a scanner, a reader, or other input device. In embodiments including the keypad 618, the keypad 618 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, for example, to enable or disable certain functions such as a screen saver and / or a sleep mode. Through such input, the classical computing component 110 can collect information / data, user interaction / input, and the like.

[0228] The classical computing component 110 may also include a volatile storage or memory 622 and / or a non-volatile storage or memory 624, which may be integrated and / or removable. For example, the 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. The 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. The 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.

[0229] In any of the above aspects, various features may be implemented in hardware or as software modules executed on one or more processors / computers.

[0230] 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, for example, a downloadable data signal provided from an Internet website, or in any other form.

[0231] For 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 obtain chemical system labels by a classical computing component of the hybrid quantum-classical computing system, evaluate a class selection metric based at least in part on the structure of the chemical system by the classical computing component, determine whether the class selection metric meets one or more class selection criteria by the classical computing component, and in response to a determination that the class selection metric does not meet one or more class selection criteria, cause the classical computing component to perform at least one of (a) providing a notification that the class selection criteria are not met by the chemical system, or (b) performing a classical approximation to generate a model of the 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, and in response to a determination that the class selection metric meets one or more class selection criteria, cause the classical computing component to provide qubit constraint information regarding the active space electronic Hamiltonian for the chemical system to a quantum computing component 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 the quantum states 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 by the classical computing component, and utilize the measurement value to generate a model of the 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.

[0232] 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 obtain chemical system labels by a classical computing component of the hybrid quantum-classical computing system, and by the classical computing component, (a) at least a portion of the atomic structure of the chemical system, (b) information about a quantum computing component of the hybrid quantum-classical computing system, or (c) evaluate a selection metric based on one or more of user inputs, select a hybrid approximation based on one or more type selection criteria and the selection metric, provide quantum bit constraint information regarding an active space electronic Hamiltonian for the chemical system to the quantum computing component of the hybrid quantum-classical computing system by the classical computing component, receive, by the classical computing component, a measurement value corresponding to an expected value of a quantum operator acting on at least a portion of the quantum states of a plurality of quantum bits 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 utilize the measurement value and the hybrid approximation to generate a model of the chemical system representing 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.

[0233] Conclusion Many modifications and other embodiments of the invention described herein will come to mind to those skilled in the art to which the invention pertains, who will benefit from the teachings presented in the foregoing description and the related drawings. Therefore, it is to be understood that the invention is not to be limited to the specific embodiments disclosed, and that modifications and other embodiments are intended to be included within the scope of the appended claims. Specific terms are used herein, but they are used for the purpose of general description only and not for purposes of limitation.

Description of the Reference Numerals

[0234] 10 Computing Entity 100 Hybrid Quantum-Classical Computing System 110 Classical Computing Component 120 Wireless Network 130 Quantum Computing Component 132 Controller 134 Quantum Bit 136 Quantum Bit Operation Element 138 Sensor 505 Processing Element 510 Memory 515 Driver Controller Element 520 Communication Interface 525 Analog-to-Digital Converter 604 Transmitter 606 Receiver 608 Processing Element 612 Antenna 616 Display 618 Keypad 620 Network Interface 622 Volatile Memory 624 Non-Volatile Memory

Claims

1. A method for simulating a chemical system using a hybrid quantum-classical computing system, comprising: obtaining, by a classical computing component of the hybrid quantum-classical computing system, labels of the chemical system; evaluating, by the classical computing component, a class selection metric based at least in part on the structure of the chemical system; determining, by the classical computing component, whether the class selection metric meets one or more class selection criteria; in response to a determination that the class selection metric does not meet the one or more class selection criteria, performing, by the classical computing component, at least one of: (a) providing a notification that the class selection criteria are not met by the chemical system, or (b) performing a classical approximation to generate a model of the chemical system that represents at least one of the structural characteristics, chemical interaction characteristics, or reaction characteristics of the chemical system; in response to a determination that the class selection metric meets the one or more class selection criteria, providing, by the classical computing component, qubit constraint information regarding an active space electronic Hamiltonian for the chemical system 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 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 to generate a model of the chemical system that represents at least one of the structural characteristics, chemical interaction characteristics, or reaction characteristics of the chemical system A method comprising the above steps.

2. The step of evaluating the class selection metric comprises the step of performing a multi-reference diagnosis of the chemical system to determine a multi-reference diagnosis number corresponding to the chemical system, and the step of determining whether the class selection metric meets the one or more class selection criteria comprises the step of determining whether the multi-reference diagnosis number corresponding to the chemical system is greater than a threshold intensity. The method according to claim 1.

3. The step of performing the multi-reference diagnosis of the chemical system comprises the step of determining a classical approximation of the multi-reference wavefunction of the chemical system and the step of determining the degree of electronic correlation of the chemical system based at least in part on the classical approximation of the multi-reference wavefunction. The method according to claim 2.

4. The classical computing component further comprises the step of causing at least one of (a) displaying a graphical representation of at least a portion of the model of the chemical system, or (b) generating a file comprising one or more parameters of the model of the chemical system and storing it in classical memory. The method according to any one of claims 1 to 3.

5. In response to the determination that the one or more class selection criteria are met, the classical computing component evaluates a type selection metric based on one or more of (a) at least a portion of the structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input, and selecting a hybrid approximation based on one or more type selection criteria and the type selection metric, wherein the classical computing component uses the hybrid approximation to generate the model of the chemical system using the measurements. The method according to any one of claims 1 to 4 further comprises.

6. The second selection criterion is evaluated based at least in part on the number of active electrons of the chemical system, the number of active orbitals of the chemical system, or one or more symmetries of the chemical system. The method according to claim 5.

7. The method according to claim 5 or 6, wherein the second selection criterion is evaluated based at least in part on the number of qubits of the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

8. The method according to any one of claims 5 to 7, wherein the hybrid approximation is one of a second-order N-electron valence state perturbation theory (NEVPT2) approximation or an AC0 approximation.

9. The method according to any one of claims 5 to 8, wherein the measured value measured by the quantum computing component is determined based on the hybrid approximation.

10. The method according to any one of claims 1 to 9, wherein the measured value comprises at least one of an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

11. The method according to claim 10, 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).

12. The method further comprises a step of generating the qubit constraint information, and the step of generating the qubit constraint information comprises: a step of determining, by the classical computing component, fermion constraint information regarding an active space electron Hamiltonian defined in an active space of two or more active orbitals of the chemical system; a step of replacing, by the classical computing component, the fermion constraint information regarding the active space electron Hamiltonian with a qubit basis to generate qubit constraint information regarding the active space electron Hamiltonian The method according to any one of claims 1 to 11.

13. The method according to claim 12, wherein the fermion constraint information regarding the active space electron Hamiltonian defined in the active space of two or more active orbitals of the chemical system is implemented as part of evaluating the class selection metric.

14. a step of performing state preparation of a plurality of qubits by the quantum computing component based at least in part on the qubit constraint information regarding the active space electron Hamiltonian; performing one or more measurement operations to determine the measurement value based on the quantum states of at least a portion of the plurality of qubits by the quantum computing component The method according to any one of claims 1 to 13, further comprising.

15. A method for simulating a chemical system using a hybrid quantum-classical computing system, comprising: obtaining an indication of the chemical system by a classical computing component of the hybrid quantum-classical computing system; evaluating a selection metric by the classical computing component based on one or more of (a) at least a portion of the atomic structure of the chemical system, (b) information about the quantum computing component of the hybrid quantum-classical computing system, or (c) user input; selecting a hybrid approximation based on one or more type selection criteria and the selection metric; providing, by the classical computing component, qubit constraint information regarding an active space electronic Hamiltonian for the chemical system to the 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 the quantum states of at least a portion 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; utilizing the measurement value and the hybrid approximation to generate a model of the chemical system representing at least one of the structural characteristics of the chemical system, the chemical interaction characteristics of the chemical system, or the reaction characteristics by the classical computing component A method comprising.

16. The method according to claim 15, wherein the second selection criterion is evaluated based at least in part on the number of active electrons in the chemical system, the number of active orbitals in the chemical system, or one or more symmetries of the chemical system.

17. The method according to claim 15 or 16, wherein the second selection criterion is evaluated based at least in part on the number of qubits of the quantum computing component, the available runtime of the quantum computing component, or the noise profile of one or more functions of the quantum computing component.

18. The method according to any one of claims 15 to 17, wherein the hybrid approximation is one of a second-order N-electron valence state perturbation theory (NEVPT2) approximation or an AC0 approximation.

19. The method according to any one of claims 15 to 18, wherein the measured value measured by the quantum computing component is determined based on the hybrid approximation.

20. The method according to any one of claims 15 to 19, wherein the measured value comprises at least one of an expected value of the active space Hamiltonian or at least one of at least one reduced density matrix (RDM).

21. A classical computing component, and a quantum computing component comprising: A hybrid quantum-classical computing system configured to perform the method according to any one of claims 1 to 20.

22. 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 perform the method according to any one of claims 1 to 20.

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