Hybrid Quantum-Classical Computing System for Chemical Simulations Using a Chemical Knowledge State Preparation Strategy

Abstract

A chemical system is simulated using a hybrid quantum-classical computing system. The hybrid quantum-classical computing system comprises a classical computing component coupled to a quantum computing component. The hybrid quantum-classical computing system is configured to determine characterization parameters that describe the chemical system, where the characterization parameters are at least partially based on the chemical structure of the chemical system, generate an operator representation of the chemical system, including a single-electron excitation operator and a two-electron excitation operator, and reconfigure the order of appearance of the single-electron excitation operator and the two-electron excitation operator in the operator representation according to the characterization parameters. The simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation.

Description

Technical Field

[0001] Cross - reference to Related Applications This application claims the priority of U.S. Application No. 63 / 344,629, filed on May 22, 2022, the entire content of which is incorporated herein by reference.

[0002] The present disclosure relates to a computing system for simulating chemical systems and a method for using such a computing system to simulate chemical systems. Exemplary embodiments relate to the use of a hybrid quantum - classical computing system for simulating chemical systems.

Background Art

[0003] Without limitation, atoms, molecules, ions, periodic solids, periodic surface slabs, an assembly of one or more atoms, molecules, and / or ions, or combinations thereof, consist of one or more atomic nuclei and at least one electron. The quantum state of the at least one electron is represented by an electron wave function, which is conveniently made from molecular (or crystal) orbitals and represented as a linear combination of Slater determinants.

[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, for example, substantially and rapidly. 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.

Summary of the Invention

Means for Solving the Problems

[0005] Various embodiments provide methods, systems, apparatuses, computer program products, etc. for simulating chemical systems. Exemplary embodiments provide methods, systems, apparatuses, computer program products, etc. for simulating chemical systems, such as atoms, molecules, ions, periodic solids, periodic surface slabs, aggregates of one or more atoms, molecules, and / or ions, or combinations thereof, using a quantum computer through the execution of a depth-reduced quantum circuit.

[0006] In various embodiments, hybrid quantum-classical computing techniques are used to accurately and efficiently model and / or simulate chemical systems. Specifically, at least one quantum circuit encoding a chemical system simulation is generated based on the conversion of a parameterized representation and / or operator representation of the chemical system from a fermionic Hilbert space to a qubit Hilbert space for the qubits of the quantum computing components to be used to execute at least one quantum circuit. The depth of at least one quantum circuit (e.g., the number of quantum gates and / or the layers of quantum gates) is reduced based on the characterizing parameters of the chemical system and / or through the rearrangement of the appearance of excitation operators in the operator representation of the chemical system. For example, in one exemplary embodiment, at least one quantum circuit is configured to cause the execution of excitation operators in the order of double-excitation operators corresponding to double excitations from one spatial orbital to a corresponding spatial orbital, any double-excitation operators (e.g., corresponding to double-electron excitations other than those from one spatial orbital to a corresponding spatial orbital), and single-electron excitation operators.

[0007] In various embodiments, any double-excitation operator is a Jordan-Wigner encoded double-excitation operator configured to act on four or more qubits (e.g., four or more qubits).

[0008] In various embodiments, the number of excitation operators in a chemical operator representation is reduced based on the symmetry of the chemical system. For example, excitations that are redundant due to the symmetry of the chemical system and / or excitations that are not allowed based on the symmetry of the chemical system are removed from the operator representation to reduce the number of gates required to implement the resulting quantum circuit. In various embodiments, when executed by the quantum computing component of a hybrid quantum-classical computing component, a deep reduction quantum circuit that determines and / or generates the wavefunction of the chemical system, how the chemical system behaves in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), the structural properties of the chemical system, etc. is determined and / or generated.

[0009] According to a first aspect, a hybrid quantum-classical computing system configured to perform a simulation of a chemical system is provided. The hybrid quantum-classical computing system comprises a classical computing component coupled to a quantum computing component. The hybrid quantum-classical computing system is configured to determine characterization parameters that describe the chemical system, where the characterization parameters are at least partially based on the chemical structure of the chemical system, generate an operator representation of the chemical system that includes single-electron excitation operators and double-electron excitation operators, and reorder the occurrences of the single-electron excitation operators and the double-electron excitation operators in the operator representation according to the characterization parameters. The simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation.

[0010] In one exemplary embodiment, the hybrid quantum-classical computing system is configured to reorder the occurrences of the single-electron excitation operators and the double-electron excitation operators to (i) double-excitation operators corresponding to double excitations from a given spatial orbital to a corresponding spatial orbital, (ii) any double-excitation operators, and (iii) any single-excitation operators.

[0011] In one exemplary embodiment, a hybrid quantum-classical computing system is configured to determine characterization parameters that describe a chemical system, apply symmetry filtering to an operator representation of the chemical system to evaluate its structural symmetry degree, generate a quantum state synthesis of the chemical system based on the symmetry degree, generate a spatial excitation synthesis of the chemical system from the quantum state synthesis, process the spatial excitation synthesis by converting spatial orbits to spin orbits therein, introduce spin orbits onto at least one quantum circuit, and generate a corresponding operator representation by using commuting sets of double excitation operators and single excitation operators to synthesize at least one quantum circuit such that a double excitation operator appears on at least one quantum circuit before a single excitation operator appears on at least one quantum circuit and each commuting set corresponds to an excitation of the chemical system.

[0012] In one exemplary embodiment, a hybrid quantum chemistry computing system is configured to reduce the number of quantum gates required in quantum circuit synthesis according to the structural symmetry degree of a chemical system.

[0013] In one exemplary embodiment, a hybrid quantum chemistry computing system is configured to apply symmetry filtering to an operator representation, which comprises at least one of identifying excitation operators of an operator representation of a chemical system that do not commute with one or more symmetries of a set of symmetries of the chemical system, or defining an Abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the Abelian point group.

[0014] In one exemplary embodiment, generating a quantum state synthesis of a chemical system comprises generating a (doubly occupied spatial orbit) reference state based on the doubly occupied spatial orbits and virtual spatial orbits of the chemical system.

[0015] In one exemplary embodiment, spatial excitation synthesis comprises converting an inter-spatial-orbital operator into a double-excitation space qubit operator.

[0016] In one exemplary embodiment, generating quantum circuit synthesis comprises converting a chemical double-excitation operator corresponding to a double excitation other than a double excitation between spatial orbitals (e.g., any double excitation operator) into any double excitation qubit operator.

[0017] In one exemplary embodiment, a hybrid quantum-classical computing entity is configured to compile into a quantum circuit executable by the quantum circuit synthesis, which in turn comprises an operator between double-excitation space qubits, any double-excitation qubit operator, and a single-excitation qubit operator.

[0018] In one exemplary embodiment, a hybrid quantum-classical computing system is further configured to cause a quantum computing component to execute at least one quantum circuit to determine at least one of a chemical system wave function, a chemical system structural property, a chemical system chemical interaction property, or a chemical system reaction property.

[0019] In one exemplary embodiment, a hybrid quantum-classical computing system is further configured to cause a classical computing component to (a) display a graphical representation of at least a portion of a simulation of a chemical system, or (b) generate and store in classical memory a file comprising one or more parameters of a simulation of a chemical system.

[0020] In one exemplary embodiment, the operator representation is generated using the unitary coupled cluster singles and doubles (UCCSD) ansatz.

[0021] According to another aspect, a method for using a hybrid quantum-classical computing system to perform a chemical simulation is provided. The hybrid quantum-classical computing system comprises a classical computing component coupled to a quantum computing component. In one exemplary embodiment, the method comprises determining characterization parameters that describe a chemical system, wherein the characterization parameters are at least partially based on the chemical structure of the chemical system; generating an operator representation of the chemical system, including a single-electron excitation operator and a double-electron excitation operator; and reordering the appearance of the single-electron excitation operator and the double-electron excitation operator in the operator representation according to the characterization parameters. The simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation.

[0022] In one exemplary embodiment, the order of appearance of the single-electron excitation operator and the double-electron excitation operator is reordered to (i) a double-excitation operator corresponding to a double excitation from a certain spatial orbital to a corresponding spatial orbital, (ii) any double-excitation operator, and (iii) any single-excitation operator.

[0023] In one exemplary embodiment, the system is configured to generate a corresponding operator representation by determining characterization parameters that describe a chemical system, applying symmetry filtering to the operator representation of the chemical system to evaluate its structural symmetry, generating a quantum state synthesis of the chemical system based on the symmetry, generating a spatial excitation synthesis of the chemical system from the quantum state synthesis, processing the spatial excitation synthesis by converting from spatial orbitals to spin orbitals therein, introducing the spin orbitals onto at least one quantum circuit, and using an exchange set of double-excitation operators and single-excitation operators to synthesize at least one quantum circuit such that the double-excitation operator appears on the at least one quantum circuit before the single-excitation operator appears, and each exchange set corresponds to an excitation of the chemical system.

[0024] In one exemplary embodiment, the hybrid quantum chemistry calculation system is configured to reduce the number of quantum gates required in quantum circuit synthesis according to the structural symmetry degree of the chemical system.

[0025] In one exemplary embodiment, applying symmetry filtering to the operator representation comprises at least one of defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more of the symmetries in the set of symmetries, or defining an Abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the Abelian point group.

[0026] In one exemplary embodiment, generating the quantum state synthesis of the chemical system comprises generating a (doubly occupied space orbital) reference state based on the doubly occupied space orbitals and virtual space orbitals of the chemical system.

[0027] In one exemplary embodiment, spatial excitation synthesis comprises converting an inter-spatial orbital operator to an inter-double excitation space qubit operator.

[0028] In one exemplary embodiment, generating the quantum circuit synthesis comprises converting a double excitation operator of the chemical system (e.g., any double excitation operator) corresponding to a double excitation other than a double excitation between spatial orbitals to an arbitrary double excitation qubit operator.

[0029] In one exemplary embodiment, the method comprises the step of compiling the quantum circuit synthesis into an executable quantum circuit, and the quantum circuit synthesis further comprises, in order, an inter-double excitation space qubit operator, an arbitrary double excitation qubit operator, and a single excitation qubit operator.

[0030] In one exemplary embodiment, the method further comprises the step of causing the quantum computing component to execute at least one quantum circuit to determine at least one of the wave function of the chemical system, the structural properties of the chemical system, the chemical interaction properties of the chemical system, or the reaction properties of the chemical system.

[0031] In one exemplary embodiment, the method further causes a classical computing component to perform at least one of: (a) displaying a graphical representation of at least a portion of a simulation of a chemical system; or (b) generating a file comprising one or more parameters of a simulation of a chemical system and storing the file in classical memory.

[0032] In one exemplary embodiment, the operator representation is generated using a unitary coupled cluster singles and doubles (UCCSD) ansatz.

[0033] According to another aspect, a computer program product is provided. In one exemplary embodiment, the computer program product comprises at least one non-transitory computer-readable medium storing executable instructions. The executable instructions, when executed by a hybrid quantum-classical computing system, cause the hybrid quantum-classical computing system to: determine characterization parameters that describe a chemical system, wherein the characterization parameters are at least partially based on the chemical structure of the chemical system; generate an operator representation of the chemical system, comprising single-electron excitation operators and double-electron excitation operators; and reorder the occurrences of the single-electron excitation operators and the double-electron excitation operators in the operator representation as a function of the characterization parameters, wherein the simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on a quantum computing component used to perform the simulation.

[0034] In one exemplary embodiment, the occurrences of the single-electron excitation operators and the double-electron excitation operators are reordered to: (i) double-excitation operators corresponding to excitations from a given spatial orbital to a corresponding spatial orbital; (ii) any double-excitation operators; and (iii) any single-excitation operators.

[0035] In one exemplary embodiment, when the executable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is caused to determine characterization parameters that describe a chemical system, apply symmetry filtering to an operator representation of the chemical system to evaluate its structural symmetry degree, generate a quantum state synthesis of the chemical system based on the symmetry degree, generate a spatial excitation synthesis of the chemical system from the quantum state synthesis, process the spatial excitation synthesis by converting from spatial orbits to spin orbits therein, generate a quantum circuit synthesis by exchanging a set of two-electron excitation operators from the processed spatial excitation synthesis, and further configure the quantum circuit synthesis by exchanging a set of single-excitation operators so that the two-electron excitation operators appear in the quantum circuit before the single-excitation operators appear in the quantum circuit synthesis, so as to generate a corresponding operator representation.

[0036] In one exemplary embodiment, when the executable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is further configured to reduce the number of quantum gates required in the quantum circuit synthesis according to the structural symmetry degree of the chemical system.

[0037] In one exemplary embodiment, applying symmetry filtering to an operator representation includes at least one of defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that do not commute with one or more of the symmetries in the set of symmetries, or defining an Abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the Abelian point group.

[0038] In one exemplary embodiment, generating a quantum state synthesis of the chemical system includes generating a (doubly occupied spatial orbit) reference state based on the doubly occupied spatial orbits and virtual spatial orbits of the chemical system.

[0039] In one exemplary embodiment, the spatial excitation synthesis includes converting an inter-spatial orbit operator into an inter-two-electron excitation spatial qubit operator.

[0040] In one exemplary embodiment, generating a quantum circuit synthesis comprises converting a chemical double excitation operator (e.g., any double excitation operator) corresponding to a double excitation other than a double excitation between spatial orbits into any double excitation qubit operator.

[0041] In one exemplary embodiment, when the executable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is further configured to compile the quantum circuit synthesis into an executable quantum circuit for the hybrid quantum-classical computing system, and the quantum circuit synthesis comprises, in turn, an operator between double excitation space qubits, any double excitation qubit operator, and a single excitation qubit operator.

[0042] In one exemplary embodiment, when the executable instructions are executed by a hybrid quantum-classical computing system, the hybrid quantum-classical computing system is further configured to cause at least one quantum circuit to be executed by a quantum computing component to determine at least one of a wave function of a chemical system, a structural property of a chemical system, a chemical interaction property of a chemical system, or a reaction property of a chemical system.

[0043] In one exemplary embodiment, when the executable 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 perform at least one of (a) displaying a graphical representation of at least a portion of a simulation of a chemical system, or (b) generating and storing in classical memory a file comprising one or more parameters of a simulation of a chemical system.

[0044] In one exemplary embodiment, the operator representation is generated using the unitary coupled cluster singles and doubles (UCCSD) ansatz.

[0045] Since the present invention has been described in general terms, reference will now be made to the accompanying drawings, which are not necessarily drawn to scale.

Brief Description of the Drawings

[0046]

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Modes for Carrying Out the Invention

[0047] With reference to the accompanying drawings, which show some but not all embodiments of the present invention, the present invention will now be described more fully hereinafter. 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 " / ") 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 to within manufacturing and / or production errors and / or within the measurement capabilities of a user, unless otherwise indicated. Throughout, like numbers refer to like elements.

[0048] 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 using a quantum circuit that includes a depth-reduced quantum circuit and / or a quantum circuit that includes fewer two-qubit quantum gates compared to a conventionally generated quantum circuit for simulating a chemical system.

[0049] Generally, quantum computers are expected to enable accurate modeling and / or simulation of chemical systems. For example, quantum computers are expected to enable accurate modeling and / or simulation of chemical systems that are too complex for conventional classical techniques. 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 the depth (e.g., the number of layers of quantum gates) and / or the number of two-qubit quantum gates in a quantum circuit increases, the effect of noise on the resulting model or simulation also increases. In conventional techniques for generating a quantum circuit for modeling and / or simulating a chemical system, the depth of the quantum circuit is O(n 4) is scaled, where n is the number of spin orbits included in the model and / or simulation. These conventional techniques lead to quantum circuits containing thousands of two-qubit quantum gates, which clearly exceed the capabilities of currently operational quantum computing components. Thus, there are technical problems regarding how to generate quantum circuits for modeling and / or simulating chemical systems that can be executed by currently operational quantum computing components, i.e., noisy intermediate-scale quantum (NISQ) devices.

[0050] Various embodiments provide technical solutions to these technical problems. Specifically, various embodiments use the symmetry of the chemical system to reduce the number of two-qubit quantum gates required to accurately model and / or simulate the chemical system. In various embodiments, the number of two-qubit quantum gates in the resulting quantum circuit is at least one-tenth less than that of the quantum circuit for modeling and / or simulating the same chemical system generated through conventional techniques. Thus, various embodiments bring improvements to the fields of chemical system modeling and / or simulation, quantum chemistry, and / or quantum circuit generation.

[0051] Generally, a quantum circuit is a series of ordered quantum operations (e.g., quantum operators applied to the quantum data of one or more qubits through single or two-qubit gates) performed on a set of qubits. A quantum computing component can execute the compiled quantum circuit to achieve quantum computing. In various scenarios, a quantum circuit includes layers of quantum operations (i.e., temporal sequences), and each layer includes a collection of quantum operations performed at each time step of the quantum computing. Thus, the depth and / or number or layer count of the layers in a quantum circuit gives an indication of the length of time required to perform the quantum computing and / or the number of quantum operations performed on individual qubits, both of which may affect the magnitude of the noise in the result of each quantum computing.

[0052] In various embodiments, hybrid quantum-classical computing techniques are used to accurately and efficiently model and / or simulate chemical systems. In various embodiments, the wave function of a chemical system, the structural properties of a chemical system, the chemical interaction properties of a chemical system, and / or the reaction properties of a chemical system are determined by executing a quantum circuit via the quantum computing component of a hybrid quantum-classical computing system. In various embodiments, executing a quantum circuit via a quantum computing component causes the quantum computing component to model and / or simulate a chemical system. In various embodiments, the model and / or simulation is a variational quantum eigenvalue solver (VQE) model and / or simulation of a chemical system.

[0053] In various embodiments, generating and / or simulating a quantum circuit includes determining characterization parameters that describe a chemical system. The characterization parameters are determined based at least in part on the chemical structure of the chemical system. For example, in various embodiments, the characterization parameters include nuclear information (e.g., the number of protons and neutrons present in each atomic nucleus) for each atomic nucleus of the chemical system, the number of electrons in the chemical system, the Cartesian coordinates of the nuclei, various symmetries of the chemical system (e.g., including, but not limited to

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[0054] In various embodiments, the generation and / or simulation of a quantum circuit includes generating a parameterized representation of a chemical system. In various embodiments, the parameterized representation of the chemical system is a wave function of the chemical system. In various embodiments, the parameterized representation of the chemical system is determined based on an operator representation of the chemical system. For example, in one exemplary embodiment, the parameterized representation is an eigenstate of the operator representation of the chemical system. In various embodiments, the operator representation of the chemical system is an effective Hamiltonian of at least a portion of the chemical system. In various embodiments, the operator representation is a UCC operator (e.g., a UCCSD operator) and / or includes the same. In various embodiments, the operator representation comprises a plurality of operators configured to operate on various spatial and / or spin orbitals of the chemical system. As should be understood, an operator acting on a first spatial and / or spin orbital can cause a change in the probability of occupancy of the first spatial and / or spin orbital of the chemical system and / or one or more second spatial and / or spin orbitals.

[0055] In various embodiments, the parameterization of the parameterized representation of the chemical system is determined based on an ansatz to be used to represent the waveform of the chemical system and / or operators incorporated to form the operator representation of the chemical system.

[0056] As should be understood, an operator is a function that acts on an element of one space to produce an element of the same or another space. For example, an excitation operator within the Hilbert space of the electrons of a chemical system is configured to act on a representation of the electrons of the chemical system to cause one or more excitations thereof. An excitation operator that has been transformed and / or mapped to the Hilbert space of the qubits of a quantum computing component acts on the quantum state of the qubits to cause the quantum state of the qubits to represent, model, and / or simulate features of the chemical system (e.g., orbital occupancy).

[0057] In various embodiments, a unitary coupled cluster (UCC) ansatz is used to represent chemical waveforms and / or chemical operators (e.g., operators integrated to provide an operator representation). In one exemplary embodiment, the ansatz is a UCCSD ansatz, which is a UCC ansatz that includes single-electron excitation operators and double-electron excitation operators.

[0058] In various embodiments, the electronic correlation of a chemical system is modeled and / or simulated using an operator representation of the chemical system (e.g., the effective Hamiltonian of at least a portion of the chemical system). In various embodiments, the basis and / or format of the operator representation is determined based on the ansatz being used. For example, in various embodiments using the UCCSD ansatz, the electronic correlation is simulated by using USSCD operators. For example, in one exemplary embodiment, a parameterized representation of the chemical system is generated based on an operator representation of the chemical system (a UCCSD operator or an operator determined by another ansatz).

[0059] In one exemplary embodiment, the operator representation is expressed as a product of Trotter-decomposed exponential functions. As is generally understood in the art, Trotter decomposition of a product of exponential functions is a truncation of the infinite series used to evaluate the product of exponential functions. For example, in an exemplary embodiment where the operator representation includes a UCCSD operator, the operator representation is

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[0060] In one exemplary embodiment, a parameterized representation of a chemical system (e.g., a wave function of a chemical system determined and / or generated based on an operator representation of the chemical system in one exemplary embodiment) and / or an operator representation (e.g., the effective Hamiltonian of at least a portion of a chemical system) is transformed and / or mapped from the Hilbert space of the chemical system to the Hilbert space of qubits of a quantum computing component. In various embodiments, the transformation and / or mapping of a parameterized representation and / or an operator representation of a chemical system from fermionic operators to qubit operators is determined 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. In one exemplary embodiment, the transformation and / or mapping is performed using Jordan-Wigner encoding, although various other encodings are used in various other embodiments.

[0061] In an embodiment using Jordan-Wigner encoding, for example, each qubit of a quantum circuit represents the electron number occupancy of each spin orbit in a chemical system. For example, when a qubit is in the |1> state, the corresponding spin orbit is occupied, and when the qubit is in the |0> state, the corresponding spin orbit is not occupied. Using Jordan-Wigner encoding, in one exemplary embodiment, an operator representation including a UCCSD operator is

Number

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[0062] In various embodiments, the generation and / or simulation of a quantum circuit includes reordering the appearance order of single-electron excitation operators and two-electron excitation operators in an operator representation of a chemical system (e.g., the effective Hamiltonian of at least a portion of the chemical system). In various embodiments, the appearance order of single-electron excitation operators and two-electron excitation operators in an operator representation of a chemical system (e.g., the effective Hamiltonian of at least a portion of the chemical system) is reordered. This reordering reduces and / or lowers the count of two-qubit quantum gates (e.g., two-qubit gates such as a controlled-not gate (CX), a ZZ-max gate, an iSWAP gate, etc.) used in the quantum circuit for modeling and / or simulating the chemical system. In various embodiments, the reordering of the appearance of single-electron excitation operators and two-electron excitation operators is performed according to the characterization parameters of the chemical system. For example, knowledge of the symmetry of the chemical system, the spin orbitals and / or spatial orbitals of the chemical system, etc. is used to reorder the appearance order of single-electron excitation operators and two-electron excitation operators in an operator representation of the chemical system (e.g., the effective Hamiltonian of at least a portion of the chemical system) in order to lower the count of two-qubit quantum gates in the resulting quantum circuit.

[0063] After the conversion and / or mapping of the operator representation of the chemical system (e.g., the effective Hamiltonian of at least a portion of the chemical system) to qubit operators and the reordering of the appearance order of single-electron excitation operators and two-electron excitation operators, a quantum circuit is compiled based on that operator representation. The quantum circuit is executed using a quantum computing component to model and / or simulate the chemical system. In one exemplary embodiment, a measurement operation is performed by the quantum computing component (e.g., as part of the quantum circuit) to extract the qubit representation of the chemical system.

[0064] Next, the qubit representation of a chemical system is processed to determine one or more of a chemical wavefunction, properties indicating how the chemical system behaves in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), structural properties of the chemical system, and the like.

[0065] As used herein, a classical computing component or classical computer is a computing entity that uses semiconductor-based computing techniques and hardware. A quantum computing component or quantum computer uses the quantum states of quantum particles (referred to as qubits) to perform computations.

[0066] Exemplary Hybrid Quantum-Classical Computing System FIG. 1 provides a block diagram of an exemplary hybrid quantum-classical computing system 100 according to various embodiments. In various embodiments, the hybrid quantum-classical computing system 100 includes classical components such as classical computing component 110 and quantum components such as quantum computing component 130.

[0067] 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 (e.g., the evolution of a controlled quantum state) of the qubits 134. The controller 132 is further configured to control the operation of sensors 138 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.

[0068] For example, in various embodiments, the qubit manipulation element 136 comprises 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 when confining qubits and / or manipulating the quantum states of qubits. For example, in various embodiments, the sensor 138 comprises a photodetector, a voltage / current sensor, a temperature sensor, a pressure sensor, and / or other sensors that can be used to determine the quantum state of a qubit and / or monitor one or more operations of the qubit manipulation element 136.

[0069] In various embodiments, the classical computing component 110 communicates with the controller 132 of the quantum computing component 130 via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication. For example, the classical computing component 110 is configured to generate a quantum circuit for modeling and / or simulating a chemical system and provide it to the quantum computing component 130 (e.g., its controller 132), and to receive, between the classical computing component 110 and the quantum computing component 130, a qubit representation of the chemical system provided by the quantum computing component 130 (e.g., its controller 132) via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication. For example, the quantum computing component 130 is configured to receive the quantum circuit provided by the classical computing component 110 and provide, between the classical computing component 110 and the quantum computing component 130, a qubit representation of the chemical system for reception by the classical computing component 110 via one or more wired or wireless networks 120 and / or via direct wired and / or wireless communication.

[0070] In various embodiments, the hybrid quantum-classical computing system 100 and / or a part thereof (e.g., the classical computing component 110 and / or the quantum computing component 130) is configured to use the InQuanto quantum chemistry application library and / or the tket software development kit to perform the various processes, operations, etc. described herein. As should be understood, in various other embodiments, various other quantum chemistry application libraries and / or software development kits may be used.

[0071] Exemplary Operations 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 the chemical system that represents, for example, the wave function of the chemical system, 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 part 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.

[0072] In various embodiments, the classical computing component 110 obtains information corresponding to the chemical system. For example, user input (e.g., received via the user input interface of the classical computing component 110) may provide access to, select, and / or elicit information corresponding to the chemical system. In one exemplary embodiment, the information corresponding to the chemical system is the chemical formula of the chemical system (H, H2O, NH4 +, OH, CH4, a specified transition state of a chemical reaction, etc.), and / or other specifications of the chemical system. In certain exemplary embodiments, 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.

[0073] In various embodiments, obtaining information corresponding to the chemical system triggers and / or causes the classical computing component 110 to determine and / or generate a model of the chemical system that represents, for example, the (fermionic) wave function of the chemical system, one or more structural characteristics of the chemical system, one or more chemical interaction characteristics of the chemical system, one or more reaction characteristics of the chemical system, etc.

[0074] For example, the classical computing component 110 may determine and / or identify characterization parameters of the chemical system, perform quantum circuit synthesis using the characterization parameters, and provide the quantum circuit to the quantum computing component 130. The quantum computing component 130 may execute the quantum circuit (e.g., using its plurality of qubits) to determine the qubit representation of the chemical system. For example, in various embodiments, the qubit representation may provide orbital occupancy information for a plurality of orbits of the chemical system. In various embodiments, the qubit representation may provide one or more reduced density matrices (RDMs) for the chemical system (e.g., spinless (i.e., spin-traced) RDMs such as one-particle RDM (1-RDM), two-particle RDM (2-RDM), etc.). In various embodiments, the qubit representation may provide a parameterized representation (e.g., a wave function) of the chemical system. In various embodiments, the qubit representation may be processed to determine one or more RDMs and / or other characteristics or properties of the chemical system.

[0075] The classical computing component 110 can then utilize and / or process the qubit representation of the chemical system to determine the chemical wave function, and / or structural, interaction, and / or other properties. For example, the classical computing entity can act on such states to complete a simulation of the chemical system, determine how the chemical system will behave in one or more interactions (e.g., with other chemical systems and / or electromagnetic radiation), determine the structural properties of the chemical system, etc., to determine an approximation of the properties of the eigenstates of the overall electronic Hamiltonian of the system, such as the expected value of a quantum operator.

[0076] Figure 2 provides a flowchart of various processes, procedures, operations, etc. performed by the hybrid quantum-classical computing system 100 in various embodiments. Starting at step / operation 202 in Figure 2, the classical computing component 110 determines the characterization parameters that describe the chemical system. For example, the classical computing component 110 can identify the chemical system and / or receive corresponding information (e.g., through user input). For example, the classical computing component 110 can receive the chemical formula of the chemical system (H, H2O, NH4 + , OH, CH4, a specified transition state of a chemical reaction, etc.), and / or other specifications 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.

[0077] Based on identifying the chemical system and / or corresponding information, classical computing component 110 determines the characterization parameters of the chemical system. In various embodiments, the characterization parameters are determined based at least in part on the chemical structure of the chemical system. In various embodiments, one or more of a look-up table regarding the structure of one or more chemical systems, processing information corresponding to the geometric arrangement of the chemical system (e.g., nuclear Cartesian coordinates), determining one or more orbits of the chemical system using Hartree-Fock techniques and / or perturbation theory techniques, etc. are used to determine the characterization parameters.

[0078] For example, in various embodiments, the characterization parameters include 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, nuclear Cartesian coordinates, various symmetries of the chemical system (e.g., but not limited to

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[0079] In step / operation 204, classical computing component 110 generates a parameterized representation and / or operator representation of the chemical system. For example, an ansatz is identified and / or selected (e.g., UCCSD and / or another suitable ansatz), and the corresponding operator representation representing the electronic correlation of the chemical system is determined based on the identified and / or selected ansatz. In various embodiments, the ansatz is identified based on user input (e.g., received via a user input device), selected based on a default ansatz, etc.

[0080] In various embodiments, a chemical operator representation comprises operators that describe the electronic correlation of a chemical system. For example, in various embodiments, a chemical operator representation includes an operator that includes a sum over each excitation operator that acts over all of the orbits of the chemical system. For example, a chemical operator representation is an integrated operator formed by summing over each excitation operator that acts over all of the spin and / or spatial orbits of the chemical system. In various embodiments, the excitation operators included in the chemical operator representation are determined based on at least a portion of one or more of the spin multiplicity of the chemical system, the number of electrons in the chemical system, and the size of the basis function system of the chemical system.

[0081] In various embodiments, a parameterized representation of a chemical system is determined based on the chemical operator representation. For example, in various embodiments, the parameterized representation is the wave function of the chemical system and the operator representation is the effective Hamiltonian of at least a portion of the chemical system. In various embodiments, the parameterization of the parameterized representation of the chemical system and / or the operator representation is determined based on an ansatz to be used to represent the waveform of the chemical system and / or the operator of the chemical system. In one exemplary embodiment, the ansatz used to represent the waveform of the chemical system and / or the operator of the chemical system is the unitary coupled cluster with single and double excitations (UCCSD) ansatz.

[0082] In various embodiments, the electronic correlation of a chemical system is modeled and / or simulated using a chemical operator representation that is an operator determined by an ansatz and / or includes such an operator. For example, in various embodiments that use the UCCSD ansatz, the electronic correlation is simulated by using the UCCSD operator. For example, in one exemplary embodiment, the chemical operator representation is the UCCSD operator or an operator determined by another ansatz.

[0083] In one exemplary embodiment, the operator representation includes a UCCSD operator represented as a product of Trotter-decomposed exponential functions. As is generally understood in the art, Trotter-decomposing a product of exponential functions is a truncation of the infinite series used to evaluate the product of exponential functions. For example, in one exemplary embodiment, the UCCSD operator is

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[0084] In one exemplary embodiment, the operator representation of the chemical system (e.g., the UCCSD operator in one exemplary embodiment) is converted and / or mapped from the Hilbert space of the chemical system to the Hilbert space of the qubits of the quantum computing component. In various embodiments, the conversion and / or mapping of the operator representation of the chemical system from fermionic operators to qubit operators is determined by and / or depends 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 protons, electrons, atomic nuclei, neutral atoms, ions, Josephson junctions, quantum dots, topological anions, and / or other quantum particles and / or systems as qubits. In one exemplary embodiment, the conversion and / or mapping is performed using Jordan-Wigner encoding, although various other encodings are used in various other embodiments.

[0085] In embodiments using Jordan-Wigner encoding, for example, each qubit of a quantum circuit represents the occupancy of the number of electrons in each spin orbit in a chemical system. For example, when a qubit is in the |1> state, the corresponding spin orbit is occupied, and when the qubit is in the |0> state, the corresponding spin orbit is not occupied. Using Jordan-Wigner encoding, the operator representation (including, for example, operators determined by UCCSD operators or other ansatz) is

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[0086] In step / operation 206, the classical computing component 110 reorders the appearance order of single-electron excitation operators and double-electron excitation operators in the operator representation of the chemical system. This reordering reduces and / or lowers the count of two-qubit quantum gates (e.g., two-qubit gates) used in the quantum circuit to model and / or simulate the chemical system. In various embodiments, the reordering of the appearance of single-electron excitation operators and double-electron excitation operators is performed as a function of the characterization parameters of the chemical system. For example, knowledge such as the symmetry of the chemical system, the spin orbit and / or spatial orbit of the chemical system is used to reorder the appearance order of single-electron excitation operators and double-electron excitation operators in the operator representation of the chemical system so as to reduce the count of two-qubit quantum gates in the resulting quantum circuit.

[0087] In various embodiments, the reordering of the appearance order of single - electron excitation operators and double - electron excitation operators in a chemical system's operator representation is performed based at least in part on the characterizing parameters of the chemical system. For example, the reordering of the appearance of single - electron excitation operators and double - electron excitation operators in a chemical system's operator representation is based on filtering excitation operators based on one or more symmetries of the chemical system, based on the type of excitation (doublet excitation between spatial orbitals, any double excitation, any single excitation), through the definition of the (doubly - occupied spatial orbitals) reference state, through converting at least a portion of the spatial orbitals to spin - orbitals, through commuting sets of electron excitation operators, etc.

[0088] In various embodiments, reordering the appearance order of single - electron excitation operators and double - electron excitation operators in a chemical system's operator representation includes applying symmetry filtering to the wavefunction representation of the chemical system to evaluate its structural symmetry degree.

[0089] For example, in one exemplary embodiment, the classical computing component 110 applies symmetry filtering by defining a set of symmetries of the chemical system and identifying one or more excitation operators in the operator representation of the chemical system that do not commute with one or more symmetries of the set of symmetries. One or more excitation operators that do not commute with one or more symmetries of the set of symmetries are removed from the operator representation of the chemical system. In one exemplary embodiment, the set of symmetries is the

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[0090] In one exemplary embodiment, the classical computing component 110 applies symmetry filtering by defining an Abelian point group of a chemical system and identifying redundant excitations of the chemical system based on the Abelian point group. For example, in one exemplary embodiment, the maximum and / or highest Abelian point group of the chemical system is defined and used to identify redundant excitations of the chemical system. The excitation operators corresponding to the excitations of the chemical system identified as redundant excitations are removed from the operator representation of the chemical system.

[0091] Conventionally, in a Trotter-decomposed operator representation (e.g., in one exemplary embodiment, in its UCCSD operator), single-electron excitation operators are applied before the application of double-electron excitation operators. According to various embodiments, the order of appearance of the excitation operators within the operator representation of the chemical system is reconfigured such that the double-electron excitation operator

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[0092] For example, in various embodiments, the classical computation component 110 may be configured such that in an embodiment using UCCSD Ansatz the effective Hamiltonian is

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[0093] In various embodiments, rearranging the order of occurrence of the single and double electronic excitation operators in the operator representation of the chemical system includes generating a quantum state synthesis of the chemical system based on a symmetry degree of the chemical system. In various embodiments, generating the quantum state synthesis comprises generating a double occupancy of the spatial orbital reference state by processing a reference HF state of the chemical system to extract spatial orbital occupancies. In an exemplary embodiment, only double occupied spatial orbitals and virtual spatial orbitals are included in the double occupancy of the spatial orbital reference state. For example, an HF state |110000> (where the first two 1's indicate a pair of occupied spin orbitals corresponding to the same spatial orbital and the four 0's correspond to two pairs of unoccupied virtual spin orbitals of the chemical system) that defines a spin orbital occupancy is processed to provide a double occupancy of the spatial orbital reference state |100>, which indicates that the first spatial orbital is double occupied and the second and third spatial orbitals are unoccupied. In an exemplary embodiment, these spatial orbital occupancies are mapped to even-indexed qubits of a quantum circuit by applying a Pauli-X gate to provide the qubit state |100000>. In one exemplary embodiment, quantum state synthesis allows qubits (eg, qubits with even indices) to encode the (dual) occupancy of a spatial orbital of a chemical system, rather than the occupancy of the spin orbital of the chemical system.

[0094] In various embodiments, reordering the appearance order of single - electron excitation operators and double - electron excitation operators in a chemical - based operator representation includes generating chemical - based spatial excitation synthesis from quantum state synthesis. In various embodiments, a double - electron spatial - orbital - to - orbital operator performs an operation of exciting a pair of electrons from a first spatial orbital to a second spatial orbital. Since the electron pair is excited together (e.g., as a pair), the electron pair can be approximated as a hard - core boson. In other words, a double - electron excitation operator corresponding to an electron pair excited from one spatial orbital to another

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[0095] In various embodiments, reordering the appearance order of single - electron excitation operators and double - electron excitation operators in a chemical - based operator representation includes performing a change in representation such that the qubits of the quantum circuit carry spin - orbital occupancy information. For example, each qubit corresponding to a spin orbital that is part of a doubly - occupied spatial orbital is made to indicate that the spin orbital is occupied. Each qubit corresponding to a spin orbital that is part of an unoccupied spatial orbital is made to indicate that the spin orbital is unoccupied. Each qubit corresponding to a spin orbital that is part of a singly - occupied spatial orbital can be switched as appropriate to indicate the appropriate single occupancy of each spatial orbital.

[0096] In various embodiments, reordering the order of appearance of single - electron excitation operators and double - electron excitation operators in a chemical - based operator representation involves generating quantum circuit synthesis by using a set of commutation operators. In various embodiments, each set of commutation operators represents an excitation. The operators of the set of commutation operators are configured to act on the qubits of the quantum computing components to be used to execute at least one resulting quantum circuit and / or to act in the qubit Hilbert space therefor. In various embodiments, the set of commutations is generated and / or determined using tket. For example, in various embodiments, the set of commutation techniques may be similar to and / or use the framework disclosed by U.S. Patent No. 11,144,689, issued October 12, 2021, the entire content of which is incorporated herein by reference.

[0097] For example, quantum circuit synthesis is generated in part by swapping a set of double - electron excitation operators from a processed spatial excitation synthesis. For example, spatial excitation synthesis corresponds to double - electron excitation operators for electron pairs excited from one spatial orbital to another spatial orbital.

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[0098] For example, in one exemplary embodiment, any double - electron excitation operator

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[0099] In various embodiments, reconfiguring the order of appearance of single-electron excitation operators and two-electron excitation operators in the operator representation of a chemical system involves modifying the quantum circuit synthesis by a commutation set of single-electron excitation operators such that two-electron excitation operators appear in the quantum circuit synthesis before single-excitation operators appear. For example, in various embodiments, the application of any single-electron excitation operator

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[0100] In various embodiments, reordering the appearance order of single - electron excitation operators and double - electron excitation operators in a chemical - based operator representation, when executed by the quantum computing component 130, results in a quantum circuit that causes the quantum computing component 130 to simulate the chemical system. Moreover, the resulting quantum circuit includes a smaller count of two - qubit quantum gates, such as controlled - NOT (CX) gates, than, for example, conventional quantum circuit synthesis techniques.

[0101] In step / operation 208, the classical computing component 110 or the controller 132 of the quantum computing component 130 compiles a quantum circuit to generate a compiled and / or executable quantum circuit that is executable by the quantum computing component 130. For example, the compiled and / or executable quantum circuit comprises a set of commands that are executable by the controller 132 to cause the various components of the quantum computing component 130 to be controlled by the controller 132 to execute the quantum circuit on the quantum computing component 130. In one exemplary embodiment, the quantum circuit is compiled using tket, although in various other embodiments various other quantum circuit compilers may be used.

[0102] In step / operation 210, the hybrid quantum - classical computing system 100 executes the compiled and / or executable quantum circuit. For example, the controller 132 controls the various components of the quantum computing component 130 (e.g., the qubit manipulation element 136 and / or the sensor 138) in a controlled manner to evolve the quantum state of the qubits 134 such that measurement results obtained as part of the execution of the compiled and / or executable quantum circuit provide a qubit representation of the chemical system.

[0103] In various embodiments, executing a compiled and / or executable quantum circuit comprises measuring the quantum state of one or more qubits to determine a qubit representation of a chemical system. In various embodiments, the controller 132 and / or classical computing component 110 processes the qubit representation of the chemical system to determine at least one of a wave function of the chemical system, a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system. For example, the controller 132 and / or classical computing component 110 performs post-processing of a model and / or simulation of the chemical system encoded by the qubit representation of the chemical system to determine at least one of a wave function of the chemical system, a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system. In various embodiments, the format or structure of the wave function corresponds to an ansatz used in the generation of a parameterized representation and / or operator representation of the chemical system.

[0104] In various embodiments, the structural properties of a chemical system characterize and / or provide information regarding the structure of the chemical system. For example, the structural properties may indicate the shape of the chemical system, the order and / or spatial distribution of atoms or groups of atoms of components in the chemical system, the properties of various bonds in the chemical system, the relative nuclear positions in the chemical system, and the like.

[0105] In various embodiments, the chemical interaction properties of a chemical system characterize and / or provide information regarding how the chemical system interacts with one or more other chemical systems of the same or different types. For example, the chemical interaction properties of the chemical system may provide information regarding how the chemical system interacts with other chemical systems of the same type / chemical formula or of a different type / chemical formula than the chemical system.

[0106] For example, the structural and / or chemical interaction properties can be a dissociation curve, binding energy, reaction energy, reaction barrier, binding energy, absorption energy, and the like.

[0107] In various embodiments, the chemical reaction characteristics characterize and / or provide information regarding how a chemical system interacts with electromagnetic radiation. For example, the chemical reaction characteristics can be excitation energy, singlet-triplet gap, photodissociation energy, photoionization energy, absorption cross-section, permittivity, dielectric function, oscillator strength, and the like.

[0108] In step / operation 212, the classical computing component 110 provides at least a portion of a model and / or simulation of the chemical system that represents the wave function, structural characteristics, chemical interaction characteristics, and / or reaction characteristics of the chemical system. In various embodiments, providing at least a portion of a model and / or simulation of the chemical system includes displaying, storing, transmitting (e.g., via one or more wired and / or wireless networks), providing, etc., a call response (e.g., an application program interface (API) call response).

[0109] For example, in one exemplary embodiment, the classical computing component 110 causes a representation of a model and / or simulation of the chemical system to be displayed on a display (e.g., display 516 shown in FIG. 5 and / or another display). For example, the graphics processing unit (GPU) of the classical computing component 110 can generate a graphical representation of at least a portion of a model and / or simulation of the chemical system that provides, for example, a visualization of the wave function, structural characteristics, chemical interaction characteristics, and / or reaction characteristics of the chemical system. The classical computing component 110 can then cause the graphical representation of at least a portion of the model and / or simulation of the chemical system to be displayed via the display for review and / or browsing by a human user.

[0110] In another example, the classical computing component 110 may generate and store (e.g., in memories 522, 524) a file comprising at least a portion of a chemical system model and / or simulation. For example, the file may comprise a wave function of the chemical system, structural properties, chemical interaction properties, reaction properties, chemical formulas, and the like. The file may then be provided as an input for one or more functions and / or calculations performed thereby to one or more programs, applications, modules, etc. operating on the classical computing component 110 or another computing entity. For example, a file storing and / or encoding at least a portion of a chemical system model and / or simulation may be used by various programs, applications, modules, etc. to generate a graphical representation and / or visualization of the chemical system and / or a part thereof and / or to perform simulations including chemical system interactions with one or more other chemical systems (of the same or different chemical formulas), to perform simulations of bulk materials including the chemical system, to perform simulations including chemical system interactions with one or more biological systems, to perform simulations to determine the optical spectrum of the chemical system, and the like.

[0111] FIG. 3 provides a flowchart showing various processes, procedures, operations, etc. performed by the hybrid quantum-classical computing system 100 to reorder the appearance order of single-electron excitation operators and two-electron excitation operators in the operator representation of a chemical system. For example, in one exemplary embodiment, the steps / operations of the flowchart shown in FIG. 3 are performed as part of step / operation 208. As described elsewhere herein, the operator representation of a chemical system includes an effective Hamiltonian for the chemical system (or for at least a portion of the electrons of the chemical system). The order in which operators with an effective Hamiltonian are ordered and / or represented (e.g., within a quantum circuit) results in the number of two-qubit quantum gates required to perform the modeling and / or simulation of the chemical system via the quantum circuit to be executed by the quantum computing component 130.

[0112] In various embodiments, symmetry filtering of excitation operators and / or treatment of double-electron space orbital excitations as bosonic excitations and corresponding qubit reference frame transformations enable modeling and / or simulation of chemical systems via a quantum circuit that requires significantly fewer (e.g., by a factor of 10 or more) two-qubit quantum gates (such as two-qubit gates like the CX gate) and / or has a smaller number of such gates compared to conventional quantum circuits for modeling and / or simulating chemical systems.

[0113] Starting at step / operation 302, classical computing component 110 applies symmetry filtering. Symmetry filtering removes and / or excludes excitation operators from operator representations of a chemical system that are not allowed and / or redundant based on the symmetry of the chemical system. This reduces the total number of excitation operators present in the operator representation of the chemical system.

[0114] For example, in various embodiments, applying symmetry filtering comprises filtering a set of excitations present in the operator representation of a chemical system using the symmetry of the chemical system (such as molecular symmetry, etc.) to identify forbidden terms in the operator representation of the chemical system. In various embodiments, a first symmetry filtering is performed. The first symmetry filtering is based on a set of symmetries of the chemical system (e.g.,

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[0115] In various embodiments, symmetry filtering is performed and / or applied by identifying and / or defining the symmetry of the chemical system. In various embodiments, the symmetry of the chemical system is identified and / or defined based at least in part on the characterization parameters of the chemical system. For example, as indicated by the characterization parameters of the chemical system, the geometric configuration of the chemical system can be processed to identify and / or determine the symmetry of the chemical system.

[0116] For example, a set of symmetries and / or a point group having the same symmetry as the chemical system is identified. The identified set of symmetries and / or point group corresponds to the degree of symmetry of the chemical system. Based on the identified set of symmetries and / or point group, excitations that are non-allowed excitations and / or redundant excitations and / or the excitation operators corresponding thereto are removed from the excitation operators present in the operator representation of the chemical system. In other words, the excitation operators identified as performing non-allowed and / or redundant excitations and / or corresponding thereto are removed from the operator representation of the chemical system, reducing the number of operations included therein.

[0117] For example, in one exemplary embodiment, the classical computing component 110 applies a first symmetry filtering by defining a set of chemical symmetries and identifying one or more excitation operators of the chemical operator representation that do not commute with one or more of the symmetries in the set of symmetries. One or more excitation operators that do not commute with one or more of the symmetries in the set of symmetries perform and / or correspond to non-allowed excitations. Accordingly, one or more excitation operators that do not commute with one or more of the symmetries in the set of symmetries are removed from the chemical operator representation. In one exemplary embodiment, the set of symmetries is the

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[0118] In one exemplary embodiment, the classical computing component 110 applies a second symmetry filtering by defining a chemical-based Abelian point group and identifying redundant excitations in the chemical system based on the Abelian point group. For example, in one exemplary embodiment, the largest and / or highest Abelian point group of the chemical system is defined and used to identify redundant excitations in the chemical system. Excitation operators corresponding to excitations in the chemical system identified as redundant excitations are removed from the operator representation of the chemical system. For example, in various embodiments, the second symmetry filtering may be implemented in a manner similar to that described by Petr Carsky et al. in "Use of molecular symmetry in coupled-cluster theory".

[0119] In various embodiments, symmetry filtering includes only one of (a) defining a set of symmetries of the chemical system and identifying non-allowed excitations based thereon, or (b) defining the largest Abelian group of the chemical system and identifying redundant excitations based thereon. In various embodiments, symmetry filtering includes both (a) defining a set of symmetries of the chemical system and identifying non-allowed excitations based thereon, and (b) defining the largest Abelian group of the chemical system and identifying redundant excitations based thereon.

[0120] After implementing and / or applying the symmetry filtering, the remaining excitation operators in the operator representation of the chemical system are processed to generate and / or synthesize a quantum circuit for modeling and / or simulating the chemical system. For example, the quantum circuit includes preparing a set of qubits to encode the spin-orbit occupancy of the chemical system through the application of an effective Hamiltonian of the chemical system (or an effective Hamiltonian for at least a portion of the electrons of the chemical system) through the transformation of the effective Hamiltonian to an effective qubit operator via quantum gates performed on the corresponding qubits.

[0121] In various embodiments, prior to any transformed and / or mapped representations and / or versions of two-electron excitation operators and / or qubit operators, qubit operators that are transformed and / or mapped representations and / or versions of excitation operators between two-electron spatial orbitals appear in the quantum circuit, and prior to any transformed and / or mapped representations and / or versions of single-electron excitation operators and / or qubit operators, qubit operators that are transformed and / or mapped representations and / or versions of two-electron excitation operators appear in the quantum circuit, such that the quantum circuit is synthesized via steps / operations 304 - 312. In one exemplary embodiment, at least a portion of steps / operations 304 - 312 is performed by classical computing component 110 using tket or another quantum circuit generation and / or compilation program.

[0122] In step / operation 304, classical computing component 110 generates a quantum state synthesis portion of the quantum circuit. In various embodiments, generating the quantum state synthesis comprises generating a (doubly occupied spatial orbital) reference state by processing a reference HF state of the chemical system to extract and / or determine the occupancy of the reference spatial orbitals. For example, in one exemplary embodiment, the reference HF state of the chemical system is provided by the characterization parameters of the chemical system. The reference HF state is processed and / or analyzed to identify the doubly occupied spatial orbitals (e.g., both spin orbitals of the spatial orbital are occupied) and / or the unoccupied virtual spatial orbitals. In one exemplary embodiment, only the doubly occupied spatial orbitals and the virtual spatial orbitals are included in the (doubly occupied spatial orbital) reference state.

[0123] An initial portion of a quantum circuit is generated that initializes a set of qubits. Each qubit is indexed by an index p. In various embodiments, the qubits are indexed by p = 2q and p = 2q + 1, where q is an integer corresponding to two spin orbits of each spatial orbit q. The initial portion of the quantum circuit is configured such that for the qubits corresponding to the doubly occupied spatial orbit q, the corresponding qubit indexed by p = 2q is initialized to the state |1>, which indicates the double occupancy of the corresponding spatial orbit, and for all other qubits, the qubits are initialized to the state |0>. For example, the initial portion of the quantum circuit may include initializing an operation such that the states of the qubits are initialized based on the double occupancy of the spatial orbits such that they are indicated by a reference HF state.

[0124] For example, for the HF state |110000> that defines spin - orbit occupancy (where the first two 1s indicate a pair of occupied spin orbits corresponding to the same spatial orbit and the four 0s correspond to two pairs of unoccupied virtual spin orbits of the chemical system), it is processed to provide double occupancy of the spatial - orbit reference state |100>, which indicates that the first spatial orbit is doubly occupied and the second and third spatial orbits are unoccupied. In one exemplary embodiment, these spatial - orbit occupancies are mapped to the qubits (indexed by p = 2q) having even indices in the quantum circuit by applying Pauli - X gates to provide the qubit state |100000>. In one exemplary embodiment, quantum - state synthesis encodes the (double) occupancy of the spatial orbits of the chemical system, rather than the occupancy of the spin orbits of the chemical system, into the qubits (e.g., qubits having even indices).

[0125] In step / operation 306, classical computing component 110 generates a spatially-excited synthesis portion of a quantum circuit. In various embodiments, an operator that excites a pair of electrons from a first spatial orbital to a second spatial orbital is transformed from a fermionic operator acting on individual spin orbitals (e.g., corresponding to a pair of spin orbitals) to a bosonic operator acting on spatial orbitals. The pair of electrons is excited together (e.g., as a pair), and the pair of electrons can be approximated as hard-core bosons (e.g., as entities having integer spin). In other words, a double-electron excitation operator corresponding to a pair of electrons excited from one spatial orbital to another spatial orbital

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[0126] Thus, the double-electron spatial orbital excitation operator of the chemical system's operator representation (e.g., the effective Hamiltonian)

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[0127] In step / operation 308, classical computing component 110 processes spatial excitation synthesis. The initial portion of the quantum circuit initializes qubits with even indices to represent double occupancy of spatial orbitals. The second portion of the quantum circuit performs an excitation operation corresponding to exciting an electron from a doubly-occupied spatial orbital to a previously unoccupied spatial orbital. Here, classical computing component 110 generates a third portion of the quantum circuit that changes the representation of the qubits. For example, the third portion of the quantum circuit changes the semantic meaning of the qubit states such that each qubit corresponds to the occupancy of its respective spin orbital.

[0128] For example, if the state of the qubit indexed by p = 2q is |1> at the end of the second portion of the quantum circuit, the corresponding spatial orbital q is doubly occupied, and the third portion of the quantum circuit sets the qubit indexed by p = 2q + 1 to the state |1>, while maintaining the qubit indexed by p = 2q in the state |1> to indicate that both spin orbitals corresponding to spatial orbital q are occupied.

[0129] Realistically, at the end of the second portion of the quantum circuit, the state of the qubit indexed by p = 2q is a superposition of the |1> state and the |0> state given by a|0> + b|1>, where a 2 + b 2It is equal to 1. The third part of the quantum circuit makes the qubit indexed by p = 2q + 1 have the same state as the qubit indexed by p = 2q for the qubits corresponding to the spatial orbitals q that were doubly occupied or unoccupied in the HF reference state.

[0130] In step / operation 310, the classical computing component 110 introduces spin-orbit on the quantum circuit. For example, the classical computing component 110 generates a fourth part of the quantum circuit that introduces spin-orbit on the quantum circuit. The fourth part of the quantum circuit initializes the qubits corresponding to the spatial orbitals that were singly occupied in the HF reference state. The initial, second, and third parts of the quantum circuit do not act on those qubits and / or do not perform quantum gates on them other than initializing the qubits corresponding to the singly occupied spatial orbitals (by the HF reference state) to the |0> state. The fourth part of the quantum circuit includes operations to switch the states of the qubits corresponding to the singly occupied spatial orbitals of the HF reference state to the state |1>0 to indicate the occupancy of their spin-orbit.

[0131] In step / operation 312, the classical computing component 110 uses a commuting set of double-excitation operators and single-excitation operators (e.g., as provided by tket in one exemplary embodiment) to synthesize the quantum circuit. For example, the classical computing component 110 generates a quantum circuit synthesis that includes a fifth part and a sixth part of the quantum circuit. In various embodiments, each chemical excitation corresponds to a commuting set of operators. In various embodiments, the commuting set of operators is a set of Pauli operators that commute with each other and are a transformed version of the excitation operators from the operator representation of the chemical system.

[0132] For example, using the commuting set of operators, the classical computing component 110 can perform any double-electron excitation operator

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[0133] In various embodiments, the application of any two-electron excitation operator

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[0134] In various embodiments, the application of any single-electron excitation operator

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[0135] In various embodiments, the classical computing component 110 generates a seventh part of the quantum circuit corresponding to performing a measurement operation to measure the state of the qubits after implementation of the sixth part of the quantum circuit. For example, the results of the measurement can form and / or be processed to form the qubit representation of the chemical system.

[0136] Accordingly, the classical computing component 110 generates a quantum circuit comprising an initial part of the quantum circuit, a second part of the quantum circuit, a third part of the quantum circuit, a fourth part of the quantum circuit, a fifth part of the quantum circuit, a sixth part of the quantum circuit, and optionally a seventh part of the quantum circuit. These parts of the quantum circuit are ordered as listed herein such that qubit operations corresponding to double-electron spatial orbital excitation operators are performed before any double-electron excitation operators, and any double-electron excitation operator is performed before any single-electron excitation operator.

[0137] Technical Advantages Generally, quantum computers are expected to enable accurate modeling and / or simulation of chemical systems. For example, quantum computers are expected to enable accurate modeling and / or simulation of chemical systems that are too complex for conventional classical techniques. However, currently operating quantum computing components, called NISQ devices as described above, tend to include a relatively small number of qubits (e.g., less than 100 qubits) and tend to be relatively noisy. As the depth (e.g., the number of layers of quantum gates) and / or the number of two-qubit quantum gates in a quantum circuit increase, the effect of noise on the resulting model or simulation also increases. In conventional techniques for generating quantum circuits for modeling and / or simulating chemical systems, the depth of the quantum circuit scales as O(n 4 ), where n is the number of spin orbitals included in the model and / or simulation. These lead to quantum circuits that include thousands of two-qubit quantum gates, which clearly exceed the capabilities of currently operable quantum computing components. Thus, there are technical problems regarding how to generate quantum circuits for modeling and / or simulating chemical systems that can be executed by currently operable quantum computing components.

[0138] Various embodiments provide technical solutions to these technical problems. Specifically, various embodiments use the symmetry of the chemical system to reduce the number of two-qubit quantum gates required to accurately model and / or simulate the chemical system. In various embodiments, the number of two-qubit quantum gates in the resulting quantum circuit is at least one-tenth less than the quantum circuit for modeling and / or simulating the same chemical system generated through conventional techniques. Thus, various embodiments bring improvements to the fields of chemical systems to be modeled and / or simulated, quantum chemistry, and / or quantum circuit generation.

[0139] Figure 6 provides a diagram of the controlled-NOT (CX) gate counts of quantum circuits used to model and / or simulate various chemical systems (e.g., OH, CH3, H 2O , CH4, and the transition state (TS) of CH3 and OH) for chemically-aware quantum circuit synthesis of an exemplary embodiment, conventional swap-set quantum circuit synthesis, and conventional naive quantum circuit synthesis. As can be seen in Figure 6, the number of two-qubit quantum gates (CX gates in the illustrated example) for each of the chemical systems is significantly reduced using the chemically-aware quantum circuit synthesis of the exemplary embodiment compared to conventional quantum circuit synthesis techniques. Thus, as shown in Figure 6, various embodiments provide improvements in the fields of chemical systems to be modeled and / or simulated, quantum chemistry, and / or quantum circuit generation.

[0140] Figure 7 provides a set of plots showing a comparison of the number of gates in a quantum circuit and an improvement in the relative error of the ground state energy determined based on the quantum circuit using an exemplary embodiment of the present disclosure and the swap-set technique. Panel a of Figure 7 shows the scaling of the two-qubit gate count for the chemical system CH4 for various active spaces of the chemical system (e.g., the number of qubits used to represent the active space) for an exemplary embodiment (labeled "chemically aware"), for the swap-set technique, and for individual techniques where the operational representation of the chemical system is directly or naively converted to a quantum circuit.

[0141] Panel b of FIG. 7 shows a comparison of two-qubit gate counts between an exemplary embodiment of the present disclosure (labeled "chemical recognition"), an exchange set technique, and an individual synthetic quantum circuit for a 10-qubit model. Panel c of FIG. 7 shows a comparison of two-qubit gate counts between an exemplary embodiment of the present disclosure (labeled "chemical recognition"), an exchange set technique, and an individual synthetic quantum circuit for a 6-qubit model. Panel d of FIG. 7 shows an improvement in the relative error of the ground state energy calculated on a noisy intermediate scale quantum (NISQ) era quantum computer using quantum circuits generated through an exemplary embodiment of the present disclosure (labeled "chemical recognition") and quantum circuits generated through an individual synthesis technique.

[0142] Exemplary controller In various embodiments, the hybrid quantum-classical computing system 100 includes a quantum computing component 130. The quantum computing component 130 is configured to perform various quantum computations and / or operations via the execution of one or more quantum circuits and / or algorithms. In various embodiments, the quantum computing component 130 is configured to control the operation of one or more components of the quantum computing component 130 (e.g., qubit manipulation elements 136, sensors 138), receive sensor signals indicative of measurement results captured by the sensors 138, and / or communicate with the classical computing component 110. The quantum computing component 130 optionally includes, but is not limited to, trapped ion qubits, cryogenically cooled Josephson junction qubits, or photonic qubits.

[0143] As shown in FIG. 4, in various embodiments, the controller 132 may include various controller elements, including a processing element 405, a memory 410, a driver controller element 415, a communication interface 420, an analog-to-digital converter element 425, and the like. For example, the processing element 405 may include one or more processing devices such as a complex programmable logic device (CPLD), a microprocessor, a coprocessing entity, an application-specific instruction set processor (ASIP), an integrated circuit, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), a programmable logic array (PLA), a hardware accelerator, other processing devices and / or circuits. The term circuit may refer to a purely hardware embodiment or a combination of hardware and a computer program product. In one exemplary embodiment, the processing element 405 of the controller 132 is a clock and / or communicates with a clock.

[0144] For example, the memory 410 may include non-transitory memory such as volatile and / or non-volatile memory storage, such as one or more of a hard disk, ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, and the like. In various embodiments, the memory 410 may store a queue of commands (e.g., an executable queue) to be executed to enable the execution of quantum algorithms and / or circuits, a qubit record corresponding to the qubits of the quantum computing components (e.g., in a qubit record data store, qubit record database, qubit record table, etc.), a calibration table, computer program code (e.g., in one or more computer languages, a dedicated controller language, etc.). In an exemplary embodiment, the execution of at least a portion of the computer program code stored in the memory 410 (e.g., by the processing element 405) causes the controller 132 to control the operation of one or more qubit operation elements 136, process sensor signals indicative of measurement results captured by the sensor 138, and / or communicate with the classical computing components 110 of the hybrid quantum-classical computing system 100 to perform one or more of the steps, operations, processes, procedures, etc. described herein.

[0145] In various embodiments, the driver controller element 410 may include one or more drivers and / or controller elements each configured to control one or more drivers. In various embodiments, the driver controller element 410 may comprise a driver and / or a driver controller. For example, the driver controller may be configured to cause one or more corresponding drivers to operate according to executable instructions, commands, etc. scheduled (e.g., by the processing element 405) and executed by the controller 132. In various embodiments, the driver controller element 415 may enable the controller 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.

[0146] In various embodiments, the controller 132 comprises means for communicating and / or receiving signals from one or more sensors (e.g., photodetectors, voltage / current sensors, temperature sensors, pressure sensors, and / or other sensors). For example, the controller 132 may comprise one or more analog-to-digital converter elements 425 configured to receive signals from one or more sensors.

[0147] In various embodiments, the controller 132 comprises a communication interface 420 for interfacing and / or communicating with the classical computing component 110 of the hybrid quantum-classical computing system 100. For example, the controller 132 receives from the classical computing component 110 one or more quantum circuits that model and / or simulate a chemical system, executable instructions, instruction sets, etc., and provides to the classical computing component 110 the output received from the quantum computing component 130 (e.g., via the sensor 138) and / or the result of processing the output to determine the qubit representation of the chemical system. 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.

[0148] Exemplary classical computing component FIG. 5 provides an exemplary schematic diagram representing an exemplary computing entity 10 that may be used with embodiments of the present invention. In various embodiments, the classical computing component 110 is configured to interface with the quantum computing component 130. For example, the classical computing component 110 is configured to interface with the quantum computing component 130 to enable an efficient and accurate modeling of a chemical system via execution of a quantum circuit in which the depth and / or the number of two-qubit quantum gates is reduced (compared to the corresponding quantum circuit generated via conventional quantum circuit synthesis techniques). For example, the classical computing component 110 may be configured to communicate with the quantum computing component 130 to enable a user (e.g., a human user or a program operating on the classical computing component 110) to provide an input to the quantum computing component 130 and receive, display, analyze, etc., the output from the quantum computing component 130.

[0149] As shown in FIG. 5, classical computing component 110 may include, respectively, an antenna 512, a transmitter 504 (e.g., wireless), a receiver 506 (e.g., wireless), and a processing element 508 that each provide signals to, and receive signals from, a transmitter 504 and a receiver 506. Signals provided to, and received from, the transmitter 504 and the receiver 506 may include signaling information / data according to the interface specifications of an applicable wireless system to communicate with various entities such as a controller 132, other classical computing components 110, and the like. 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.

[0150] For example, the classical computing component 110 can be configured to receive and / or provide communication using a wired data transmission protocol such as fiber distributed data interface (FDDI), digital subscriber line (DSL), Ethernet, asynchronous transfer mode (ATM), frame relay, data over cable service interface specification (DOCSIS), or any other wired transmission protocol.Similarly, the classical computing component 110 may be configured to communicate via a wireless external communication network using any of 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 standards to communicate using, for example, Border Gateway Protocol (BGP), Dynamic Host Configuration Protocol (DHCP), Domain Name System (DNS), File Transfer Protocol (FTP), Hypertext Transfer Protocol (HTTP), HTTP over TLS / SSL / Secure, Internet Message Access Protocol (IMAP), Network Time Protocol (NTP), Simple Mail Transfer Protocol (SMTP), Telnet, Transport Layer Security (TLS), Secure Sockets Layer (SSL), Internet Protocol (IP), Transmission Control Protocol (TCP), User Datagram Protocol (UDP), Datagram Congestion Control Protocol (DCCP), Stream Control Transmission Protocol (SCTP), HyperText Markup Language (HTML), etc.

[0151] Through 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.

[0152] In various embodiments, the classical computing component 110 may comprise, for example, a network interface 520 for interfacing with and / or communicating with the controller 132. For example, the classical computing component 110 provides qubit constraint information, executable instructions, instruction sets, etc. for reception by the controller 132, and / or comprises a network interface 520 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 can communicate directly via wired and / or wireless connections and / or via one or more wired and / or wireless networks 120.

[0153] In various embodiments, processing element 508 may comprise one or more processing devices, such as a Complex Programmable Logic Device (CPLD), a microprocessor, a coprocessing entity, an Application Specific Instruction Set Processor (ASIP), an integrated circuit, an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA), a Programmable Logic Array (PLA), a hardware accelerator, a Graphics Processing Unit (GPU), a Central Processing Unit (CPU), other processing devices, and / or circuitry. The term circuitry may refer to purely hardware embodiments or combinations of hardware and computer program products.

[0154] The classical computing component 110 may also include a user interface device having one or more user input / output interfaces (e.g., a display 516 and / or speaker / speaker driver coupled to the processing element 508, and a touch screen, keyboard, mouse, and / or microphone coupled to the processing element 508). For example, the user output interface is configured to provide applications, browsers, user interfaces, interfaces, dashboards, screens, web pages, pages, 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 include any of a number of devices that enable the computing entity 10 to receive data, such as a keypad 518 (hard or soft), a touch display, a mouse, a voice / speech or motion interface, a scanner, a reader, or other input device. In embodiments including the keypad 518, the keypad 518 may include (or cause the display of) conventional numbers (0-9) and associated keys (#, *), and other keys used to operate the classical computing component 110, and may include a set of keys that can be driven to provide a complete set of alphabetic keys or a complete set of alphanumeric keys. In addition to providing input, the user input interface may be used to enable or disable certain functions, such as a screen saver and / or sleep mode. Through such input, the classical computing component 110 can collect information / data, user interactions / inputs, etc.

[0155] The classical computing component 110 may also include volatile storage or memory 522 and / or non-volatile storage or memory 524, which may be embedded and / or removable. For example, non-volatile memory can be ROM, PROM, EPROM, EEPROM, flash memory, MMC, SD memory card, memory stick, CBRAM, PRAM, FeRAM, RRAM, SONOS, racetrack memory, etc. Volatile memory can be RAM, DRAM, SRAM, FPM DRAM, EDO DRAM, SDRAM, DDR SDRAM, DDR2 SDRAM, DDR3 SDRAM, RDRAM, RIMM, DIMM, SIMM, VRAM, cache memory, register memory, etc. Volatile and non-volatile storage or memory can store databases, database instances, database management system entities, data, applications, programs, program modules, scripts, source code, object code, bytecode, compiled code, interpreted code, machine code, executable instructions, etc. to implement the functions of the classical computing component 110.

[0156] In any of the above aspects, various features can be implemented in hardware or as software modules executed on one or more processors / computers.

[0157] 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 on 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.

[0158] For example, the present disclosure is extended to a computer program comprising executable instructions which, when executed by a hybrid quantum-classical computing system, cause the hybrid quantum-classical computing system to (i) determine characterization parameters describing a chemical system, wherein the characterization parameters are at least partially based on the chemical structure of the chemical system, (ii) generate an operator representation of the chemical system, including a single-electron excitation operator and a double-electron excitation operator, and (iii) reconfigure the order of the appearance of the single-electron excitation operator and the double-electron excitation operator in the operator representation according to the characterization parameters, and the simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on a quantum computing component used to perform the simulation.

[0159] Conclusion Many modifications and other embodiments of the invention described herein will come to mind to those skilled in the art related to the invention who benefit from the teachings presented in the above description and the related drawings. Accordingly, 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 only for the meaning of general description and not for limitation.

Explanation of Signs

[0160] 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 405 Processing element 410 Memory 415 Driver controller element 420 Communication interface 425 Analog-to-digital converter 504 Transmitter 506 Receiver 508 Processing element 512 Antenna 516 Display 518 Keypad 520 Network interface 522 Volatile memory 524 Non-volatile memory

Claims

1. A hybrid quantum-classical computing system configured to perform a chemical simulation, the hybrid quantum-classical computing system comprising a classical computing component coupled to a quantum computing component, the hybrid quantum-classical computing system being (i) determining characterization parameters that describe the chemical system, the characterization parameters being at least partially based on the chemical structure of the chemical system; (ii) generating an operator representation of the chemical system, including a single-electron excitation operator and a two-electron excitation operator; (iii) reordering the occurrences of the single-electron excitation operator and the two-electron excitation operator in the operator representation according to the characterization parameters configured to perform, the simulation being executable using fewer two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation. A hybrid quantum-classical computing system.

2. The hybrid quantum-classical computing system reorders the occurrences of the single-electron excitation operator and the two-electron excitation operator to (i) a two-excitation operator corresponding to a two-excitation from a certain spatial orbital to a corresponding spatial orbital, (ii) any two-excitation operator, and (iii) any single-excitation operator configured to reconstruct to, the hybrid quantum-classical computing system according to claim 1.

3. The hybrid quantum-classical computing system determines the characterization parameters that describe the chemical system, (i) applying symmetry filtering to the operator representation of the chemical system to evaluate its structural symmetry; (ii) generating a quantum state synthesis of the chemical system based on the symmetry; (iii) generating a spatial excitation synthesis of the chemical system from the quantum state synthesis using a hardcore boson operator; (iv) processing the spatial excitation synthesis by converting from a spatial orbital to a spin orbital therein; (v) introducing spin orbitals on the at least one quantum circuit, and (vi) using a set of double-excitation operators and single-excitation operators to synthesize the at least one quantum circuit such that the double-excitation operators appear in the at least one quantum circuit before the single-excitation operators appear in the at least one quantum circuit and each exchange set corresponds to an excitation of the chemical system The hybrid quantum-classical computing system according to claim 1 or 2, configured to generate a corresponding operator representation thereby. **Claim 4** The hybrid quantum-classical computing system according to claim 3, configured to reduce the number of quantum gates required in the quantum circuit synthesis according to the structural symmetry degree of the chemical system. **Claim 5** Applying the symmetry filtering to the operator representation can define a set of symmetries of the chemical system and identify the excitation operators of the operator representation of the chemical system that do not commute with one or more of the symmetries in the set of symmetries, or define the Abelian point group of the chemical system and identify the redundant excitations of the chemical system based on the Abelian point group The hybrid quantum-classical computing system according to claim 3 or 4, comprising at least one of the above. **Claim 6** Generating the quantum state synthesis of the chemical system comprises generating a reference state based on the doubly occupied spatial orbitals and virtual spatial orbitals of the chemical system. The hybrid quantum-classical computing system according to any one of claims 3 to 5. **Claim 7** Generating the spatial excitation synthesis comprises converting an inter-spatial-orbital operator into an inter-double-excitation-spatial-qubit operator. The hybrid quantum-classical computing system according to any one of claims 3 to 6. **Claim 8** Generating the quantum circuit synthesis comprises converting the double-excitation operator of the chemical system corresponding to double excitations other than double excitations between spatial orbitals into an arbitrarily double-excitation qubit operator encoded by Jordan-Wigner configured to act on four or more qubits. The hybrid quantum-classical computing system according to claim 7. **Claim 9** The hybrid quantum-classical computing system is configured to compile the quantum circuit synthesis into a quantum circuit capable of executing the quantum circuit synthesis, and the quantum circuit synthesis sequentially includes an operator between double-excitation space qubits, any double-excitation qubit operator encoded by Jordan-Wigner, and a single-excitation qubit operator. The hybrid quantum-classical computing system according to claim 8.

10. The hybrid quantum-classical computing system is further configured to cause the quantum computing component to execute at least one of the at least one quantum circuit to determine at least one of the wave function of the chemical system, 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 according to any one of claims 1 to 9.

11. The hybrid quantum-classical computing system is further configured to cause the classical computing component to perform at least one of (a) displaying a graphical representation of at least a part of the simulation of the chemical system, or (b) generating and storing in classical memory a file comprising one or more parameters of the simulation of the chemical system. The hybrid quantum-classical computing system according to claim 10.

12. The operator representation is generated using a unitary coupled cluster singles and doubles (UCCSD) ansatz. The hybrid quantum-classical computing system according to any one of claims 1 to 11.

13. A method for using a hybrid quantum-classical computing system to perform a simulation of a chemical system, the hybrid quantum-classical computing system comprising a classical computing component coupled to a quantum computing component, the method comprising: (i) determining characterization parameters that describe the chemical system, the characterization parameters being at least partially based on the chemical structure of the chemical system; (ii) generating an operator representation of the chemical system, including a single-electron excitation operator and a double-electron excitation operator; (iii) reordering the occurrences of the single-electron excitation operator and the double-electron excitation operator in the operator representation according to the characterization parameters A method comprising, and the simulation being executable using fewer two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation.

14. The order of the appearance of the single-electron excitation operator and the double-electron excitation operator is (i) a double-excitation operator corresponding to a double excitation from a certain spatial orbital to a corresponding spatial orbital, (ii) any double-excitation operator, and (iii) any single-excitation operator The method according to claim 13, which is reconfigured to.

15. The system determines the characterization parameters that describe the chemical system, (i) applying symmetry filtering to the operator representation of the chemical system to evaluate its structural symmetry degree, (ii) generating quantum state synthesis of the chemical system based on the symmetry degree, (iii) using a hardcore boson operator to generate spatial excitation synthesis of the chemical system from the quantum state synthesis, (iv) processing the spatial excitation synthesis by converting from a spatial orbital to a spin orbital therein, (v) introducing spin orbitals on the at least one quantum circuit, and (vi) the double-excitation operator appears on the at least one quantum circuit before the single-excitation operator appears on the at least one quantum circuit, and using the exchange set of the double-excitation operator and the single-excitation operator to synthesize the at least one quantum circuit so that each exchange set corresponds to an excitation of the chemical system The method according to claim 13 or 14, which is configured to generate a corresponding operator representation.

16. The hybrid quantum chemistry calculation system is configured to reduce the number of controlled NOT gates required in the quantum circuit synthesis according to the structural symmetry degree of the chemical system, Applying the symmetry filtering to the operator representation includes defining a set of symmetries of the chemical system and identifying excitation operators of the operator representation of the chemical system that are not commutative with one or more of the symmetries in the set of symmetries. Applying the symmetry filtering to the operator representation includes defining an Abelian point group of the chemical system and identifying redundant excitations of the chemical system based on the Abelian point group. generating the quantum state synthesis of the chemical system comprising generating a reference state based on the doubly occupied spatial orbitals and virtual spatial orbitals of the chemical system; generating the spatial excitation synthesis comprising converting an inter-spatial orbital operator into an inter-doubly excited spatial qubit operator; or the quantum circuit synthesis comprising converting the double excitation operator of the chemical system corresponding to a double excitation other than a double excitation from a spatial orbital to a spatial orbital into an arbitrarily double excited qubit operator encoded by Jordan-Wigner configured to act on four or more qubits The method according to claim 15, comprising at least one of the above.

17. The method according to claim 16, further comprising the step of compiling the quantum circuit synthesis into an executable quantum circuit, wherein the quantum circuit synthesis sequentially comprises the inter-doubly excited spatial qubit operator, the arbitrarily double excited qubit operator encoded by Jordan-Wigner, and a single excited qubit operator.

18. executing the at least one quantum circuit by the quantum computing component to determine at least one of a wave function of the chemical system, a structural property of the chemical system, a chemical interaction property of the chemical system, or a reaction property of the chemical system; and causing the classical computing component to perform at least one of (a) displaying a graphical representation of at least a portion of a model of the chemical system, or (b) generating and storing in classical memory a file comprising one or more parameters of a model of the chemical system The method according to any one of claims 13 to 17, further comprising the above.

19. The method according to any one of claims 13 to 18, wherein the operator representation is generated using a unitary coupled cluster singles and doubles (UCCSD) ansatz.

20. A computer program product comprising at least one non-transitory computer-readable medium storing executable instructions, which when executed by a hybrid quantum-classical computing system, cause the hybrid quantum-classical computing system to (i) Determining characterization parameters that describe the chemical system, wherein the characterization parameters are at least partially based on the chemical structure of the chemical system; (ii) Generating an operator representation of the chemical system, including a single-electron excitation operator and a two-electron excitation operator; (iii) Reordering the occurrences of the single-electron excitation operator and the two-electron excitation operator in the operator representation according to the characterization parameters configured to cause, wherein the simulation is executable using a smaller number of two-qubit quantum gates used in at least one quantum circuit executable on the quantum computing component used to perform the simulation, a computer program product.

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