| CPC G06N 10/00 (2019.01) [G06F 9/455 (2013.01); G06F 17/16 (2013.01)] | 20 Claims |
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1. A method performed by a hybrid quantum-classical computing device for a quantum simulation of a physical system characterized by a respective Hamiltonian, the method comprising:
selecting, by one or more classical processors included in the hybrid quantum-classical computing device, a first set of basis functions for the quantum simulation, wherein the first set of basis functions comprises i) an active set of orbitals, and ii) a virtual set of orbitals;
defining, by the one or more classical processors, a set of expansion operators for the quantum simulation, wherein expansion operators in the set of expansion operators approximate fermionic excitations in an active space spanned by the active set of orbitals and a virtual space spanned by the virtual set of orbitals and act on both qubits that define the active space and additional qubits that define the virtual space;
performing multiple quantum computations to determine a matrix representation of the Hamiltonian in a second set of basis functions, wherein each basis function in the second set of basis functions comprises a respective expansion operator applied to a wavefunction prepared using the qubits that define the active space, and wherein determining the matrix representation of the Hamiltonian comprises, for each of one or more matrix elements:
determining, by the one or more classical processors, that the matrix element comprises operators that act on the virtual space,
in response to determining that the matrix element comprises operators that act on the virtual space, performing, by the one or more classical processors, a classical computation to contract the matrix element to a matrix element comprising operators that act on the active space only, and
preparing the qubits that define the active space in a quantum state that represents the wavefunction and measuring, by a quantum computing device included in the hybrid quantum-classical computing device and using the quantum state, the operators that act on the active space only to determine a value for the matrix element that comprises contributions from the virtual space that extend beyond the active space without requiring the additional qubits that define the virtual space;
computing, by the one or more classical processors and using the determined matrix representation of the Hamiltonian in the second set of basis functions, eigenvalues and eigenvectors of the Hamiltonian; and
determining, by the one or more classical processors, properties of the physical system using the computed eigenvalues and eigenvectors.
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