Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer

• URL: http://arxiv.org/abs/2210.09883v2
• Date: Fri, 3 Nov 2023 16:56:36 GMT
• Title: Exhaustive search for optimal molecular geometries using imaginary-time evolution on a quantum computer
• Authors: Taichi Kosugi, Hirofumi Nishi, Yuichiro Matsushita
• Abstract summary: We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states. We show that the circuit depth scales as O (n_e2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a nonvariational scheme for geometry optimization of molecules for the first-quantized eigensolver, a recently proposed framework for quantum chemistry using the probabilistic imaginary-time evolution (PITE) on a quantum computer. While the electrons in a molecule are treated in the scheme as quantum mechanical particles, the nuclei are treated as classical point charges. We encode both electronic states and candidate molecular geometries as a superposition of many-qubit states, leading to quantum advantage. The histogram formed by outcomes of repeated measurements gives the global minimum of the energy surface. We demonstrate that the circuit depth scales as O (n_e^2 poly(log n_e)) for the electron number n_e, which can be reduced to O (n_e poly(log n_e)) if extra O (n_e log n_e) qubits are available. We corroborate the scheme via numerical simulations. The new efficient scheme will be helpful for achieving scalability of practical quantum chemistry on quantum computers. As a special case of the scheme, a classical system composed only of charged particles is admitted. We also examine the scheme adapted to variational calculations that prioritize saving circuit depths for noisy intermediate-scale quantum (NISQ) devices.

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