Geometric optimization based on first-quantized Hamiltonian using imaginary-time evolution on a quantum computer*

Quantum computation has been thought of as a promising alternative to classical one due to its expressing power for encoding spatial grids of a wave function. Recently, a nonvariational approach for calculating the ground state in the many body problems has been presented, called the imaginary-time evolution (PITE) method. In this work, we propose a quantum algorithm employing the PITE technique for the geometry optimization of molecules based on the first quantization Hamiltonian. In the proposed framework, we treat the nuclei as classical point charges while the electrons treat as quantum mechanical particles and employ an exhaustive search from the geometric candidates. The encoding of nuclei as classical point charges is efficient because we alleviate to prepare huge qubits for expressing femtometer scale wave functions. We obtain a histogram that gives the global minimum of the energy surface from the repeated measurements of the output state generated by the PITE circuit. We hope that the proposed scheme could be helpful in realizing practical quantum computation for quantum chemistry.