Imaginary-time evolution using forward and backward real-time evolution with a single ancilla: First-quantized eigensolver algorithm for quantum chemistry

Abstract

Imaginary-time evolution (ITE) on a quantum computer is a promising formalism for obtaining the ground state of a quantum system. The probabilistic ITE (PITE) exploits measurements to implement nonunitary operations, and it can avoid the restriction of dynamics to a low-dimensional subspace imposed by variational parameters unlike other types of ITE. In this paper, we propose a PITE approach that uses only one ancillary qubit. Unlike the existing PITE approaches, the one proposed here constructs, under a practical approximation, the circuit from forward and backward real-time evolution (RTE) gates as black boxes for the original Hamiltonian. Thus all efficient unitary algorithms for RTE can be transferred to the ITE without any modifications. Our approach can be used to obtain the Gibbs state at a finite temperature and partition function. We validate the approach via several illustrative systems where the trial states are found to converge rapidly to the ground states. In addition, we discuss its applicability to quantum chemistry by focusing on the scaling of computational cost; this leads to the development of a framework referred to as a first-quantized eigensolver. The nonvariational generic approach will expand the scope of practical quantum computation for versatile objectives.