Imaginary-time evolution with a single ancilla: first-quantized eigensolver for electronic structure calculation in quantum chemistry

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, it can avoid the restriction of dynamics to a low-dimensional subspace imposed by variational

parameters unlike other types of ITE.In this study, we propose a new PITE approach that uses only one ancillary qubit. Unlike the existing PITE approaches, the new one under a practical approximation constructs the circuit from forward and backward real-time evolution gates. 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 novel framework referred to as a first-quantized eigensolver (FQE). The nonvariational generic approach will expand the scope of practical quantum computation for versatile objectives.