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

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