  Imaginary-time evolution (ITE) on a quantum computer is a promising formalism
for obtaining the ground state of a quantum system. As a kind of it, the
probabilistic ITE (PITE) takes advantage of measurements to implement the
nonunitary operations. We propose a new approach of PITE which requires only a
single ancillary qubit. Under a practical approximation, the circuit is
constructed from the forward and backward real-time evolution (RTE) gates as
black boxes, generated by the original many-qubit Hamiltonian. All the
efficient unitary quantum algorithms for RTE proposed so far and those in the
future can thus be transferred to ITE exactly as they are. Our approach can
also be used for obtaining the Gibbs state at a finite temperature and the
partition function. We apply the approach to several systems as illustrative
examples to see its validity. We also discuss the application of our approach
to quantum chemistry by focusing on the scaling of computational cost, leading
to a novel framework denoted by first-quantized quantum eigensolver.
