Probabilistic imaginary-time evolution by using forward and backward real-time evolution with a single ancilla: first-quantized eigensolver of quantum chemistry for ground states

TL;DR

This paper introduces a single-ancilla probabilistic imaginary-time evolution method that leverages forward and backward real-time evolution gates, enabling efficient ground state and finite-temperature state calculations in quantum chemistry.

Contribution

The authors propose a novel PITE approach using only one ancilla qubit and real-time evolution gates, facilitating first-quantized quantum eigensolver applications for quantum chemistry.

Findings

Validated on several systems demonstrating effectiveness

Allows transfer of existing RTE algorithms to ITE

Enables computation of Gibbs states and partition functions

Abstract

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.