Quantum Imaginary-Time Evolution with Polynomial Resources in Time

TL;DR

This paper introduces a quantum algorithm for imaginary-time evolution that maintains high success probability over long times, uses polynomial resources, and is effective for ground-state and open system simulations.

Contribution

The authors develop a stable, efficient quantum algorithm for imaginary-time evolution with polynomial resource scaling and broad applicability to quantum many-body problems.

Findings

Algorithm achieves polynomial accuracy with polynomial gates

Success probability remains stable over long evolution times

Numerical validation up to evolution time of 50

Abstract

Imaginary-time evolution is fundamental for analyzing quantum many-body systems, yet classical simulation requires exponentially growing resources in both system size and evolution time. While quantum approaches reduce the system-size scaling, existing methods rely on heuristic techniques with measurement precision or success probability that deteriorates as evolution time increases. We present a quantum algorithm that prepares normalized imaginary-time evolved states using an adaptive normalization factor to maintain a stable success probability over long imaginary-time intervals. Our algorithm approximates the target state with error polynomially small in the inverse imaginary time using a polynomial number of elementary quantum gates and a single ancilla qubit, with success probability close to one. When the initial state has reasonable overlap with the ground state, this algorithm also achieves polynomial resource cost in the system size. Numerical experiments validate our theoretical analysis for evolution time up to 50, demonstrating the algorithm's effectiveness for long-time evolution. Building on this technique, we further develop imaginary-time-evolution-based algorithms for ground-state-related problems and for simulating open quantum systems. These algorithms reduce circuit depth compared with existing methods and illustrate the effectiveness of imaginary-time evolution in early fault-tolerant quantum computing.