Quantum Imaginary-Time Evolution with Polynomial Resources in Evolution Time

Abstract

Imaginary-time evolution is fundamental for analyzing quantum many-body systems, with applications spanning quantum chemistry, condensed matter physics, and quantum field theory, 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 query complexity in the system size. To our knowledge, this is the first quantum algorithm for imaginary-time evolution with provably polynomial resource scaling in evolution time. 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 can reduce circuit depth in certain regimes compared with existing methods, at the expense of higher total query complexity, advancing the practical feasibility of quantum simulation on early fault-tolerant devices.