Quantum Algorithm to Prepare Quasi-Stationary States

TL;DR

This paper introduces a quantum algorithm that efficiently prepares quasi-stationary states within dense many-body spectra, enabling analysis of quantum dynamics at finite temperatures with polynomial time scaling.

Contribution

The work presents a novel quantum search algorithm using quantum singular value transformations that achieves quadratic speedup for preparing thermal-like states in many-body systems.

Findings

Algorithm produces states with inverse polynomial energy width.

States enable analysis of many-body dynamics up to polynomial times.

Provides a primitive for studying thermalization mechanisms.

Abstract

Quantum dynamics can be analyzed via the structure of energy eigenstates. However, in the many-body setting, preparing eigenstates associated with finite temperatures requires time scaling exponentially with system size. In this work we present an efficient quantum search algorithm which produces quasi-stationary states, having energies supported within narrow windows of a dense many-body spectrum. In time scaling polynomially with system size, the algorithm produces states with inverse polynomial energy width, which can in turn be used to analyze many-body dynamics out to polynomial times. The algorithm is based on quantum singular value transformations and quantum signal processing, and provides a quadratic speedup over measurement-based approaches. We discuss how this algorithm can be used as a primitive to investigate the mechanisms underlying thermalization and hydrodynamics in many-body quantum systems.