Quantum Algorithm to Prepare Quasi-Stationary States

• URL: http://arxiv.org/abs/2407.07893v1
• Date: Wed, 10 Jul 2024 17:59:26 GMT
• Title: Quantum Algorithm to Prepare Quasi-Stationary States
• Authors: Samuel J. Garratt, Soonwon Choi,
• Abstract summary: We present an efficient quantum search algorithm which produces quasi-stationary states in a dense many-body spectrum. In time scaling with system size, the algorithm produces states with inverse energy, which can be used to analyze many-body dynamics out to times. We discuss how this algorithm can be used as a primitive to investigate the mechanisms underlying thermalization transformations and hydrodynamics in many-body quantum systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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