Optimal/Nearly-optimal simulation of multi-periodic time-dependent Hamiltonians

TL;DR

This paper introduces a quantum algorithm based on quantum eigenvalue transformation for efficiently simulating multi-periodic time-dependent Hamiltonians, including Floquet and quasiperiodic systems, with near-optimal query complexity.

Contribution

It extends existing quantum simulation techniques to handle multi-periodic time-dependent Hamiltonians with optimal or nearly-optimal query complexity.

Findings

Achieves optimal/nearly-optimal query complexity in simulation

Handles a broad class of time-dependent Hamiltonians including Floquet systems

Uses simple oracles similar to time-independent Hamiltonian simulation

Abstract

Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singularvalue transformation with the optimal query complexity in time $t$ and desirable accuracy $\varepsilon$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians with optimal/nearly-optimal query complexity both in time $t$ and desirable accuracy $\varepsilon$, and simple oracles as well as the optimal algorithm for time-independent cases.