Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws

Fuente: arXiv
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Main Authors: Zhao, Hongzheng, Bukov, Marin, Heyl, Markus, Moessner, Roderich
Format: Preprint
Published: 2023
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author Zhao, Hongzheng
Bukov, Marin
Heyl, Markus
Moessner, Roderich
author_facet Zhao, Hongzheng
Bukov, Marin
Heyl, Markus
Moessner, Roderich
contents Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer timesteps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time-dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time-independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [PRX Quantum 4, 030319]. We validate the algorithm for a time-dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
format Preprint
id arxiv_https___arxiv_org_abs_2307_10327
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
Zhao, Hongzheng
Bukov, Marin
Heyl, Markus
Moessner, Roderich
Quantum Physics
Quantum Gases
Statistical Mechanics
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer timesteps, and increased error rate on account of the larger circuit depth. We present an adaptive Trotterization algorithm to cope with time-dependent Hamiltonians, where we propose a concept of piecewise "conserved" quantities to estimate errors in the time evolution between two (nearby) points in time; these allow us to bound the errors accumulated over the full simulation period. They reduce to standard conservation laws in the case of time-independent Hamiltonians, for which we first developed an adaptive Trotterization scheme [PRX Quantum 4, 030319]. We validate the algorithm for a time-dependent quantum spin chain, demonstrating that it can outperform the conventional Trotter algorithm with a fixed step size at a controlled error.
title Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
topic Quantum Physics
Quantum Gases
Statistical Mechanics
url https://arxiv.org/abs/2307.10327