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

• URL: http://arxiv.org/abs/2307.10327v2
• Date: Thu, 20 Jun 2024 06:22:34 GMT
• Title: Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
• Authors: Hongzheng Zhao, Marin Bukov, Markus Heyl, Roderich Moessner,
• Abstract summary: Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. We present an adaptive Trotterization algorithm to cope with time-dependent Hamiltonians. 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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