Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
arxiv(2023)
摘要
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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