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Digital quantum simulation relies on Trotterization to discretize timeevolution into elementary quantum gates. On current quantum processors withnotable gate imperfections, there is a critical tradeoff between improvedaccuracy for finer timesteps, and increased error rate on account of the largercircuit depth. We present an adaptive Trotterization algorithm to cope withtime-dependent Hamiltonians, where we propose a concept of instantaneous"conserved" quantities to estimate errors in the time evolution between two(nearby) points in time; these allow us to bound the errors accumulated overthe full simulation period. They reduce to standard conservation laws in thecase of time-independent Hamiltonians, for which we first developed an adaptiveTrotterization scheme. We validate the algorithm for a time-dependent quantumspin chain, demonstrating that it can outperform the conventional Trotteralgorithm with a fixed step size at a controlled error.

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