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

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.

7+5pages, 5+2 figures. Accepted in PRL

References in corpus (6)

• Equilibrium states of generic quantum systems subject to periodic driving
• Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
• Digital quantum simulation of spin models with circuit quantum electrodynamics
• Experimental simulation of open quantum system dynamics via Trotterization
• Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
• Problem specific classical optimization of Hamiltonian simulation

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• Effective (Floquet) Lindblad generators from spectral unwinding
• Prospects for NMR Spectral Prediction on Fault-Tolerant Quantum Computers
• Correcting and extending Trotterized quantum many-body dynamics
• Single-Period Floquet Control of Bosonic Codes with Quantum Lattice Gates