Adaptive Trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws
arXiv:2307.10327 · doi:10.1103/PhysRevLett.133.010603
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 (32)
- Equilibrium states of generic quantum systems subject to periodic driving
- Nonthermal pathways to ultrafast control in quantum materials
- The randomized measurement toolbox
- A Race Track Trapped-Ion Quantum Processor
- Demonstration of fault-tolerant universal quantum gate operations
- Information Scrambling in Computationally Complex Quantum Circuits
- Quantum simulation of time-dependent Hamiltonians and the convenient illusion of Hilbert space
- Digital quantum simulation of spin models with circuit quantum electrodynamics
- Real- and imaginary-time evolution with compressed quantum circuits
- Continuous Symmetry Breaking in a Two-dimensional Rydberg Array
- Efficient estimation of Pauli observables by derandomization
- Digital quantum simulation of open quantum systems using quantum imaginary time evolution
- Adaptive Variational Quantum Dynamics Simulations
- Realizing a dynamical topological phase in a trapped-ion quantum simulator
- Classically optimized Hamiltonian simulation
- Calibrated decoders for experimental quantum error correction
- Quantum and classical Floquet prethermalization
- Quantum simulation of open quantum systems in heavy-ion collisions
- Experimental simulation of open quantum system dynamics via Trotterization
- Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
- Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure
- Variational Hamiltonian simulation for translational invariant systems via classical pre-processing
- Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
- Time-dependent Hamiltonian Simulation of Highly Oscillatory Dynamics and Superconvergence for Schrödinger Equation
- Optimal compression of quantum many-body time evolution operators into brickwall circuits
- Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning
- Quantum algorithm for time-dependent Hamiltonian simulation by permutation expansion
- Self-healing of Trotter error in digital adiabatic state preparation
- Low-depth Hamiltonian Simulation by Adaptive Product Formula
- Problem specific classical optimization of Hamiltonian simulation
- Fermionic correlation functions from randomized measurements in programmable atomic quantum devices
- Minimum Trotterization Formulas for a Time-Dependent Hamiltonian
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- Measuring Trotter error and its application to precision-guaranteed Hamiltonian simulations
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- Statistics of topological defects across a phase transition in a digital superconducting quantum processor
- Unifying framework for quantum simulation algorithms for time-dependent Hamiltonian dynamics
- 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