Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation

Abstract

Quantum metrology allows for measuring properties of a quantum system at the optimal Heisenberg limit. However, when the relevant quantum states are prepared using digital Hamiltonian simulation, the accrued algorithmic errors will cause deviations from this fundamental limit. In this work, we show how algorithmic errors due to Trotterized time evolution can be mitigated through the use of standard polynomial interpolation techniques. Our approach is to extrapolate to zero Trotter step size, akin to zero-noise extrapolation techniques for mitigating hardware errors. We perform a rigorous error analysis of the interpolation approach for estimating eigenvalues and time-evolved expectation values, and show that the Heisenberg limit is achieved up to polylogarithmic factors in the error. Our work suggests that accuracies approaching those of state-of-the-art simulation algorithms may be achieved using Trotter and classical resources alone for a number of relevant algorithmic tasks.

67 pages, 6 figures

References in corpus (4)

• The Magnus expansion and some of its applications
• Simulating Hamiltonian dynamics with a truncated Taylor series
• Entanglement-free Heisenberg-limited phase estimation
• On the complexity of implementing Trotter steps

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• High-fidelity initialization a logical qubit with multiple injections
• On the commutator scaling in Hamiltonian simulation with multi-product formulas
• Direct Analysis of Zero-Noise Extrapolation: Polynomial Methods, Error Bounds, and Simultaneous Physical-Algorithmic Error Mitigation