Improved Accuracy for Trotter Simulations Using Chebyshev Interpolation

Journal Article · 25 February 2024 · Quantum

DOI: https://doi.org/10.22331/q-2024-02-26-1266 · OSTI ID:2311917

Rendon, Gumaro ^[1]; Watkins, Jacob ^[2]; Wiebe, Nathan ^[3]

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1. Zapata Computing Inc., Boston, MA 02110, USA
2. Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824, USA
3. Department of Computer Science, University of Toronto, Toronto, ON M5S 2E4, Canada, Pacific Northwest National Laboratory, Richland, WA 99352, USA

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.

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0023658; SC0012704
• OSTI ID: 2311917
• Journal Information: Quantum, Journal Name: Quantum Vol. 8; ISSN 2521-327X
• Publisher: Verein zur Forderung des Open Access Publizierens in den QuantenwissenschaftenCopyright Statement
• Country of Publication: Austria
• Language: English