Observable-Driven Speed-ups in Quantum Simulations

TL;DR

This paper demonstrates how leveraging observable knowledge can significantly reduce errors and gate counts in quantum simulations, enhancing efficiency for near-term quantum devices.

Contribution

It introduces observable-driven methods to optimize product formulas, achieving size-independent errors and quadratic error reductions for specific observables.

Findings

Observable knowledge reduces simulation errors and gate counts.

Tailored product formulas achieve size-independent errors for local/global observables.

Quadratic error reductions are achieved for observables with evenly distributed Pauli coefficients.

Abstract

As quantum technology advances, quantum simulation becomes increasingly promising, with significant implications for quantum many-body physics and quantum chemistry. Despite being one of the most accessible simulation methods, the product formula encounters challenges due to the pessimistic gate count estimation. In this work, we elucidate how observable knowledge can accelerate quantum simulations. By focusing on specific families of observables, we reduce product-formula simulation errors and gate counts in both short-time and arbitrary-time scenarios. For short-time simulations, we deliberately design and tailor product formulas to achieve size-independent errors for local and certain global observables. In arbitrary-time simulations, we reveal that Pauli-summation structured observables generally reduce average errors. Specifically, we obtain quadratic error reductions proportional to the number of summands for observables with evenly distributed Pauli coefficients. Our advanced error analyses, supported by numerical studies, indicate improved gate count estimation. We anticipate that the explored speed-ups can pave the way for efficiently realizing quantum simulations and demonstrating advantages on near-term quantum devices.