Observable-driven speed-ups in quantum simulations

Quantum simulation represents a cornerstone application for quantum computers, offering the potential to solve classically intractable problems in physics, chemistry, and materials science. 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 knowledge 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 with a typically quadratic error reduction. 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. The promise of quantum simulation is challenged by resource estimates that far exceed the capabilities of current devices. This work shows that tailoring simulations, especially product-formula methods, to the specific observable being measured provides significant speed-ups, including size-independent errors and quadratic reductions in gate counts.