Randomizing multi-product formulas for Hamiltonian simulation

Quantum simulation, the simulation of quantum processes on computers, suggests a path forward for efficient problems in condensed-matter physics, chemistry, and materials science. While majority algorithms are deterministic, recent surge ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce scheme unites advantages randomized compiling one hand higher-order multi-product formulas, as they used example linear-combination-of-unitaries (LCU) or error mitigation, other hand. doing so, propose framework sampling is expected to be useful programmable simulators present two new formula tailored it. Our reduces circuit depth by circumventing need oblivious amplitude amplification required implementation formulas using standard LCU methods, rendering it especially early computers estimate dynamics systems instead performing full-fledged phase estimation. achieve shrinks exponentially with depth. To corroborate their functioning, prove rigorous performance bounds well concentration procedure. We demonstrate functioning approach several physically meaningful examples Hamiltonians, including fermionic Sachdev–Ye–Kitaev model, which method provides favorable scaling effort.