SAMOP 2021 – scientific programme
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QI: Fachverband Quanteninformation
QI 12: Quantum Simulation and Many-Body Systems
QI 12.4: Talk
Friday, September 24, 2021, 12:00–12:15, H3
Randomizing multi-product formulas for improved Hamiltonian simulation — •Paul K. Fährmann1, Mark Steudtner1, Richard Küng2, Mária Kieferová3, and Jens Eisert1,4 — 1Freie Universität Berlin — 2Johannes Kepler Universität Linz — 3University of Technology Sydney — 4Helmholtz-Zentrum Berlin
Quantum simulation suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry and materials science. While most quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. This work introduces a scheme for quantum simulation uniting the advantages of randomized compiling on the one hand and higher-order multi-product formulas as they are used for example in linear-combination-of-unitaries (LCU) algorithms on the other hand. In doing so, we propose a framework of randomized sampling that is expected to be useful for programmable quantum simulators and present two new multi-product formula algorithms tailored to it. Our framework greatly reduces the circuit depth, circumventing the need for oblivious amplitude amplification required for standard LCU methods, rendering it especially useful for near-term quantum computing. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. We prove rigorous performance bounds and concentration of the randomized sampling procedure. Furthermore, we demonstrate the functioning for several physically meaningful examples of Hamiltonians for which the method provides a favorable scaling in the effort.