Efficient quantum-enhanced classical simulation for patches of quantum landscapes

Abstract:Understanding the capabilities of classical simulation methods is key to identifying where quantum computers are advantageous. Not only does this ensure that quantum computers are used only where necessary, but also one can potentially identify subroutines that can be offloaded onto a classical device. In this work, we show that it is always possible to generate a classical surrogate of a sub-region (dubbed a "patch") of an expectation landscape produced by a parameterized quantum circuit. That is, we provide a quantum-enhanced classical algorithm which, after simple measurements on a quantum device, allows one to classically simulate approximate expectation values of a subregion of a landscape. We provide time and sample complexity guarantees for a range of families of circuits of interest, and further numerically demonstrate our simulation algorithms on an exactly verifiable simulation of a Hamiltonian variational ansatz and long-time dynamics simulation on a 127-qubit heavy-hex topology.

Quantum Physics (quant-ph); Machine Learning (cs.LG); Machine Learning (stat.ML)

arXiv:2411.19896 [quant-ph]

(or arXiv:2411.19896v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2411.19896 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1103/fhc5-8sm6 Focus to learn more DOI(s) linking to related resources

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