4.6 Article

Signatures of a sampling quantum advantage in driven quantum many-body systems

Journal

QUANTUM SCIENCE AND TECHNOLOGY
Volume 8, Issue 2, Pages -

Publisher

IOP Publishing Ltd
DOI: 10.1088/2058-9565/acbd69

Keywords

analog quantum simulators; thermalization; driven quantum many-body systems; quantum supremacy; sampling quantum advantage; random matrix ensembles

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This work formally proves that the sampling of bit-strings from a periodic evolution of a unitary drawn from the circular orthogonal ensemble (COE) cannot be efficiently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems, this suggests that those driven systems could potentially have a sampling quantum advantage. Numerical examples of driven disordered Ising chains and 1D driven Bose-Hubbard model are provided to support this.
A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can perform a computation task that is classically intractable. A key question is to identify setups that can achieve such goal within current technologies. In this work, we provide formal evidence that sampling bit-strings from a periodic evolution of a unitary drawn from the circular orthogonal ensemble (COE) cannot be efficiently simulated with classical computers. As the statistical properties of COE coincide with a large class of driven analog quantum systems thanks to the Floquet eigenstate thermalization hypothesis, our results indicate the possibility that those driven systems could constitute practical candidates for a sampling quantum advantage. To further support this, we give numerical examples of driven disordered Ising chains and 1D driven Bose-Hubbard model.

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