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- W2969534823 abstract "Demonstrating a quantum computational speed-up is a crucial milestone for near-term quantum technology. Recently, sampling protocols for quantum simulators have been proposed that have the potential to show such a quantum advantage, based on commonly made assumptions. The key challenge in the theoretical analysis of this scheme---as of other comparable schemes such as boson sampling---is to lessen the assumptions and close the theoretical loopholes, replacing them by rigorous arguments. In this work, we prove two open conjectures for a simple sampling protocol that is based on the continuous time evolution of a translation-invariant Ising Hamiltonian: anticoncentration of the generated probability distributions and average-case hardness of exactly evaluating those probabilities. The latter is proven building upon recently developed techniques for random circuit sampling. For the former, we exploit the insight that approximate 2-designs for the unitary group admit anticoncentration. We then develop new techniques to prove that the 2D time evolution of the protocol gives rise to approximate 2-designs. Our work provides the strongest theoretical evidence to date that Hamiltonian quantum simulators are classically intractable." @default.
- W2969534823 created "2019-08-29" @default.
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- W2969534823 date "2020-12-17" @default.
- W2969534823 modified "2023-10-17" @default.
- W2969534823 title "Closing Gaps of a Quantum Advantage with Short-Time Hamiltonian Dynamics" @default.
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- W2969534823 doi "https://doi.org/10.1103/physrevlett.125.250501" @default.
- W2969534823 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/33416354" @default.
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