Coherent parallelization of universal classical computation

Previously, higher-order Hamiltonians (HoH) had been shown to offer an advantage in both metrology and quantum energy storage. Here, we axiomatize a model of computation that allows us to consider such Hamiltonians for the purposes of computation. From this axiomatic model, we formally prove that an HoH-based algorithm can gain up to a quadratic speed-up over classical sequential algorithms-for any possible classical computation. We show how our axiomatic model is grounded in the same physics as that used in HoH-based quantum advantage for metrology and battery charging. Thus we argue that any advance in implementing HoH-based quantum advantage in those scenarios can be co-opted for the purpose of speeding up computation.

Automated summary

Research has shown that algorithms based on higher-order Hamiltonians can achieve a quadratic speed-up over classical computation, and are grounded in the same physics as quantum advantage for metrology and battery charging. Therefore, advancements in implementing quantum advantage in these scenarios could potentially be utilized to speed up computation.