Perez-Delgado C., Vinjanampathy S., 2021, ‘Coherent Parallelization of Universal Classical Computation’ New J. Phys. in press https://doi.org/10.1088/1367-2630/ac3a17.
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.