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arXiv · 1712.07395

The Feynman-Kitaev computer's clock: bias, gaps, idling and pulse tuning

Libor Caha·Zeph Landau·Daniel Nagaj
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Abstract

We present a collection of results about the clock in Feynman's computer construction and Kitaev's Local Hamiltonian problem. First, by analyzing the spectra of quantum walks on a line with varying endpoint terms, we find a better lower bound on the gap of the Feynman Hamiltonian, which translates into a less strict promise gap requirement for the QMA-complete Local Hamiltonian problem. We also translate this result into the language of adiabatic quantum computation. Second, introducing an idling clock construction with a large state space but fast Cesaro mixing, we provide a way for achieving an arbitrarily high success probability of computation with Feynman's computer with only a logarithmic increase in the number of clock qubits. Finally, we tune and thus improve the costs (locality, gap scaling) of implementing a (pulse) clock with a single excitation.

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Libor Caha, Zeph Landau, Daniel Nagaj. 2017-12-20. The Feynman-Kitaev computer's clock: bias, gaps, idling and pulse tuning. https://doi.org/10.1103/physreva.97.062306

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