Work

Clocks in Feynman's computer and Kitaev's local Hamiltonian: Bias, gaps, idling, and pulse tuning

Year: 2018

Type: article

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 end-point 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 quantum-Merlin-Arthur--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 and gap scaling) of implementing a (pulse) clock with a single excitation.

Source: Physical Review A

DOI: 10.1103/physreva.97.062306

Authors: Libor Caha, Zeph Landau, Daniel Nagaj

Institutions: Slovak Academy of Sciences, Institute of Physics of the Slovak Academy of Sciences, University of California, Berkeley

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Slovenská Akadémia Vied, Seventh Framework Programme, Army Research Office

Awards: G4556764370, AF: Medium: Quantum Hamiltonian Complexity: Through the Computational Lens, G8337768007