Title: Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

Abstract

Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze several counterexamples from the class of perturbed Hamming weight optimization problems with qubit permutation symmetry. We first show that, for these problems, the adiabatic dynamics that make tunneling possible should be understood not in terms of the cost function but rather the semiclassical potential arising from the spin-coherent path-integral formalism. We then provide an example where the shape of the barrier in the final cost function is short and wide, which might suggest no quantum advantage for QA, yet where tunneling renders QA superior to simulated annealing in the adiabatic regime. However, the adiabatic dynamics turn out not be optimal. Instead, an evolution involving a sequence of diabatic transitions through many avoided-level crossings, involving no tunneling, is optimal and outperforms adiabatic QA. We show that this phenomenon of speedup by diabatic transitions is not unique to this example, and we provide an example where it provides an exponential speedup over adiabatic QA. In yet another twist, we show that a classical algorithm, spin-vector dynamics, ismore » at least as efficient as diabatic QA. Lastly, in a different example with a convex cost function, the diabatic transitions result in a speedup relative to both adiabatic QA with tunneling and classical spin-vector dynamics.« less

Authors:

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

Publication Date:

Thu Jul 21 00:00:00 EDT 2016

Research Org.:

Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); UT-Batelle, LLC, Oak Ridge, TN (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1267545

Alternate Identifier(s):

OSTI ID: 1299215

Grant/Contract Number:  

AC05-00OR22725

Resource Type:

Published Article

Journal Name:

Physical Review. X

Additional Journal Information:

Journal Name: Physical Review. X Journal Volume: 6 Journal Issue: 3; Journal ID: ISSN 2160-3308

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; tridiagonal transition matrices; mean passage times; model