Program

SESSION 10: Quantum computation and quantum tunneling (Pavilion I - III)

Chair: Todd Brun (Southern California)
8:30 am - 9:15 amSeth Lloyd, (MIT)
Quantum algorithms for topological data analysis

Abstract. This talk shows how quantum computers can supply an exponential speedup over classical computers to reveal the topology of data.

9:15 am - 9:45 amZhang Jiang, (NASA Ames)
Instantons in thermally-assisted tunneling and quantum Monte Carlo simulations

Abstract. Despite the big body of literature in spin tunneling, it has only been studied, using path integrals, in systems with fixed total spin. We introduce a non-perturbative spin path-integral instanton calculus for systems where, due to thermal fluctuations, the total spin is not preserved. We demonstrate in a closed analytical form of the scaling equivalence between the transition rate of quantum Monte Carlo, and the quantum tunneling rate when the later is dominated by the most probable path (an instanton). Our analytical results are confirmed by detailed numerical studies.

9:45 am - 10:15 amLucas Brady, van Dam group (UC Santa Barbara)
Efficient tunnelling in quantum adiabatic optimization and its quantum Monte Carlo simulations

Abstract. We explore the behavior of Quantum Adiabatic Optimization (QAO) and path-integral Quantum Monte Carlo (QMC) methods while tunneling through potential barriers of varying size. We focus on n-qubit systems with a symmetric cost function where the annealing algorithms must tunnel through a barrier that has (width x height) proportional to (n^a x n^b). By tuning the exponents a and b it is possible to make a successful QAO algorithm take constant, polynomial, or exponential time in n. First we examine for which values of a and b these complexity transitions occur and numerically compare the run times of QAO with QMC which we find are correlated. Furthermore we find evidence that the time complexities of these two algorithms scale with each other in a way that suggests that QMC algorithms tunnel efficiently in the same setting as where QAO is efficient. See the linked manuscript for more details. Next, we look at the behavior of QAO in the polynomial scaling region of a and b. To do this, we compare our system to several similar toy models, and using these we rederive a folklore result by Goldstone that says that asymptotically the spectral gap scales as n^(1/2-a-b) for a+b>1/2 and 2a+b<1. We show numerically that our problem approaches the same asymptotic scaling limit as these toy problems, but in both cases, extremely large n are needed to realize the asymptotic limit.

SQuInT Chief Organizer
Prof. Akimasa Miyake
amiyake@unm.edu

SQuInT Co-Organizer
Prof. Elohim Becerra
fbecerra@unm.edu

SQuInT Founder
Prof. Ivan Deutsch
ideutsch@unm.edu

SQuInT Administrator
Gloria Cordova
gjcordo1@unm.edu
505 277-1850

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