FET: Small: Improved Catalysts for Adiabatic Quantum Computing

Michigan State University, East Lansing MI

Investigators

Abstract

Many practical and consequential problems in present-day industries, from determining efficient shipping routes to optimizing investment portfolios and designing novel medicinal compounds, amount to finding the best compromise among competing constraints. Classical computers often fail to solve hard optimization problems such as these, and thus one of the major research directions in quantum computing is to determine whether certain quantum computers might be significantly more effective — if so, the implications for countless fields would be transformative. The standard approach for leveraging quantum fluctuations to better solve optimization problems is termed “adiabatic quantum computation” (AQC). Unfortunately, despite some encouraging initial studies, it is now understood that conventional AQC is likely to struggle for similar reasons as do classical algorithms. As a result, recent research in the topic has turned towards intelligent modifications to AQC — termed “catalysts” — that are intended to circumvent the difficulties faced by the conventional approach. This project will apply tools and ideas from statistical physics to elucidate the potential and limitations of such catalysts. Just as the physics-based method has led to a better understanding of conventional AQC, so will it here inform the development of the next generation of quantum-computing algorithms for optimization problems. More precisely, the awarded work consists of two major thrusts. First is to investigate whether catalysts proposed in the literature continue to show an advantage when applied to spin-glass models (the statistical-physics analogues of hard optimization problems), and to identify the physical mechanisms underlying those successes and/or failures. Second is to apply that understanding to develop improvements to the catalysts which address their weaknesses. Since the difficulty of optimization problems can be described in physical terms via their “free energy landscapes”, a central concept in statistical physics, this project will specifically use techniques from that field — path integrals, mean-field decouplings, the replica method — to calculate the landscapes in canonical spin-glass models and quantify the manner in which different catalysts modify said landscapes, as well as characterize their robustness to imperfections such as finite temperature and noise. This will in turn identify which features of the catalysts are essential to their functioning and which are extraneous, thus informing how best to adapt the catalysts to different applications. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.