Quantum Optimization and Approximation Algorithms

Technical Report · Sat Dec 01 04:00:00 EST 2018

DOI:https://doi.org/10.2172/1492737· OSTI ID:1492737

Parekh, Ojas D. ^[1]; Ryan-Anderson, Ciaran ^[2]; Gharibian, Sevag ^[3]

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1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2. Swansea Univ. (United Kingdom)
3. Univ. Paderborn (Germany)

Shor's groundbreaking quantum algorithm for integer factoring provides an exponential speedup over the best-known classical algorithms. In the 20 years since Shor's algorithm was conceived, only a handful of fundamental quantum algorithmic kernels, generally providing modest polynomial speedups over classical algorithms, have been invented. To better understand the potential advantage quantum resources provide over their classical counterparts, one may consider other resources than execution time of algorithms. Quantum Approximation Algorithms direct the power of quantum computing towards optimization problems where quantum resources provide higher-quality solutions instead of faster execution times. We provide a new rigorous analysis of the recent Quantum Approximate Optimization Algorithm, demonstrating that it provably outperforms the best known classical approximation algorithm for special hard cases of the fundamental Maximum Cut graph-partitioning problem. We also develop new types of classical approximation algorithms for finding near-optimal low-energy states of physical systems arising in condensed matter by extending seminal discrete optimization techniques. Our interdisciplinary work seeks to unearth new connections between discrete optimization and quantum information science.

• Research Organization: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC04-94AL85000; NA0003525
• OSTI ID: 1492737
• Report Number(s): SAND--2019-0739; 671780
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING