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Title: Quantum Optimization and Approximation Algorithms.

Abstract

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 polyno- mial speedups over classical algorithms, have been invented. To better understand the potential advantage quantum resources provide over their classical counterparts, one may consider other re- sources 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 ex- tending seminal discrete optimization techniques. Our interdisciplinary work seeks to unearth new connections between discrete optimization and quantum information science.

Authors:
; ;
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1492737
Report Number(s):
SAND2019-0739
671780
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English

Citation Formats

Parekh, Ojas D., Ryan-Anderson, Ciaran, and Gharibian, Sevag. Quantum Optimization and Approximation Algorithms.. United States: N. p., 2019. Web. doi:10.2172/1492737.
Parekh, Ojas D., Ryan-Anderson, Ciaran, & Gharibian, Sevag. Quantum Optimization and Approximation Algorithms.. United States. doi:10.2172/1492737.
Parekh, Ojas D., Ryan-Anderson, Ciaran, and Gharibian, Sevag. Tue . "Quantum Optimization and Approximation Algorithms.". United States. doi:10.2172/1492737. https://www.osti.gov/servlets/purl/1492737.
@article{osti_1492737,
title = {Quantum Optimization and Approximation Algorithms.},
author = {Parekh, Ojas D. and Ryan-Anderson, Ciaran and Gharibian, Sevag},
abstractNote = {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 polyno- mial speedups over classical algorithms, have been invented. To better understand the potential advantage quantum resources provide over their classical counterparts, one may consider other re- sources 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 ex- tending seminal discrete optimization techniques. Our interdisciplinary work seeks to unearth new connections between discrete optimization and quantum information science.},
doi = {10.2172/1492737},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {1}
}