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Title: Efficiently embedding QUBO problems on adiabatic quantum computers

Abstract

Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2]; ORCiD logo [2]
  1. Rensselaer Polytechnic Inst., Troy, NY (United States)
  2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1557505
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Quantum Information Processing
Additional Journal Information:
Journal Volume: 18; Journal Issue: 4; Journal ID: ISSN 1570-0755
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Adiabatic quantum computing; Embedding; Quadratic unconstrained binary optimization (QUBO)

Citation Formats

Date, Prasanna, Patton, Robert, Schuman, Catherine, and Potok, Thomas. Efficiently embedding QUBO problems on adiabatic quantum computers. United States: N. p., 2019. Web. doi:10.1007/s11128-019-2236-3.
Date, Prasanna, Patton, Robert, Schuman, Catherine, & Potok, Thomas. Efficiently embedding QUBO problems on adiabatic quantum computers. United States. doi:10.1007/s11128-019-2236-3.
Date, Prasanna, Patton, Robert, Schuman, Catherine, and Potok, Thomas. Tue . "Efficiently embedding QUBO problems on adiabatic quantum computers". United States. doi:10.1007/s11128-019-2236-3.
@article{osti_1557505,
title = {Efficiently embedding QUBO problems on adiabatic quantum computers},
author = {Date, Prasanna and Patton, Robert and Schuman, Catherine and Potok, Thomas},
abstractNote = {Adiabatic quantum computers like the D-Wave 2000Q can approximately solve the QUBO problem, which is an NP-hard problem, and have been shown to outperform classical computers on several instances. Solving the QUBO problem literally means solving virtually any NP-hard problem like the traveling salesman problem, airline scheduling problem, protein folding problem, genotype imputation problem, thereby enabling significant scientific progress, and potentially saving millions/billions of dollars in logistics, airlines, healthcare and many other industries. Yet, before QUBO problems are solved on quantum computers, they must be embedded (or compiled) onto the hardware of quantum computers, which in itself is a very hard problem. Here, we propose an efficient embedding algorithm, that lets us embed QUBO problems fast, uses less qubits and gets the objective function value close to the global minimum value. We then compare the performance of our embedding algorithm to that of D-Wave’s embedding algorithm, which is the current state of the art, and show that our embedding algorithm convincingly outperforms D-Wave’s embedding algorithm. Our embedding approach works with perfect Chimera graphs, i.e., Chimera graphs with no missing qubits.},
doi = {10.1007/s11128-019-2236-3},
journal = {Quantum Information Processing},
number = 4,
volume = 18,
place = {United States},
year = {2019},
month = {3}
}

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