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Title: Quantum isomer search

Abstract

Isomer search or molecule enumeration refers to the problem of finding all the isomers for a given molecule. Many classical search methods have been developed in order to tackle this problem. However, the availability of quantum computing architectures has given us the opportunity to address this problem with new (quantum) techniques. This paper describes a quantum isomer search procedure for determining all the structural isomers of alkanes. We first formulate the structural isomer search problem as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO formulation is for general use on either annealing or gate-based quantum computers. We use the D-Wave quantum annealer to enumerate all structural isomers of all alkanes with fewer carbon atoms (n < 10) than Decane (C10H22). The number of isomer solutions increases with the number of carbon atoms. We find that the sampling time needed to identify all solutions scales linearly with the number of carbon atoms in the alkane. We probe the problem further by employing reverse annealing as well as a perturbed QUBO Hamiltonian and find that the combination of these two methods significantly reduces the number of samples required to find all isomers.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]; ORCiD logo [3]
+ Show Author Affiliations
  1. Univ. of Georgia, Athens, GA (United States); Brown Univ., Providence, RI (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. Univ. of Texas at Dallas, Richardson, TX (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)
OSTI Identifier:
1630853
Report Number(s):
LA-UR-19-26724
Journal ID: ISSN 1932-6203
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
PLoS ONE
Additional Journal Information:
Journal Volume: 15; Journal Issue: 1; Journal ID: ISSN 1932-6203
Publisher:
Public Library of Science
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; computer science; mathematics; isomers; alkanes; carbon; quibits; perturbation theory; quantum computing; constitutional isomers; simulated annealing

Citation Formats

Terry, Jason Patrick, Akrobotu, Prosper D., Negre, Christian Francisco Andres, and Mniszewski, Susan M. Quantum isomer search. United States: N. p., 2020. Web. doi:10.1371/journal.pone.0226787.
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Terry, Jason Patrick, Akrobotu, Prosper D., Negre, Christian Francisco Andres, & Mniszewski, Susan M. Quantum isomer search. United States. https://doi.org/10.1371/journal.pone.0226787
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Terry, Jason Patrick, Akrobotu, Prosper D., Negre, Christian Francisco Andres, and Mniszewski, Susan M. Wed . "Quantum isomer search". United States. https://doi.org/10.1371/journal.pone.0226787. https://www.osti.gov/servlets/purl/1630853.
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@article{osti_1630853,
title = {Quantum isomer search},
author = {Terry, Jason Patrick and Akrobotu, Prosper D. and Negre, Christian Francisco Andres and Mniszewski, Susan M.},
abstractNote = {Isomer search or molecule enumeration refers to the problem of finding all the isomers for a given molecule. Many classical search methods have been developed in order to tackle this problem. However, the availability of quantum computing architectures has given us the opportunity to address this problem with new (quantum) techniques. This paper describes a quantum isomer search procedure for determining all the structural isomers of alkanes. We first formulate the structural isomer search problem as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO formulation is for general use on either annealing or gate-based quantum computers. We use the D-Wave quantum annealer to enumerate all structural isomers of all alkanes with fewer carbon atoms (n < 10) than Decane (C10H22). The number of isomer solutions increases with the number of carbon atoms. We find that the sampling time needed to identify all solutions scales linearly with the number of carbon atoms in the alkane. We probe the problem further by employing reverse annealing as well as a perturbed QUBO Hamiltonian and find that the combination of these two methods significantly reduces the number of samples required to find all isomers.},
doi = {10.1371/journal.pone.0226787},
journal = {PLoS ONE},
number = 1,
volume = 15,
place = {United States},
year = {2020},
month = {1}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1371/journal.pone.0226787
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Figures / Tables:

Fig 1 Fig 1: Isomorphism of trees. Two isomorphic tree graphs with degree sequences (1,2,2,1) (left) and (1,1,2,2) (middle) that both correspond to the straight chain isomer (right) of C4 H10.
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