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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]
  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.
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
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.
@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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

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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Works referenced in this record:

Applications of artificial intelligence for chemical inference. I. Number of possible organic compounds. Acyclic structures containing carbon, hydrogen, oxygen, and nitrogen
journal, May 1969

  • Lederberg, Joshua; Sutherland, Georgia L.; Buchanan, Bruce G.
  • Journal of the American Chemical Society, Vol. 91, Issue 11
  • DOI: 10.1021/ja01039a025

Subspace-search variational quantum eigensolver for excited states
journal, October 2019


The role of two-dimensional nuclear magnetic resonance spectroscopy in computer-enhanced structure elucidation
journal, May 1991

  • Christie, Bradley D.; Munk, Morton E.
  • Journal of the American Chemical Society, Vol. 113, Issue 10
  • DOI: 10.1021/ja00010a018

Quantum annealing correction for random Ising problems
journal, April 2015


Cocon: From NMR Correlation Data to Molecular Constitutions
journal, August 1997

  • Lindel, Thomas; Junker, Jochen; K�ck, Matthias
  • Journal of Molecular Modeling, Vol. 3, Issue 8
  • DOI: 10.1007/s008940050052

X-PERT: a user-friendly expert system for molecular structure elucidation by spectral methods
journal, January 1997


Quantum annealing correction for random Ising problems
text, January 2014


Exact Ising model simulation on a quantum computer
journal, December 2018


Assemble 2.0: a structure generator
journal, May 2000

  • Badertscher, Martin; Korytko, Andrew; Schulz, Klaus-Peter
  • Chemometrics and Intelligent Laboratory Systems, Vol. 51, Issue 1
  • DOI: 10.1016/S0169-7439(00)00056-3

Ising formulations of many NP problems
journal, January 2014


Stochastic Generator of Chemical Structure. 2. Using Simulated Annealing To Search the Space of Constitutional Isomers
journal, January 1996

  • Faulon, Jean-Loup
  • Journal of Chemical Information and Computer Sciences, Vol. 36, Issue 4
  • DOI: 10.1021/ci950179a

Elucidation of Drug Metabolite Structural Isomers Using Molecular Modeling Coupled with Ion Mobility Mass Spectrometry
journal, January 2016


Applications of artificial intelligence for chemical inference—XX
journal, January 1977


Application of a New Expert System for the Structure Elucidation of Natural Products from Their 1D and 2D NMR Data
journal, May 2002

  • Elyashberg, Mikhail E.; Blinov, Kirill A.; Williams, Antony J.
  • Journal of Natural Products, Vol. 65, Issue 5
  • DOI: 10.1021/np0103315

Exact Ising model simulation on a quantum computer
text, January 2018


Graph Partitioning using Quantum Annealing on the D-Wave System
conference, January 2017

  • Ushijima-Mwesigwa, Hayato; Negre, Christian F. A.; Mniszewski, Susan M.
  • Proceedings of the Second International Workshop on Post Moores Era Supercomputing - PMES'17
  • DOI: 10.1145/3149526.3149531

What is the Computational Value of Finite-Range Tunneling?
journal, August 2016


Expert system for elucidation of structures of organic compounds (ESESOC): —Algorithm on stereoisomer generation
journal, October 2000

  • Hao, Junfeng; Xu, Lu; Hu, Changyu
  • Science in China Series B: Chemistry, Vol. 43, Issue 5
  • DOI: 10.1007/BF02969496

What is the Computational Value of Finite Range Tunneling?
text, January 2015


Elucidation by progressive intersection of ordered substructures from carbon-13 nuclear magnetic resonance
journal, October 1988

  • Carabedian, Michel.; Dagane, Ishay.; Dubois, Jacques Emile.
  • Analytical Chemistry, Vol. 60, Issue 20
  • DOI: 10.1021/ac00171a005

Detecting multiple communities using quantum annealing on the D-Wave system
journal, February 2020


Exhaustive generation of organic isomers. 1. Acyclic structures
journal, July 1992

  • Contreras, M. L.; Valdivia, R.; Rozas, R.
  • Journal of Chemical Information and Computer Sciences, Vol. 32, Issue 4
  • DOI: 10.1021/ci00008a011

Exhaustive generation of structural isomers for a given empirical formula - a new algorithm
journal, February 1982

  • Zhu, Si Yu; Zhang, Jin Pei
  • Journal of Chemical Information and Computer Sciences, Vol. 22, Issue 1
  • DOI: 10.1021/ci00033a007

Stochastic Generator of Chemical Structure. 1. Application to the Structure Elucidation of Large Molecules
journal, September 1994

  • Faulon, Jean-Loup
  • Journal of Chemical Information and Modeling, Vol. 34, Issue 5
  • DOI: 10.1021/ci00021a031

Structure generation by reduction: a new strategy for computer-assisted structure elucidation
journal, May 1988

  • Christie, Bradley D.; Munk, Morton E.
  • Journal of Chemical Information and Computer Sciences, Vol. 28, Issue 2
  • DOI: 10.1021/ci00058a009