Quantum annealing algorithms for Boolean tensor networks
Abstract
Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$$$\{0, 1\}$$$$ ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.
- Authors:
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 1869036
- Alternate Identifier(s):
- OSTI ID: 1870634
- Report Number(s):
- LA-UR-21-27414
Journal ID: ISSN 2045-2322; 8539; PII: 12611
- Grant/Contract Number:
- 20190020DR; BG05M2OP001-1.001-0003; 89233218CNA000001
- Resource Type:
- Published Article
- Journal Name:
- Scientific Reports
- Additional Journal Information:
- Journal Name: Scientific Reports Journal Volume: 12 Journal Issue: 1; Journal ID: ISSN 2045-2322
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United Kingdom
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; D-Wave; Quantum annealing; Tensor networks; Tucker; Tensor train; Tucker decomposition; Parallel quantum annealing; Computer science; Quantum information; Qubits; Software
Citation Formats
Pelofske, Elijah, Hahn, Georg, O’Malley, Daniel, Djidjev, Hristo N., and Alexandrov, Boian S. Quantum annealing algorithms for Boolean tensor networks. United Kingdom: N. p., 2022.
Web. doi:10.1038/s41598-022-12611-9.
Pelofske, Elijah, Hahn, Georg, O’Malley, Daniel, Djidjev, Hristo N., & Alexandrov, Boian S. Quantum annealing algorithms for Boolean tensor networks. United Kingdom. https://doi.org/10.1038/s41598-022-12611-9
Pelofske, Elijah, Hahn, Georg, O’Malley, Daniel, Djidjev, Hristo N., and Alexandrov, Boian S. Fri .
"Quantum annealing algorithms for Boolean tensor networks". United Kingdom. https://doi.org/10.1038/s41598-022-12611-9.
@article{osti_1869036,
title = {Quantum annealing algorithms for Boolean tensor networks},
author = {Pelofske, Elijah and Hahn, Georg and O’Malley, Daniel and Djidjev, Hristo N. and Alexandrov, Boian S.},
abstractNote = {Abstract Quantum annealers manufactured by D-Wave Systems, Inc., are computational devices capable of finding high-quality heuristic solutions of NP-hard problems. In this contribution, we explore the potential and effectiveness of such quantum annealers for computing Boolean tensor networks. Tensors offer a natural way to model high-dimensional data commonplace in many scientific fields, and representing a binary tensor as a Boolean tensor network is the task of expressing a tensor containing categorical (i.e., $$\{0, 1\}$$ { 0 , 1 } ) values as a product of low dimensional binary tensors. A Boolean tensor network is computed by Boolean tensor decomposition, and it is usually not exact. The aim of such decomposition is to minimize the given distance measure between the high-dimensional input tensor and the product of lower-dimensional (usually three-dimensional) tensors and matrices representing the tensor network. In this paper, we introduce and analyze three general algorithms for Boolean tensor networks: Tucker, Tensor Train, and Hierarchical Tucker networks. The computation of a Boolean tensor network is reduced to a sequence of Boolean matrix factorizations, which we show can be expressed as a quadratic unconstrained binary optimization problem suitable for solving on a quantum annealer. By using a novel method we introduce called parallel quantum annealing, we demonstrate that Boolean tensor’s with up to millions of elements can be decomposed efficiently using a DWave 2000Q quantum annealer.},
doi = {10.1038/s41598-022-12611-9},
journal = {Scientific Reports},
number = 1,
volume = 12,
place = {United Kingdom},
year = {Fri May 20 00:00:00 EDT 2022},
month = {Fri May 20 00:00:00 EDT 2022}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1038/s41598-022-12611-9
https://doi.org/10.1038/s41598-022-12611-9
Other availability
Search WorldCat to find libraries that may hold this journal
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Practical Annealing-Based Quantum Computing
journal, June 2019
- McGeoch, Catherine C.; Harris, Richard; Reinhardt, Steven P.
- Computer, Vol. 52, Issue 6
Boolean Tensor Factorizations
conference, December 2011
- Miettinen, Pauli
- 2011 IEEE 11th International Conference on Data Mining (ICDM)
Adiabatic quantum computation
journal, January 2018
- Albash, Tameem; Lidar, Daniel A.
- Reviews of Modern Physics, Vol. 90, Issue 1
Some mathematical notes on three-mode factor analysis
journal, September 1966
- Tucker, Ledyard R.
- Psychometrika, Vol. 31, Issue 3
Ising formulations of many NP problems
journal, January 2014
- Lucas, Andrew
- Frontiers in Physics, Vol. 2
Breaking the Curse of Dimensionality, Or How to Use SVD in Many Dimensions
journal, January 2009
- Oseledets, I. V.; Tyrtyshnikov, E. E.
- SIAM Journal on Scientific Computing, Vol. 31, Issue 5
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
The Expression of a Tensor or a Polyadic as a Sum of Products
journal, April 1927
- Hitchcock, Frank L.
- Journal of Mathematics and Physics, Vol. 6, Issue 1-4
Quantum annealing: A new method for minimizing multidimensional functions
journal, March 1994
- Finnila, A. B.; Gomez, M. A.; Sebenik, C.
- Chemical Physics Letters, Vol. 219, Issue 5-6
Pseudo-Boolean optimization
journal, November 2002
- Boros, Endre; Hammer, Peter L.
- Discrete Applied Mathematics, Vol. 123, Issue 1-3
Solving large minimum vertex cover problems on a quantum annealer
conference, April 2019
- Pelofske, Elijah; Hahn, Georg; Djidjev, Hristo
- CF '19: Computing Frontiers Conference, Proceedings of the 16th ACM International Conference on Computing Frontiers
Tucker-1 Boolean Tensor Factorization with Quantum Annealers
conference, December 2020
- O'Malley, Daniel; Djidjev, Hristo N.; Alexandrov, Boian S.
- 2020 International Conference on Rebooting Computing (ICRC)
Nonnegative/Binary matrix factorization with a D-Wave quantum annealer
journal, December 2018
- O’Malley, Daniel; Vesselinov, Velimir V.; Alexandrov, Boian S.
- PLOS ONE, Vol. 13, Issue 12
Colloquium : Quantum annealing and analog quantum computation
journal, September 2008
- Das, Arnab; Chakrabarti, Bikas K.
- Reviews of Modern Physics, Vol. 80, Issue 3
Parallel quantum annealing
journal, March 2022
- Pelofske, Elijah; Hahn, Georg; Djidjev, Hristo N.
- Scientific Reports, Vol. 12, Issue 1
Tensor Decompositions and Applications
journal, August 2009
- Kolda, Tamara G.; Bader, Brett W.
- SIAM Review, Vol. 51, Issue 3
Tensor-Train Decomposition
journal, January 2011
- Oseledets, I. V.
- SIAM Journal on Scientific Computing, Vol. 33, Issue 5
The Discrete Basis Problem
journal, October 2008
- Miettinen, P.; Mielikainen, T.; Gionis, A.
- IEEE Transactions on Knowledge and Data Engineering, Vol. 20, Issue 10
Matplotlib: A 2D Graphics Environment
journal, January 2007
- Hunter, John D.
- Computing in Science & Engineering, Vol. 9, Issue 3
Categorical Tensor Network States
journal, December 2011
- Biamonte, Jacob D.; Clark, Stephen R.; Jaksch, Dieter
- AIP Advances, Vol. 1, Issue 4
Finding Maximum Cliques on the D-Wave Quantum Annealer
journal, May 2018
- Chapuis, Guillaume; Djidjev, Hristo; Hahn, Georg
- Journal of Signal Processing Systems, Vol. 91, Issue 3-4
Learning the parts of objects by non-negative matrix factorization
journal, October 1999
- Lee, Daniel D.; Seung, H. Sebastian
- Nature, Vol. 401, Issue 6755
Tensor rank is NP-complete
journal, December 1990
- Håstad, Johan
- Journal of Algorithms, Vol. 11, Issue 4
Tensor Rank and the Ill-Posedness of the Best Low-Rank Approximation Problem
journal, January 2008
- de Silva, Vin; Lim, Lek-Heng
- SIAM Journal on Matrix Analysis and Applications, Vol. 30, Issue 3
Reverse annealing for nonnegative/binary matrix factorization
journal, January 2021
- Golden, John; O’Malley, Daniel
- PLOS ONE, Vol. 16, Issue 1
Boolean Hierarchical Tucker Networks on Quantum Annealers
book, March 2022
- Pelofske, Elijah; Hahn, Georg; O’Malley, Daniel
- Large-Scale Scientific Computing
On the Early History of the Singular Value Decomposition
journal, December 1993
- Stewart, G. W.
- SIAM Review, Vol. 35, Issue 4
Quantum Annealing versus Digital Computing: An Experimental Comparison
journal, December 2021
- Jünger, Michael; Lobe, Elisabeth; Mutzel, Petra
- ACM Journal of Experimental Algorithmics, Vol. 26
Perspectives of quantum annealing: methods and implementations
journal, May 2020
- Hauke, Philipp; Katzgraber, Helmut G.; Lechner, Wolfgang
- Reports on Progress in Physics, Vol. 83, Issue 5