Benchmarking treewidth as a practical component of tensor network simulations

Dumitrescu, Eugene F.; Fisher, Allison L.; Goodrich, Timothy D.; Humble, Travis S.; Sullivan, Blair D.; Wright, Andrew L.

doi:10.1371/journal.pone.0207827

Title: Benchmarking treewidth as a practical component of tensor network simulations

Abstract

Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and futuremore »« less

Authors:

^[1]; Fisher, Allison L. ^[2];

^[2];

^[1];

^[2]; Wright, Andrew L. ^[2]

Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
North Carolina State Univ., Raleigh, NC (United States)

Publication Date:: Tue Dec 18 00:00:00 EST 2018

Research Org.:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1490605

Grant/Contract Number:: AC05-00OR22725

Resource Type:: Accepted Manuscript

Journal Name:: PLoS ONE

Additional Journal Information:: Journal Volume: 13; Journal Issue: 12; Journal ID: ISSN 1932-6203

Publisher:: Public Library of Science

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING

Citation Formats


                    Dumitrescu, Eugene F., Fisher, Allison L., Goodrich, Timothy D., Humble, Travis S., Sullivan, Blair D., and Wright, Andrew L. Benchmarking treewidth as a practical component of tensor network simulations.  United States: N. p., 2018. 
Web.  doi:10.1371/journal.pone.0207827.

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                    Dumitrescu, Eugene F., Fisher, Allison L., Goodrich, Timothy D., Humble, Travis S., Sullivan, Blair D., & Wright, Andrew L. Benchmarking treewidth as a practical component of tensor network simulations.  United States.  https://doi.org/10.1371/journal.pone.0207827

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                    Dumitrescu, Eugene F., Fisher, Allison L., Goodrich, Timothy D., Humble, Travis S., Sullivan, Blair D., and Wright, Andrew L. Tue .  
"Benchmarking treewidth as a practical component of tensor network simulations".  United States.  https://doi.org/10.1371/journal.pone.0207827.  https://www.osti.gov/servlets/purl/1490605.

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@article{osti_1490605,

  title        = {Benchmarking treewidth as a practical component of tensor network simulations},

  author       = {Dumitrescu, Eugene F. and Fisher, Allison L. and Goodrich, Timothy D. and Humble, Travis S. and Sullivan, Blair D. and Wright, Andrew L.},

  abstractNote = {Tensor networks are powerful factorization techniques which reduce resource requirements for numerically simulating principal quantum many-body systems and algorithms. The computational complexity of a tensor network simulation depends on the tensor ranks and the order in which they are contracted. Unfortunately, computing optimal contraction sequences (orderings) in general is known to be a computationally difficult (NP-complete) task. In 2005, Markov and Shi showed that optimal contraction sequences correspond to optimal (minimum width) tree decompositions of a tensor network’s line graph, relating the contraction sequence problem to a rich literature in structural graph theory. While treewidth-based methods have largely been ignored in favor of dataset-specific algorithms in the prior tensor networks literature, we demonstrate their practical relevance for problems arising from two distinct methods used in quantum simulation: multi-scale entanglement renormalization ansatz (MERA) datasets and quantum circuits generated by the quantum approximate optimization algorithm (QAOA). We exhibit multiple regimes where treewidth-based algorithms outperform domain-specific algorithms, while demonstrating that the optimal choice of algorithm has a complex dependence on the network density, expected contraction complexity, and user run time requirements. We further provide an open source software framework designed with an emphasis on accessibility and extendability, enabling replicable experimental evaluations and future exploration of competing methods by practitioners.},

  doi          = {10.1371/journal.pone.0207827},

  journal      = {PLoS ONE},

  number       = 12,

  volume       = 13,

  place        = {United States},

  year         = {Tue Dec 18 00:00:00 EST 2018},

  month        = {Tue Dec 18 00:00:00 EST 2018}

}

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https://doi.org/10.1371/journal.pone.0207827

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Cited by: 7 works

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Fig 1: (Top) A 1D binary MERA with a 16-site lattice and 3 levels of coarsening; three operator placements are highlighted (red, blue, green). (Bottom) Causal cones and final tensor networks for each of the three highlighted operators. Note that the tensor networks for the left-most (red) and right-most (green)more »

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Similar Records

Title: Benchmarking treewidth as a practical component of tensor network simulations

Abstract

Citation Formats

Figures / Tables:

Tree tensor network approach to simulating Shor's algorithm journal, December 2017

Colloquium : Area laws for the entanglement entropy journal, February 2010

Tensor-Network Simulations of the Surface Code under Realistic Noise journal, July 2017

On Optimizing a Class of Multi-Dimensional Loops with Reduction for Parallel Execution journal, June 1997

Characterizing quantum supremacy in near-term devices journal, April 2018

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence journal, June 2015

Class of Quantum Many-Body States That Can Be Efficiently Simulated journal, September 2008

Simulating Quantum Computation by Contracting Tensor Networks journal, January 2008

Classifying quantum phases using matrix product states and projected entangled pair states journal, October 2011

Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation journal, May 2014

Efficient Classical Simulation of Slightly Entangled Quantum Computations journal, October 2003

Complexity of Finding Embeddings in a k -Tree journal, April 1987

Tensor Network Contractions for #SAT journal, June 2015

Faster identification of optimal contraction sequences for tensor networks journal, September 2014

Improving the efficiency of variational tensor network algorithms journal, June 2014

qTorch: The quantum tensor contraction handler journal, December 2018

Improving the efficiency of variational tensor network algorithms text, January 2013

Tensor-Network Simulations of the Surface Code under Realistic Noise text, January 2016

Characterizing Quantum Supremacy in Near-Term Devices text, January 2016

A tree tensor network approach to simulating Shor's algorithm text, January 2017

qTorch: The Quantum Tensor Contraction Handler text, January 2017

Efficient classical simulation of slightly entangled quantum computations text, January 2003

Simulating quantum computation by contracting tensor networks text, January 2005

A partial k-arboretum of graphs with bounded treewidth journal, December 1998

Tensor Networks and Quantum Error Correction journal, July 2014

Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems journal, June 2016

Density matrix formulation for quantum renormalization groups journal, November 1992

Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems journal, November 2004

Treewidth and Minimum Fill-in: Grouping the Minimal Separators journal, January 2001

Algorithms for entanglement renormalization text, January 2007

Improving the efficiency of variational tensor network algorithms text, January 2013

Tensor Network Contractions for #SAT text, January 2014

Faster Computation of Path-Width preprint, January 2016

Characterizing Quantum Supremacy in Near-Term Devices text, January 2016

Efficient classical simulation of slightly entangled quantum computations text, January 2003

Simulating quantum computation by contracting tensor networks text, January 2005

Tree tensor network approach to simulating Shor's algorithm
journal, December 2017

Colloquium : Area laws for the entanglement entropy
journal, February 2010

Tensor-Network Simulations of the Surface Code under Realistic Noise
journal, July 2017

On Optimizing a Class of Multi-Dimensional Loops with Reduction for Parallel Execution
journal, June 1997

Characterizing quantum supremacy in near-term devices
journal, April 2018

Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
journal, June 2015

Class of Quantum Many-Body States That Can Be Efficiently Simulated
journal, September 2008

Simulating Quantum Computation by Contracting Tensor Networks
journal, January 2008

Classifying quantum phases using matrix product states and projected entangled pair states
journal, October 2011

Tensor Networks for Lattice Gauge Theories and Atomic Quantum Simulation
journal, May 2014

Efficient Classical Simulation of Slightly Entangled Quantum Computations
journal, October 2003

Complexity of Finding Embeddings in a k -Tree
journal, April 1987

Tensor Network Contractions for #SAT
journal, June 2015

Faster identification of optimal contraction sequences for tensor networks
journal, September 2014

Improving the efficiency of variational tensor network algorithms
journal, June 2014

qTorch: The quantum tensor contraction handler
journal, December 2018

Improving the efficiency of variational tensor network algorithms
text, January 2013

Tensor-Network Simulations of the Surface Code under Realistic Noise
text, January 2016

Characterizing Quantum Supremacy in Near-Term Devices
text, January 2016

A tree tensor network approach to simulating Shor's algorithm
text, January 2017

qTorch: The Quantum Tensor Contraction Handler
text, January 2017

Efficient classical simulation of slightly entangled quantum computations
text, January 2003

Simulating quantum computation by contracting tensor networks
text, January 2005

A partial k-arboretum of graphs with bounded treewidth
journal, December 1998

Tensor Networks and Quantum Error Correction
journal, July 2014

Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems
journal, June 2016

Density matrix formulation for quantum renormalization groups
journal, November 1992

Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems
journal, November 2004

Treewidth and Minimum Fill-in: Grouping the Minimal Separators
journal, January 2001

Algorithms for entanglement renormalization
text, January 2007

Improving the efficiency of variational tensor network algorithms
text, January 2013

Tensor Network Contractions for #SAT
text, January 2014

Faster Computation of Path-Width
preprint, January 2016

Characterizing Quantum Supremacy in Near-Term Devices
text, January 2016

Efficient classical simulation of slightly entangled quantum computations
text, January 2003

Simulating quantum computation by contracting tensor networks
text, January 2005