ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

Lyakh, Dmitry I.; Nguyen, Thien; Claudino, Daniel; Dumitrescu, Eugene; McCaskey, Alexander J.

doi:10.3389/fams.2022.838601

Title: ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

Abstract

We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.

Authors:: Lyakh, Dmitry I.; Nguyen, Thien; Claudino, Daniel; Dumitrescu, Eugene; McCaskey, Alexander J.

Publication Date:: Wed Jul 06 00:00:00 EDT 2022

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

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:: 2325498

Alternate Identifier(s):: OSTI ID: 1876320

Grant/Contract Number:: AC05-00OR22725; ERKCG13/ERKCG23

Resource Type:: Published Article

Journal Name:: Frontiers in Applied Mathematics and Statistics

Additional Journal Information:: Journal Name: Frontiers in Applied Mathematics and Statistics Journal Volume: 8; Journal ID: ISSN 2297-4687

Publisher:: Frontiers Media SA

Country of Publication:: Switzerland

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; tensor network; quantum many-body theory; quantum computing; quantum circuit; high performance computing; GPU

Citation Formats


                    Lyakh, Dmitry I., Nguyen, Thien, Claudino, Daniel, Dumitrescu, Eugene, and McCaskey, Alexander J. ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale.  Switzerland: N. p., 2022. 
Web.  doi:10.3389/fams.2022.838601.

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                    Lyakh, Dmitry I., Nguyen, Thien, Claudino, Daniel, Dumitrescu, Eugene, & McCaskey, Alexander J. ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale.  Switzerland.  https://doi.org/10.3389/fams.2022.838601

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                    Lyakh, Dmitry I., Nguyen, Thien, Claudino, Daniel, Dumitrescu, Eugene, and McCaskey, Alexander J. Wed .  
"ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale".  Switzerland.  https://doi.org/10.3389/fams.2022.838601.

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@article{osti_2325498,

  title        = {ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale},

  author       = {Lyakh, Dmitry I. and Nguyen, Thien and Claudino, Daniel and Dumitrescu, Eugene and McCaskey, Alexander J.},

  abstractNote = {We present ExaTN (Exascale Tensor Networks), a scalable GPU-accelerated C++ library which can express and process tensor networks on shared- as well as distributed-memory high-performance computing platforms, including those equipped with GPU accelerators. Specifically, ExaTN provides the ability to build, transform, and numerically evaluate tensor networks with arbitrary graph structures and complexity. It also provides algorithmic primitives for the optimization of tensor factors inside a given tensor network in order to find an extremum of a chosen tensor network functional, which is one of the key numerical procedures in quantum many-body theory and quantum-inspired machine learning. Numerical primitives exposed by ExaTN provide the foundation for composing rather complex tensor network algorithms. We enumerate multiple application domains which can benefit from the capabilities of our library, including condensed matter physics, quantum chemistry, quantum circuit simulations, as well as quantum and classical machine learning, for some of which we provide preliminary demonstrations and performance benchmarks just to emphasize a broad utility of our library.},

  doi          = {10.3389/fams.2022.838601},

  journal      = {Frontiers in Applied Mathematics and Statistics},

  number       = ,

  volume       = 8,

  place        = {Switzerland},

  year         = {Wed Jul 06 00:00:00 EDT 2022},

  month        = {Wed Jul 06 00:00:00 EDT 2022}

}

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Works referenced in this record:

Corner Transfer Matrix Renormalization Group Method
journal, April 1996

Nishino, Tomotoshi; Okunishi, Kouichi
Journal of the Physical Society of Japan, Vol. 65, Issue 4
DOI: 10.1143/JPSJ.65.891

An Ab Initio Exciton Model Including Charge-Transfer Excited States
journal, July 2017

Li, Xin; Parrish, Robert M.; Liu, Fang
Journal of Chemical Theory and Computation, Vol. 13, Issue 8
DOI: 10.1021/acs.jctc.7b00171

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale
preprint, January 2021

Nguyen, Thien; Lyakh, Dmitry; Dumitrescu, Eugene
arXiv
DOI: 10.48550/ARXIV.2104.10523

Valence-bond states for quantum computation
journal, December 2004

Verstraete, F.; Cirac, J. I.
Physical Review A, Vol. 70, Issue 6
DOI: 10.1103/PhysRevA.70.060302

What Limits the Simulation of Quantum Computers?
journal, November 2020

Zhou, Yiqing; Stoudenmire, E. Miles; Waintal, Xavier
Physical Review X, Vol. 10, Issue 4
DOI: 10.1103/PhysRevX.10.041038

Renormalization and tensor product states in spin chains and lattices
journal, December 2009

Cirac, J. Ignacio; Verstraete, Frank
Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 50
DOI: 10.1088/1751-8113/42/50/504004

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

Vidal, G.
Physical Review Letters, Vol. 101, Issue 11
DOI: 10.1103/PhysRevLett.101.110501

Simulating Quantum Computation by Contracting Tensor Networks
journal, January 2008

Markov, Igor L.; Shi, Yaoyun
SIAM Journal on Computing, Vol. 38, Issue 3
DOI: 10.1137/050644756

Validating quantum-classical programming models with tensor network simulations
journal, December 2018

McCaskey, Alexander; Dumitrescu, Eugene; Chen, Mengsu
PLOS ONE, Vol. 13, Issue 12
DOI: 10.1371/journal.pone.0206704

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
journal, April 2013

Nakatani, Naoki; Chan, Garnet Kin-Lic
The Journal of Chemical Physics, Vol. 138, Issue 13
DOI: 10.1063/1.4798639

Tensor Completion Algorithms in Big Data Analytics
journal, January 2019

Song, Qingquan; Ge, Hancheng; Caverlee, James
ACM Transactions on Knowledge Discovery from Data, Vol. 13, Issue 1
DOI: 10.1145/3278607

quimb: A python package for quantum information and many-body calculations
journal, September 2018

Gray, Johnnie
Journal of Open Source Software, Vol. 3, Issue 29
DOI: 10.21105/joss.00819

Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions
conference, October 2020

Holmes, Adam; Matsuura, A. Y.
2020 IEEE International Conference on Quantum Computing and Engineering (QCE)
DOI: 10.1109/QCE49297.2020.00030

Hyper-optimized tensor network contraction
journal, March 2021

Gray, Johnnie; Kourtis, Stefanos
Quantum, Vol. 5
DOI: 10.22331/q-2021-03-15-410

Tensor Network Renormalization
journal, October 2015

Evenbly, G.; Vidal, G.
Physical Review Letters, Vol. 115, Issue 18
DOI: 10.1103/PhysRevLett.115.180405

Entanglement Renormalization
journal, November 2007

Vidal, G.
Physical Review Letters, Vol. 99, Issue 22
DOI: 10.1103/PhysRevLett.99.220405

cuTT: A High-Performance Tensor Transpose Library for CUDA Compatible GPUs
preprint, January 2017

Hynninen, Antti-Pekka; Lyakh, Dmitry I.
arXiv
DOI: 10.48550/arXiv.1705.01598

A practical introduction to tensor networks: Matrix product states and projected entangled pair states
journal, October 2014

Orús, Román
Annals of Physics, Vol. 349
DOI: 10.1016/j.aop.2014.06.013

Real-Time Evolution Using the Density Matrix Renormalization Group
journal, August 2004

White, Steven R.; Feiguin, Adrian E.
Physical Review Letters, Vol. 93, Issue 7
DOI: 10.1103/PhysRevLett.93.076401

AutoHOOT: Automatic High-Order Optimization for Tensors
conference, September 2020

Ma, Linjian; Ye, Jiayu; Solomonik, Edgar
PACT '20: International Conference on Parallel Architectures and Compilation Techniques, Proceedings of the ACM International Conference on Parallel Architectures and Compilation Techniques
DOI: 10.1145/3410463.3414647

Density matrix formulation for quantum renormalization groups
journal, November 1992

White, Steven R.
Physical Review Letters, Vol. 69, Issue 19
DOI: 10.1103/PhysRevLett.69.2863

TensorTrace: an application to contract tensor networks
preprint, January 2019

Evenbly, Glen
arXiv
DOI: 10.48550/arXiv.1911.02558

Ab Initio Nonadiabatic Dynamics of Multichromophore Complexes: A Scalable Graphical-Processing-Unit-Accelerated Exciton Framework
journal, July 2014

Sisto, Aaron; Glowacki, David R.; Martinez, Todd J.
Accounts of Chemical Research, Vol. 47, Issue 9
DOI: 10.1021/ar500229p

Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation
journal, December 2020

Schutski, Roman; Khakhulin, Taras; Oseledets, Ivan
Physical Review A, Vol. 102, Issue 6
DOI: 10.1103/PhysRevA.102.062614

XACC: a system-level software infrastructure for heterogeneous quantum–classical computing
journal, February 2020

McCaskey, Alexander J.; Lyakh, Dmitry I.; Dumitrescu, Eugene F.
Quantum Science and Technology, Vol. 5, Issue 2
DOI: 10.1088/2058-9565/ab6bf6

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
journal, February 2007

Vidal, G.
Physical Review Letters, Vol. 98, Issue 7
DOI: 10.1103/PhysRevLett.98.070201

Multi-Tensor Contraction for XEB Verification of Quantum Circuits
preprint, January 2021

Kalachev, Gleb; Panteleev, Pavel; Yung, Man-Hong
arXiv
DOI: 10.48550/arXiv.2108.05665

Tensorized Embedding Layers
conference, January 2020

Hrinchuk, Oleksii; Khrulkov, Valentin; Mirvakhabova, Leyla
Findings of the Association for Computational Linguistics: EMNLP 2020
DOI: 10.18653/v1/2020.findings-emnlp.436

A Multi-Scale Tensor Network Architecture for Classification and Regression
preprint, January 2020

Reyes, Justin; Stoudenmire, Miles
arXiv
DOI: 10.48550/arXiv.2001.08286

Efficient 2D Tensor Network Simulation of Quantum Systems
conference, November 2020

Pang, Yuchen; Hao, Tianyi; Dugad, Annika
SC20: International Conference for High Performance Computing, Networking, Storage and Analysis
DOI: 10.1109/SC41405.2020.00018

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Schollwöck, Ulrich
Annals of Physics, Vol. 326, Issue 1
DOI: 10.1016/j.aop.2010.09.012

A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware
journal, October 2019

Villalonga, Benjamin; Boixo, Sergio; Nelson, Bron
npj Quantum Information, Vol. 5, Issue 1
DOI: 10.1038/s41534-019-0196-1

Generative machine learning with tensor networks: Benchmarks on near-term quantum computers
journal, April 2021

Wall, Michael L.; Abernathy, Matthew R.; Quiroz, Gregory
Physical Review Research, Vol. 3, Issue 2
DOI: 10.1103/PhysRevResearch.3.023010

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
journal, July 2016

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki
The Journal of Chemical Physics, Vol. 145, Issue 1
DOI: 10.1063/1.4955108

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
journal, May 2005

Troyer, Matthias; Wiese, Uwe-Jens
Physical Review Letters, Vol. 94, Issue 17
DOI: 10.1103/PhysRevLett.94.170201

Entanglement and Tensor Networks for Supervised Image Classification
preprint, January 2020

Martyn, John; Vidal, Guifre; Roberts, Chase
arXiv
DOI: 10.48550/arXiv.2007.06082

The density-matrix renormalization group
journal, April 2005

Schollwöck, U.
Reviews of Modern Physics, Vol. 77, Issue 1
DOI: 10.1103/RevModPhys.77.259

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

Pfeifer, Robert N. C.; Haegeman, Jutho; Verstraete, Frank
Physical Review E, Vol. 90, Issue 3
DOI: 10.1103/PhysRevE.90.033315

Quantum supremacy using a programmable superconducting processor
journal, October 2019

Arute, Frank; Arya, Kunal; Babbush, Ryan
Nature, Vol. 574, Issue 7779
DOI: 10.1038/s41586-019-1666-5

Classical simulation of quantum many-body systems with a tree tensor network
journal, August 2006

Shi, Y. -Y.; Duan, L. -M.; Vidal, G.
Physical Review A, Vol. 74, Issue 2
DOI: 10.1103/PhysRevA.74.022320

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
journal, April 2015

Lyakh, Dmitry I.
Computer Physics Communications, Vol. 189
DOI: 10.1016/j.cpc.2014.12.013

Tensor-Train Decomposition
journal, January 2011

Oseledets, I. V.
SIAM Journal on Scientific Computing, Vol. 33, Issue 5
DOI: 10.1137/090752286

Establishing the quantum supremacy frontier with a 281 Pflop/s simulation
journal, April 2020

Villalonga, Benjamin; Lyakh, Dmitry; Boixo, Sergio
Quantum Science and Technology, Vol. 5, Issue 3
DOI: 10.1088/2058-9565/ab7eeb

NCON: A tensor network contractor for MATLAB
preprint, January 2014

Pfeifer, Robert N. C.; Evenbly, Glen; Singh, Sukhwinder
arXiv
DOI: 10.48550/arXiv.1402.0939

Multilevel Algorithms for Multi-Constraint Graph Partitioning
conference, January 1998

Karypis, G.; Kumar, V.
SC98 - High Performance Networking and Computing Conference, Proceedings of the IEEE/ACM SC98 Conference
DOI: 10.1109/SC.1998.10018

Compressing deep neural networks by matrix product operators
journal, June 2020

Gao, Ze-Feng; Cheng, Song; He, Rong-Qiang
Physical Review Research, Vol. 2, Issue 2
DOI: 10.1103/PhysRevResearch.2.023300

Number-State Preserving Tensor Networks as Classifiers for Supervised Learning
preprint, January 2019

Evenbly, Glen
arXiv
DOI: 10.48550/arXiv.1905.06352

Advances on tensor network theory: symmetries, fermions, entanglement, and holography
journal, November 2014

Orús, Román
The European Physical Journal B, Vol. 87, Issue 11
DOI: 10.1140/epjb/e2014-50502-9

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

Vidal, Guifré
Physical Review Letters, Vol. 91, Issue 14
DOI: 10.1103/PhysRevLett.91.147902

The ITensor Software Library for Tensor Network Calculations
preprint, January 2020

Fishman, Matthew; White, Steven R.; Stoudenmire, E. Miles
arXiv
DOI: 10.48550/arXiv.2007.14822

Efficient classical simulation of noisy random quantum circuits in one dimension
journal, September 2020

Noh, Kyungjoo; Jiang, Liang; Fefferman, Bill
Quantum, Vol. 4
DOI: 10.22331/q-2020-09-11-318

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Title: ExaTN: Scalable GPU-Accelerated High-Performance Processing of General Tensor Networks at Exascale

Abstract

Citation Formats

Corner Transfer Matrix Renormalization Group Method journal, April 1996

An Ab Initio Exciton Model Including Charge-Transfer Excited States journal, July 2017

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale preprint, January 2021

Valence-bond states for quantum computation journal, December 2004

What Limits the Simulation of Quantum Computers? journal, November 2020

Renormalization and tensor product states in spin chains and lattices journal, December 2009

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

Simulating Quantum Computation by Contracting Tensor Networks journal, January 2008

Validating quantum-classical programming models with tensor network simulations journal, December 2018

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm journal, April 2013

Tensor Completion Algorithms in Big Data Analytics journal, January 2019

quimb: A python package for quantum information and many-body calculations journal, September 2018

Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions conference, October 2020

Hyper-optimized tensor network contraction journal, March 2021

Tensor Network Renormalization journal, October 2015

Entanglement Renormalization journal, November 2007

cuTT: A High-Performance Tensor Transpose Library for CUDA Compatible GPUs preprint, January 2017

A practical introduction to tensor networks: Matrix product states and projected entangled pair states journal, October 2014

Real-Time Evolution Using the Density Matrix Renormalization Group journal, August 2004

AutoHOOT: Automatic High-Order Optimization for Tensors conference, September 2020

Density matrix formulation for quantum renormalization groups journal, November 1992

TensorTrace: an application to contract tensor networks preprint, January 2019

Ab Initio Nonadiabatic Dynamics of Multichromophore Complexes: A Scalable Graphical-Processing-Unit-Accelerated Exciton Framework journal, July 2014

Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation journal, December 2020

XACC: a system-level software infrastructure for heterogeneous quantum–classical computing journal, February 2020

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension journal, February 2007

Multi-Tensor Contraction for XEB Verification of Quantum Circuits preprint, January 2021

Tensorized Embedding Layers conference, January 2020

A Multi-Scale Tensor Network Architecture for Classification and Regression preprint, January 2020

Efficient 2D Tensor Network Simulation of Quantum Systems conference, November 2020

The density-matrix renormalization group in the age of matrix product states journal, January 2011

A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware journal, October 2019

Generative machine learning with tensor networks: Benchmarks on near-term quantum computers journal, April 2021

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms journal, July 2016

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal, May 2005

Entanglement and Tensor Networks for Supervised Image Classification preprint, January 2020

The density-matrix renormalization group journal, April 2005

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

Quantum supremacy using a programmable superconducting processor journal, October 2019

Classical simulation of quantum many-body systems with a tree tensor network journal, August 2006

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU journal, April 2015

Tensor-Train Decomposition journal, January 2011

Establishing the quantum supremacy frontier with a 281 Pflop/s simulation journal, April 2020

NCON: A tensor network contractor for MATLAB preprint, January 2014

Multilevel Algorithms for Multi-Constraint Graph Partitioning conference, January 1998

Compressing deep neural networks by matrix product operators journal, June 2020

Number-State Preserving Tensor Networks as Classifiers for Supervised Learning preprint, January 2019

Advances on tensor network theory: symmetries, fermions, entanglement, and holography journal, November 2014

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

The ITensor Software Library for Tensor Network Calculations preprint, January 2020

Efficient classical simulation of noisy random quantum circuits in one dimension journal, September 2020

Corner Transfer Matrix Renormalization Group Method
journal, April 1996

An Ab Initio Exciton Model Including Charge-Transfer Excited States
journal, July 2017

Tensor Network Quantum Virtual Machine for Simulating Quantum Circuits at Exascale
preprint, January 2021

Valence-bond states for quantum computation
journal, December 2004

What Limits the Simulation of Quantum Computers?
journal, November 2020

Renormalization and tensor product states in spin chains and lattices
journal, December 2009

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

Simulating Quantum Computation by Contracting Tensor Networks
journal, January 2008

Validating quantum-classical programming models with tensor network simulations
journal, December 2018

Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm
journal, April 2013

Tensor Completion Algorithms in Big Data Analytics
journal, January 2019

quimb: A python package for quantum information and many-body calculations
journal, September 2018

Efficient Quantum Circuits for Accurate State Preparation of Smooth, Differentiable Functions
conference, October 2020

Hyper-optimized tensor network contraction
journal, March 2021

Tensor Network Renormalization
journal, October 2015

Entanglement Renormalization
journal, November 2007

cuTT: A High-Performance Tensor Transpose Library for CUDA Compatible GPUs
preprint, January 2017

A practical introduction to tensor networks: Matrix product states and projected entangled pair states
journal, October 2014

Real-Time Evolution Using the Density Matrix Renormalization Group
journal, August 2004

AutoHOOT: Automatic High-Order Optimization for Tensors
conference, September 2020

Density matrix formulation for quantum renormalization groups
journal, November 1992

TensorTrace: an application to contract tensor networks
preprint, January 2019

Ab Initio Nonadiabatic Dynamics of Multichromophore Complexes: A Scalable Graphical-Processing-Unit-Accelerated Exciton Framework
journal, July 2014

Simple heuristics for efficient parallel tensor contraction and quantum circuit simulation
journal, December 2020

XACC: a system-level software infrastructure for heterogeneous quantum–classical computing
journal, February 2020

Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
journal, February 2007

Multi-Tensor Contraction for XEB Verification of Quantum Circuits
preprint, January 2021

Tensorized Embedding Layers
conference, January 2020

A Multi-Scale Tensor Network Architecture for Classification and Regression
preprint, January 2020

Efficient 2D Tensor Network Simulation of Quantum Systems
conference, November 2020

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

A flexible high-performance simulator for verifying and benchmarking quantum circuits implemented on real hardware
journal, October 2019

Generative machine learning with tensor networks: Benchmarks on near-term quantum computers
journal, April 2021

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
journal, July 2016

Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations
journal, May 2005

Entanglement and Tensor Networks for Supervised Image Classification
preprint, January 2020

The density-matrix renormalization group
journal, April 2005

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

Quantum supremacy using a programmable superconducting processor
journal, October 2019

Classical simulation of quantum many-body systems with a tree tensor network
journal, August 2006

An efficient tensor transpose algorithm for multicore CPU, Intel Xeon Phi, and NVidia Tesla GPU
journal, April 2015

Tensor-Train Decomposition
journal, January 2011

Establishing the quantum supremacy frontier with a 281 Pflop/s simulation
journal, April 2020

NCON: A tensor network contractor for MATLAB
preprint, January 2014

Multilevel Algorithms for Multi-Constraint Graph Partitioning
conference, January 1998

Compressing deep neural networks by matrix product operators
journal, June 2020

Number-State Preserving Tensor Networks as Classifiers for Supervised Learning
preprint, January 2019

Advances on tensor network theory: symmetries, fermions, entanglement, and holography
journal, November 2014

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

The ITensor Software Library for Tensor Network Calculations
preprint, January 2020

Efficient classical simulation of noisy random quantum circuits in one dimension
journal, September 2020