Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Miao, Qiang; Barthel, Thomas

doi:10.1103/PhysRevA.109.L050402

Title: Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Journal Article · 13 May 2024 · Physical Review A

DOI: https://doi.org/10.1103/PhysRevA.109.L050402 · OSTI ID:2356941

Miao, Qiang; Barthel, Thomas

Not Available

View Accepted Manuscript (Publisher)

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019449

OSTI ID:: 2356941

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 5 Vol. 109; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (71)

Barren plateaus in quantum neural network training landscapes McClean, Jarrod R.; Boixo, Sergio; Smelyanskiy, Vadim N. Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-018-07090-4	journal	November 2018
Local Random Quantum Circuits are Approximate Polynomial-Designs Brandão, Fernando G. S. L.; Harrow, Aram W.; Horodecki, Michał Communications in Mathematical Physics, Vol. 346, Issue 2 https://doi.org/10.1007/s00220-016-2706-8	journal	August 2016
Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz Mele, Antonio A.; Mbeng, Glen B.; Santoro, Giuseppe E. Physical Review A, Vol. 106, Issue 6 https://doi.org/10.1103/PhysRevA.106.L060401	journal	December 2022
Typicality in random matrix product states Garnerone, Silvano; de Oliveira, Thiago R.; Zanardi, Paolo Physical Review A, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevA.81.032336	journal	March 2010
Efficient Measure for the Expressivity of Variational Quantum Algorithms Du, Yuxuan; Tu, Zhuozhuo; Yuan, Xiao Physical Review Letters, Vol. 128, Issue 8 https://doi.org/10.1103/PhysRevLett.128.080506	journal	February 2022
Optimizing quantum circuits with Riemannian gradient flow Wiersema, Roeland; Killoran, Nathan Physical Review A, Vol. 107, Issue 6 https://doi.org/10.1103/PhysRevA.107.062421	journal	June 2023
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Trainability of Dissipative Perceptron-Based Quantum Neural Networks Sharma, Kunal; Cerezo, M.; Cincio, Lukasz Physical Review Letters, Vol. 128, Issue 18 https://doi.org/10.1103/PhysRevLett.128.180505	journal	May 2022
Emergent statistical mechanics of entanglement in random unitary circuits Zhou, Tianci; Nahum, Adam Physical Review B, Vol. 99, Issue 17 https://doi.org/10.1103/PhysRevB.99.174205	journal	May 2019
Connecting Ansatz Expressibility to Gradient Magnitudes and Barren Plateaus Holmes, Zoë; Sharma, Kunal; Cerezo, M. PRX Quantum, Vol. 3, Issue 1 https://doi.org/10.1103/PRXQuantum.3.010313	journal	January 2022
Variational quantum eigensolver with fewer qubits Liu, Jin-Guo; Zhang, Yi-Hong; Wan, Yuan Physical Review Research, Vol. 1, Issue 2 https://doi.org/10.1103/PhysRevResearch.1.023025	journal	September 2019
Quantum Entanglement Growth under Random Unitary Dynamics Nahum, Adam; Ruhman, Jonathan; Vijay, Sagar Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031016	journal	July 2017
Simulating strongly correlated quantum systems with tree tensor networks Murg, V.; Verstraete, F.; Legeza, Ö. Physical Review B, Vol. 82, Issue 20 https://doi.org/10.1103/PhysRevB.82.205105	journal	November 2010
On the closedness and geometry of tensor network state sets Barthel, Thomas; Lu, Jianfeng; Friesecke, Gero Letters in Mathematical Physics, Vol. 112, Issue 4 https://doi.org/10.1007/s11005-022-01552-z	journal	July 2022
Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group Rommer, Stefan; Östlund, Stellan Physical Review B, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevB.55.2164	journal	January 1997
Exact and approximate unitary 2-designs and their application to fidelity estimation Dankert, Christoph; Cleve, Richard; Emerson, Joseph Physical Review A, Vol. 80, Issue 1 https://doi.org/10.1103/PhysRevA.80.012304	journal	July 2009
Synergistic pretraining of parametrized quantum circuits via tensor networks Rudolph, Manuel S.; Miller, Jacob; Motlagh, Danial Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-43908-6	journal	December 2023
Entanglement-Induced Barren Plateaus Ortiz Marrero, Carlos; Kieferová, Mária; Wiebe, Nathan PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040316	journal	October 2021
The Power of Quantum Systems on a Line Aharonov, Dorit; Gottesman, Daniel; Irani, Sandy Communications in Mathematical Physics, Vol. 287, Issue 1 https://doi.org/10.1007/s00220-008-0710-3	journal	January 2009
Presence and Absence of Barren Plateaus in Tensor-Network Based Machine Learning Liu, Zidu; Yu, Li-Wei; Duan, L. -M. Physical Review Letters, Vol. 129, Issue 27 https://doi.org/10.1103/PhysRevLett.129.270501	journal	December 2022
Barren plateaus from learning scramblers with local cost functions Garcia, Roy J.; Zhao, Chen; Bu, Kaifeng Journal of High Energy Physics, Vol. 2023, Issue 1 https://doi.org/10.1007/JHEP01(2023)090	journal	January 2023
Large gradients via correlation in random parameterized quantum circuits Volkoff, Tyler; Coles, Patrick J. Quantum Science and Technology, Vol. 6, Issue 2 https://doi.org/10.1088/2058-9565/abd891	journal	January 2021
Simulation of two-dimensional quantum systems using a tree tensor network that exploits the entropic area law Tagliacozzo, L.; Evenbly, G.; Vidal, G. Physical Review B, Vol. 80, Issue 23 https://doi.org/10.1103/PhysRevB.80.235127	journal	December 2009
Bloch vectors for qudits Bertlmann, Reinhold A.; Krammer, Philipp Journal of Physics A: Mathematical and Theoretical, Vol. 41, Issue 23 https://doi.org/10.1088/1751-8113/41/23/235303	journal	May 2008
Expressibility and Entangling Capability of Parameterized Quantum Circuits for Hybrid Quantum‐Classical Algorithms Sim, Sukin; Johnson, Peter D.; Aspuru‐Guzik, Alán Advanced Quantum Technologies, Vol. 2, Issue 12 https://doi.org/10.1002/qute.201900070	journal	October 2019
Equivalence of quantum barren plateaus to cost concentration and narrow gorges Arrasmith, Andrew; Holmes, Zoë; Cerezo, M. Quantum Science and Technology, Vol. 7, Issue 4 https://doi.org/10.1088/2058-9565/ac7d06	journal	August 2022
Riemannian optimization of isometric tensor networks Hauru, Markus; Van Damme, Maarten; Haegeman, Jutho SciPost Physics, Vol. 10, Issue 2 https://doi.org/10.21468/SciPostPhys.10.2.040	journal	January 2021
Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus Zhao, Chen; Gao, Xiao-Shan Quantum, Vol. 5 https://doi.org/10.22331/q-2021-06-04-466	journal	June 2021
Abrupt transitions in variational quantum circuit training Campos, Ernesto; Nasrallah, Aly; Biamonte, Jacob Physical Review A, Vol. 103, Issue 3 https://doi.org/10.1103/PhysRevA.103.032607	journal	March 2021
Quantum variational algorithms are swamped with traps Anschuetz, Eric R.; Kiani, Bobak T. Nature Communications, Vol. 13, Issue 1 https://doi.org/10.1038/s41467-022-35364-5	journal	December 2022
Classical simulation of quantum many-body systems with a tree tensor network Shi, Y. -Y.; Duan, L. -M.; Vidal, G. Physical Review A, Vol. 74, Issue 2 https://doi.org/10.1103/PhysRevA.74.022320	journal	August 2006
The Complexity of Translationally Invariant Spin Chains with Low Local Dimension Bausch, Johannes; Cubitt, Toby; Ozols, Maris Annales Henri Poincaré, Vol. 18, Issue 11 https://doi.org/10.1007/s00023-017-0609-7	journal	October 2017
The density-matrix renormalization group in the age of matrix product states Schollwöck, Ulrich Annals of Physics, Vol. 326, Issue 1 https://doi.org/10.1016/j.aop.2010.09.012	journal	January 2011
An initialization strategy for addressing barren plateaus in parametrized quantum circuits Grant, Edward; Wossnig, Leonard; Ostaszewski, Mateusz Quantum, Vol. 3 https://doi.org/10.22331/q-2019-12-09-214	journal	December 2019
Finitely correlated states on quantum spin chains Fannes, M.; Nachtergaele, B.; Werner, R. F. Communications in Mathematical Physics, Vol. 144, Issue 3 https://doi.org/10.1007/BF02099178	journal	March 1992
Random Quantum Circuits Fisher, Matthew P. A.; Khemani, Vedika; Nahum, Adam Annual Review of Condensed Matter Physics, Vol. 14, Issue 1 https://doi.org/10.1146/annurev-conmatphys-031720-030658	journal	March 2023
A Practical Guide to the Numerical Implementation of Tensor Networks I: Contractions, Decompositions, and Gauge Freedom Evenbly, Glen Frontiers in Applied Mathematics and Statistics, Vol. 8 https://doi.org/10.3389/fams.2022.806549	journal	June 2022
Quantum-classical eigensolver using multiscale entanglement renormalization Miao, Qiang; Barthel, Thomas Physical Review Research, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevResearch.5.033141	journal	August 2023
Expressibility of the alternating layered ansatz for quantum computation Nakaji, Kouhei; Yamamoto, Naoki Quantum, Vol. 5 https://doi.org/10.22331/q-2021-04-19-434	journal	April 2021
Variational Power of Quantum Circuit Tensor Networks Haghshenas, Reza; Gray, Johnnie; Potter, Andrew C. Physical Review X, Vol. 12, Issue 1 https://doi.org/10.1103/PhysRevX.12.011047	journal	March 2022
Entanglement Renormalization Vidal, G. Physical Review Letters, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevLett.99.220405	journal	November 2007
Simulating physics with computers Feynman, Richard P. International Journal of Theoretical Physics, Vol. 21, Issue 6-7 https://doi.org/10.1007/BF02650179	journal	June 1982
Class of Quantum Many-Body States That Can Be Efficiently Simulated Vidal, G. Physical Review Letters, Vol. 101, Issue 11 https://doi.org/10.1103/PhysRevLett.101.110501	journal	September 2008
Gottesman, Daniel; Irani, Sandy Theory of Computing, Vol. 9, Issue 1 https://doi.org/10.4086/toc.2013.v009a002	journal	January 2013
Operator Spreading in Random Unitary Circuits Nahum, Adam; Vijay, Sagar; Haah, Jeongwan Physical Review X, Vol. 8, Issue 2 https://doi.org/10.1103/PhysRevX.8.021014	journal	April 2018
Topics in quantum probability Accardi, Luigi Physics Reports, Vol. 77, Issue 3 https://doi.org/10.1016/0370-1573(81)90070-3	journal	November 1981
Riemannian geometry and automatic differentiation for optimization problems of quantum physics and quantum technologies Luchnikov, Ilia A.; Krechetov, Mikhail E.; Filippov, Sergey N. New Journal of Physics, Vol. 23, Issue 7 https://doi.org/10.1088/1367-2630/ac0b02	journal	July 2021
Algorithms for entanglement renormalization Evenbly, G.; Vidal, G. Physical Review B, Vol. 79, Issue 14 https://doi.org/10.1103/PhysRevB.79.144108	journal	April 2009
Emergent Statistical Mechanics from Properties of Disordered Random Matrix Product States Haferkamp, Jonas; Bertoni, Christian; Roth, Ingo PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040308	journal	October 2021
Cost function dependent barren plateaus in shallow parametrized quantum circuits Cerezo, M.; Sone, Akira; Volkoff, Tyler Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-21728-w	journal	March 2021
Variational quantum algorithms Cerezo, M.; Arrasmith, Andrew; Babbush, Ryan Nature Reviews Physics, Vol. 3, Issue 9 https://doi.org/10.1038/s42254-021-00348-9	journal	August 2021
Holographic quantum algorithms for simulating correlated spin systems Foss-Feig, Michael; Hayes, David; Dreiling, Joan M. Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033002	journal	July 2021
Training Variational Quantum Algorithms Is NP-Hard Bittel, Lennart; Kliesch, Martin Physical Review Letters, Vol. 127, Issue 12 https://doi.org/10.1103/PhysRevLett.127.120502	journal	September 2021
Matrix product state pre-training for quantum machine learning Dborin, James; Barratt, Fergus; Wimalaweera, Vinul Quantum Science and Technology, Vol. 7, Issue 3 https://doi.org/10.1088/2058-9565/ac7073	journal	May 2022
Absence of Barren Plateaus in Quantum Convolutional Neural Networks Pesah, Arthur; Cerezo, M.; Wang, Samson Physical Review X, Vol. 11, Issue 4 https://doi.org/10.1103/PhysRevX.11.041011	journal	October 2021
Layerwise learning for quantum neural networks Skolik, Andrea; McClean, Jarrod R.; Mohseni, Masoud Quantum Machine Intelligence, Vol. 3, Issue 1 https://doi.org/10.1007/s42484-020-00036-4	journal	January 2021
Density-matrix renormalization-group study of the spin-½ XXZ antiferromagnet on the Bethe lattice Otsuka, Hiromi Physical Review B, Vol. 53, Issue 21 https://doi.org/10.1103/PhysRevB.53.14004	journal	June 1996
The Bloch vector for N-level systems Kimura, Gen Physics Letters A, Vol. 314, Issue 5-6 https://doi.org/10.1016/S0375-9601(03)00941-1	journal	August 2003
Holographic Simulation of Correlated Electrons on a Trapped-Ion Quantum Processor Niu, Daoheng; Haghshenas, Reza; Zhang, Yuxuan PRX Quantum, Vol. 3, Issue 3 https://doi.org/10.1103/PRXQuantum.3.030317	journal	August 2022
Entanglement and the foundations of statistical mechanics Popescu, Sandu; Short, Anthony J.; Winter, Andreas Nature Physics, Vol. 2, Issue 11 https://doi.org/10.1038/nphys444	journal	October 2006
Ground states of VBS models on cayley trees Fannes, M.; Nachtergaele, B.; Werner, R. F. Journal of Statistical Physics, Vol. 66, Issue 3-4 https://doi.org/10.1007/BF01055710	journal	February 1992
Real-Space Renormalization Yields Finite Correlations Barthel, Thomas; Kliesch, Martin; Eisert, Jens Physical Review Letters, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevLett.105.010502	journal	July 2010
The Complexity of the Local Hamiltonian Problem Kempe, Julia; Kitaev, Alexei; Regev, Oded SIAM Journal on Computing, Vol. 35, Issue 5 https://doi.org/10.1137/S0097539704445226	journal	January 2006
Avoiding Barren Plateaus Using Classical Shadows Sack, Stefan H.; Medina, Raimel A.; Michailidis, Alexios A. PRX Quantum, Vol. 3, Issue 2 https://doi.org/10.1103/PRXQuantum.3.020365	journal	June 2022
Unitary block optimization for variational quantum algorithms Slattery, Lucas; Villalonga, Benjamin; Clark, Bryan K. Physical Review Research, Vol. 4, Issue 2 https://doi.org/10.1103/PhysRevResearch.4.023072	journal	April 2022
Statistical properties of random matrix product states Garnerone, Silvano; de Oliveira, Thiago R.; Haas, Stephan Physical Review A, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevA.82.052312	journal	November 2010
Dimers on a Rectangular Lattice Baxter, R. J. Journal of Mathematical Physics, Vol. 9, Issue 4 https://doi.org/10.1063/1.1664623	journal	April 1968
Canonical Typicality Goldstein, Sheldon; Lebowitz, Joel L.; Tumulka, Roderich Physical Review Letters, Vol. 96, Issue 5 https://doi.org/10.1103/PhysRevLett.96.050403	journal	February 2006
Entanglement devised barren plateau mitigation Patti, Taylor L.; Najafi, Khadijeh; Gao, Xun Physical Review Research, Vol. 3, Issue 3 https://doi.org/10.1103/PhysRevResearch.3.033090	journal	July 2021
Barren plateaus in quantum tensor network optimization Cervero Martín, Enrique; Plekhanov, Kirill; Lubasch, Michael Quantum, Vol. 7 https://doi.org/10.22331/q-2023-04-13-974	journal	April 2023
Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates Harrow, Aram W.; Mehraban, Saeed Communications in Mathematical Physics, Vol. 401, Issue 2 https://doi.org/10.1007/s00220-023-04675-z	journal	May 2023

Similar Records

Absence of Barren Plateaus and Scaling of Gradients in the Energy Optimization of Isometric Tensor Network States

Journal Article · 2025 · Communications in Mathematical Physics · OSTI ID:2532455

Barthel, Thomas; Miao, Qiang

Effect of barren plateaus on gradient-free optimization

Journal Article · 2021 · Quantum · OSTI ID:1835781

Cerezo de la Roca, Marco Vinicio Sebastian; Arrasmith, Andrew Thomas; Czarnik, Piotr Jan; +2 more

Absence of Barren Plateaus in Quantum Convolutional Neural Networks

Journal Article · 2021 · Physical Review. X · OSTI ID:1826245

Pesah, Arthur; Cerezo, M.; Wang, Samson; +3 more

Title: Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus

Citation Formats

References (71)

Similar Records

Related Subjects