- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Scalable quantum dynamics compilation via quantum machine learning

Yuxuan Zhang1,2,*, Roeland Wiersema2,3,*, Juan Carrasquilla4,†, Lukasz Cincio5,‡, and Yong Baek Kim1,§

  • 1Department of Physics and Centre for Quantum Information and Quantum Control, University of Toronto, 60 Saint George Street, Toronto, Ontario M5S 1A7, Canada
  • 2Vector Institute, W1140-108 College Street, Schwartz Reisman Innovation Campus, Toronto, Ontario M5G 0C6, Canada
  • 3Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 4Institute for Theoretical Physics, ETH Zürich, 8093 Zurich, Switzerland
  • 5Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

  • *These authors contributed equally to this work.
  • †Contact author: jcarrasquill@ethz.ch
  • ‡Contact author: lcincio@lanl.gov
  • §Contact author: ybkim@physics.utoronto.ca
PDF

Phys. Rev. Research 8, 023128 – Published 7 May, 2026

DOI: https://doi.org/10.1103/wswv-nq6d

Abstract

Quantum dynamics compilation is an important task for improving quantum simulation efficiency: It aims to synthesize multiqubit target dynamics into a circuit consisting of as few elementary gates as possible. Compared to deterministic methods such as Trotterization, variational quantum compilation (VQC) methods employ variational optimization to reduce gate costs while maintaining high accuracy. In this work, we make a paradigm shift in VQC’s framework design. First, we use a cost function from recently established out-of-distribution generalization results in quantum machine learning: By learning the action of a given many-body dynamics on a small dataset of product states, we can obtain a unitary circuit that generalizes to highly entangled states such as the Haar random states. Moreover, a key observation is that the low complexity in the data states allows us to use tensor-network methods to compress such time-evolved product states by exploiting their low entanglement features. Utilizing warm start methods, our approach exceeds state-of-the-art compilation results in both system size and accuracy in one dimension. For the first time, we extend VQC to systems to two-dimensional systems, demonstrating a significant resource advantage over standard Trotterization methods. The flexibility of our framework highlights the method's promise for advancing quantum simulation tasks on near-term quantum processors.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (127)

  1. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
  2. S. Aaronson and A. Arkhipov, The computational complexity of linear optics, in Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing, edited by L. Fortnow and S. P. Vadhan (ACM, New York, NY, 2011), pp. 333–342
  3. J. Preskill, Quantum computing and the entanglement frontier, arXiv:1203.5813.
  4. S. Aaronson and A. Arkhipov, Bosonsampling is far from uniform, arXiv:1309.7460.
  5. A. M. Childs, D. Gosset, and Z. Webb, Universal computation by multiparticle quantum walk, Science 339, 791 (2013).
  6. S. Aaronson and L. Chen, Complexity-theoretic foundations of quantum supremacy experiments, arXiv:1612.05903.
  7. A. Bouland, B. Fefferman, C. Nirkhe, and U. Vazirani, On the complexity and verification of quantum random circuit sampling, Nat. Phys. 15, 159 (2019).
  8. R. Movassagh, Efficient unitary paths and quantum computational supremacy: A proof of average-case hardness of random circuit sampling, arXiv:1810.04681.
  9. S. Aaronson and Y. Zhang, On verifiable quantum advantage with peaked circuit sampling, arXiv:2404.14493.
  10. H. Gharibyan, M. Z. Mullath, N. E. Sherman, V. P. Su, H. Tepanyan, and Y. Zhang, Heuristic quantum advantage with peaked circuits, arXiv:2510.25838.
  11. Y. Zhang, Complexity and hardness of random peaked circuits, arXiv:2510.00132.
  12. S. P. Jordan, H. Krovi, K. S. Lee, and J. Preskill, BQP-completeness of scattering in scalar quantum field theory, Quantum 2, 44 (2018).
  13. M. Kreshchuk, W. M. Kirby, G. Goldstein, H. Beauchemin, and P. J. Love, Quantum simulation of quantum field theory in the light-front formulation, Phys. Rev. A 105, 032418 (2022).
  14. I. Kassal, S. P. Jordan, P. J. Love, M. Mohseni, and A. Aspuru-Guzik, Polynomial-time quantum algorithm for the simulation of chemical dynamics, Proc. Natl. Acad. Sci. USA 105, 18681 (2008).
  15. Y. Cao, J. Romero, J. P. Olson, M. Degroote, P. D. Johnson, M. Kieferová, I. D. Kivlichan, T. Menke, B. Peropadre, N. P. D. Sawaya, S. Sim, L. Veis, and A. Aspuru-Guzik, Quantum chemistry in the age of quantum computing, Chem. Rev. 119, 10856 (2019).
  16. R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
  17. I.-D. Potirniche, A. C. Potter, M. Schleier-Smith, A. Vishwanath, and N. Y. Yao, Floquet symmetry-protected topological phases in cold-atom systems, Phys. Rev. Lett. 119, 123601 (2017).
  18. N. Y. Yao, A. C. Potter, I.-D. Potirniche, and A. Vishwanath, Discrete time crystals: Rigidity, criticality, and realizations, Phys. Rev. Lett. 118, 030401 (2017).
  19. E. Farhi, J. Goldstone, and S. Gutmann, A quantum approximate optimization algorithm, arXiv:1411.4028.
  20. E. Farhi and A. W. Harrow, Quantum supremacy through the quantum approximate optimization algorithm, arXiv:1602.07674.
  21. G. G. Guerreschi and A. Y. Matsuura, QAOA for Max-Cut requires hundreds of qubits for quantum speed-up, Sci. Rep. 9, 6903 (2019).
  22. L. Zhou, S.-T. Wang, S. Choi, H. Pichler, and M. D. Lukin, Quantum approximate optimization algorithm: Performance, mechanism, and implementation on near-term devices, Phys. Rev. X 10, 021067 (2020).
  23. Y. Zhang, R. Zhang, and A. C. Potter, QED driven QAOA for network-flow optimization, Quantum 5, 510 (2021).
  24. S. Kanno, K. Sugisaki, H. Nakamura, H. Yamauchi, R. Sakuma, T. Kobayashi, Q. Gao, and N. Yamamoto, Tensor-based quantum phase difference estimation for large-scale demonstration, Proc. Natl. Acad. Sci. USA 122, e2425026122 (2025).
  25. D. Layden, G. Mazzola, R. V. Mishmash, M. Motta, P. Wocjan, J.-S. Kim, and S. Sheldon, Quantum-enhanced Markov chain Monte Carlo, Nature (London) 619, 282 (2023).
  26. H. F. Trotter, On the product of semi-groups of operators, Proc. Am. Math. Soc. 10, 545 (1959).
  27. M. Suzuki, Generalized Trotter's formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems, Commun. Math. Phys. 51, 183 (1976).
  28. L. Cincio, Y. Subaşı, A. T. Sornborger, and P. J. Coles, Learning the quantum algorithm for state overlap, New J. Phys. 20, 113022 (2018).
  29. S. Khatri, R. LaRose, A. Poremba, L. Cincio, A. T. Sornborger, and P. J. Coles, Quantum-assisted quantum compiling, Quantum 3, 140 (2019).
  30. C. Cîrstoiu, Z. Holmes, J. Iosue, L. Cincio, P. J. Coles, and A. Sornborger, Variational fast forwarding for quantum simulation beyond the coherence time, npj Quantum Inf. 6, 82 (2020).
  31. S.-H. Lin, R. Dilip, A. G. Green, A. Smith, and F. Pollmann, Real- and imaginary-time evolution with compressed quantum circuits, PRX Quantum 2, 010342 (2021).
  32. Y.-X. Yao, N. Gomes, F. Zhang, C.-Z. Wang, K.-M. Ho, T. Iadecola, and P. P. Orth, Adaptive variational quantum dynamics simulations, PRX Quantum 2, 030307 (2021).
  33. E. Kökcü, D. Camps, L. Bassman Oftelie, J. K. Freericks, W. A. de Jong, R. Van Beeumen, and A. F. Kemper, Algebraic compression of quantum circuits for Hamiltonian evolution, Phys. Rev. A 105, 032420 (2022).
  34. E. Kökcü, T. Steckmann, Y. Wang, J. K. Freericks, E. F. Dumitrescu, and A. F. Kemper, Fixed depth Hamiltonian simulation via Cartan decomposition, Phys. Rev. Lett. 129, 070501 (2022).
  35. C. Mc Keever and M. Lubasch, Classically optimized Hamiltonian simulation, Phys. Rev. Res. 5, 023146 (2023).
  36. C. Mc Keever and M. Lubasch, Towards adiabatic quantum computing using compressed quantum circuits, PRX Quantum 5, 020362 (2024).
  37. A. M. Childs, A. Ostrander, and Y. Su, Faster quantum simulation by randomization, Quantum 3, 182 (2019).
  38. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  39. Y. Zhang, D. Niu, A. Shabani, and H. Shapourian, Quantum volume for photonic quantum processors, Phys. Rev. Lett. 130, 110602 (2023).
  40. A. Cervera-Lierta, Exact Ising model simulation on a quantum computer, Quantum 2, 114 (2018).
  41. B. Peng, S. Gulania, Y. Alexeev, and N. Govind, Quantum time dynamics employing the Yang-Baxter equation for circuit compression, Phys. Rev. A 106, 012412 (2022).
  42. Y. Atia and D. Aharonov, Fast-forwarding of Hamiltonians and exponentially precise measurements, Nat. Commun. 8, 1572 (2017).
  43. Y. Zhang, J. Carrasquilla, and Y. B. Kim, Observation of a non-Hermitian supersonic mode on a trapped-ion quantum computer, Nat. Commun. 16, 3286 (2025).
  44. J. P. Palao and R. Kosloff, Forcing a unitary transformation by an external field: Comparing two approaches based on optimal control theory, arXiv:quant-ph/0208147.
  45. Y. Zhang, S. Jahanbani, A. Riswadkar, S. Shankar, and A. C. Potter, Sequential quantum simulation of spin chains with a single circuit QED device, Phys. Rev. A 109, 022606 (2024).
  46. K. Mizuta, Y. O. Nakagawa, K. Mitarai, and K. Fujii, Local variational quantum compilation of large-scale Hamiltonian dynamics, PRX Quantum 3, 040302 (2022).
  47. S. Kanasugi, S. Tsutsui, Y. O. Nakagawa, K. Maruyama, H. Oshima, and S. Sato, Computation of Green's function by local variational quantum compilation, Phys. Rev. Res. 5, 033070 (2023).
  48. S. Kanasugi, Y. Hidaka, Y. O. Nakagawa, S. Tsutsui, N. Matsumoto, K. Maruyama, H. Oshima, and S. Sato, Subspace-based local compilation of variational quantum circuits for large-scale quantum many-body simulation, Phys. Rev. Res. 7, 023298 (2025).
  49. J. Schachenmayer, B. P. Lanyon, C. F. Roos, and A. J. Daley, Entanglement growth in quench dynamics with variable range interactions, Phys. Rev. X 3, 031015 (2013).
  50. H. Zhao, M. Bukov, M. Heyl, and R. Moessner, Adaptive trotterization for time-dependent Hamiltonian quantum dynamics using piecewise conservation laws, Phys. Rev. Lett. 133, 010603 (2024).
  51. T. Barthel and Y. Zhang, Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms, Ann. Phys. (NY) 418, 168165 (2020).
  52. L. Banchi, J. Pereira, and S. Pirandola, Generalization in quantum machine learning: A quantum information standpoint, PRX Quantum 2, 040321 (2021).
  53. H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Power of data in quantum machine learning, Nat. Commun. 12, 2631 (2021).
  54. M. C. Caro, H.-Y. Huang, M. Cerezo, K. Sharma, A. Sornborger, L. Cincio, and P. J. Coles, Generalization in quantum machine learning from few training data, Nat. Commun. 13, 4919 (2022).
  55. M. C. Caro, H.-Y. Huang, N. Ezzell, J. Gibbs, A. T. Sornborger, L. Cincio, P. J. Coles, and Z. Holmes, Out-of-distribution generalization for learning quantum dynamics, Nat. Commun. 14, 3751 (2023).
  56. S. Jerbi, J. Gibbs, M. S. Rudolph, M. C. Caro, P. J. Coles, H.-Y. Huang, and Z. Holmes, The power and limitations of learning quantum dynamics incoherently, arXiv:2303.12834.
  57. L. G. Valiant, A theory of the learnable, in Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing—STOC'84, edited by R. A. DeMillo (ACM Press, New York, NY, 1984), pp. 436–445.
  58. S. Ben-David, J. Blitzer, K. Crammer, A. Kulesza, F. Pereira, and J. W. Vaughan, A theory of learning from different domains, Mach. Learn. 79, 151 (2010).
  59. T. Haug and M. S. Kim, Generalization of quantum machine learning models using quantum Fisher information metric, Phys. Rev. Lett. 133, 050603 (2024).
  60. F. Zhuang, Z. Qi, K. Duan, D. Xi, Y. Zhu, H. Zhu, H. Xiong, and Q. He, A comprehensive survey on transfer learning, Proc. IEEE 109, 43 (2021).
  61. M. Cerezo, A. Sone, T. Volkoff, L. Cincio, and P. J. Coles, Cost function dependent barren plateaus in shallow parametrized quantum circuits, Nat. Commun. 12, 1791 (2021).
  62. A. A. Mele, G. B. Mbeng, G. E. Santoro, M. Collura, and P. Torta, Avoiding barren plateaus via transferability of smooth solutions in a Hamiltonian variational ansatz, Phys. Rev. A 106, L060401 (2022).
  63. R. Puig, M. Drudis, S. Thanasilp, and Z. Holmes, Variational quantum simulation: A case study for understanding warm starts, PRX Quantum 6, 010317 (2025).
  64. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2001), Vol. 2.
  65. N. F. Berthusen, T. V. Trevisan, T. Iadecola, and P. P. Orth, Quantum dynamics simulations beyond the coherence time on noisy intermediate-scale quantum hardware by variational Trotter compression, Phys. Rev. Res. 4, 023097 (2022).
  66. M. A. Nielsen, A simple formula for the average gate fidelity of a quantum dynamical operation, Phys. Lett. A 303, 249 (2002).
  67. F. Verstraete, J. J. García-Ripoll, and J. I. Cirac, Matrix product density operators: Simulation of finite-temperature and dissipative systems, Phys. Rev. Lett. 93, 207204 (2004).
  68. G. Vidal, Efficient simulation of one-dimensional quantum many-body systems, Phys. Rev. Lett. 93, 040502 (2004).
  69. I. P. McCulloch, From density-matrix renormalization group to matrix product states, J. Stat. Mech. (2007) P10014.
  70. B. Pirvu, V. Murg, J. I. Cirac, and F. Verstraete, Matrix product operator representations, New J. Phys. 12, 025012 (2010).
  71. J. Gibbs and L. Cincio, Deep circuit compression for quantum dynamics via tensor networks, Quantum 9, 1789 (2025).
  72. I. N. M. Le, S. Sun, and C. B. Mendl, Riemannian quantum circuit optimization based on matrix product operators, Quantum 9, 1833 (2025).
  73. M. B. Hastings, An area law for one-dimensional quantum systems, J. Stat. Mech. (2007) P08024.
  74. N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Computational complexity of projected entangled pair states, Phys. Rev. Lett. 98, 140506 (2007).
  75. J. Haferkamp, D. Hangleiter, J. Eisert, and M. Gluza, Contracting projected entangled pair states is average-case hard, Phys. Rev. Res. 2, 013010 (2020).
  76. M. S. Leifer and D. Poulin, Quantum graphical models and belief propagation, Ann. Phys. (NY) 323, 1899 (2008).
  77. C. Guo, D. Poletti, and I. Arad, Block belief propagation algorithm for two-dimensional tensor networks, Phys. Rev. B 108, 125111 (2023).
  78. G. Park, J. Gray, and G. K. Chan, Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation, Phys. Rev. B 112, 174310 (2025).
  79. J. Tindall and M. Fishman, Gauging tensor networks with belief propagation, SciPost Phys. 15, 222 (2023).
  80. S. Midha and Y. F. Zhang, Beyond belief propagation: Cluster-corrected tensor network contraction with exponential convergence, arXiv:2510.02290.
  81. T. Begušić, J. Gray, and G. K.-L. Chan, Fast and converged classical simulations of evidence for the utility of quantum computing before fault tolerance, Sci. Adv. 10, eadk4321 (2024).
  82. H.-C. Jiang, Z.-Y. Weng, and T. Xiang, Accurate determination of tensor network state of quantum lattice models in two dimensions, Phys. Rev. Lett. 101, 090603 (2008).
  83. M. Lubasch, J. I. Cirac, and M.-C. Banuls, Unifying projected entangled pair state contractions, New J. Phys. 16, 033014 (2014).
  84. M. Lubasch, J. I. Cirac, and M.-C. Banuls, Algorithms for finite projected entangled pair states, Phys. Rev. B 90, 064425 (2014).
  85. N. Pancotti and J. Gray, One-step replica symmetry breaking in the language of tensor networks, arXiv:2306.15004.
  86. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nat. Commun. 9, 4812 (2018).
  87. A. Arrasmith, M. Cerezo, P. Czarnik, L. Cincio, and P. J. Coles, Effect of barren plateaus on gradient-free optimization, Quantum 5, 558 (2021).
  88. M. Ragone, B. N. Bakalov, F. Sauvage, A. F. Kemper, C. Ortiz Marrero, M. Larocca, and M. Cerezo, A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits, Nat. Commun. 15, 7172 (2024).
  89. D. P. Kingma and J. Ba, ADAM: A method for stochastic optimization, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 79, 2015, Conference Track Proceedings, edited by Y. Bengio and Y. LeCun (International Conference on Learning Representations (ICLR), San Diego, CA, 2015).
  90. J. Gray, quimb: A Python library for quantum information and many-body calculations, J. Open Source Software 3, 819 (2018).
  91. A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, et al., PyTorch: An imperative style, high-performance deep learning library, in Advances in Neural Information Processing Systems, Vol. 32 (Curran Associates, Inc., Red Hook, NY, 2019), pp. 8024–8035.
  92. R. Wiersema and Y. Zhang, Scalable quantum dynamics compilation via quantum machine learning (2024), https://github.com/therooler/variational_compilation.
  93. M. Žnidarič, T. Prosen, and P. Prelovšek, Many-body localization in the Heisenberg XXZ magnet in a random field, Phys. Rev. B 77, 064426 (2008).
  94. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109, 017202 (2012).
  95. M. Serbyn, Z. Papić, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems, Phys. Rev. Lett. 110, 260601 (2013).
  96. Y. Kim, A. Eddins, S. Anand, K. X. Wei, E. van den Berg, S. Rosenblatt, H. Nayfeh, Y. Wu, M. Zaletel, K. Temme, and A. Kandala, Evidence for the utility of quantum computing before fault tolerance, Nature (London) 618, 500 (2023).
  97. R. Haghshenas, E. Chertkov, M. Mills, W. Kadow, S.-H. Lin, Y.-H. Chen, C. Cade, I. Niesen, T. Begušić, M. S. Rudolph, et al., Digital quantum magnetism at the frontier of classical simulations, arXiv:2503.20870.
  98. J. Gibbs, Z. Holmes, M. C. Caro, N. Ezzell, H.-Y. Huang, L. Cincio, A. T. Sornborger, and P. J. Coles, Dynamical simulation via quantum machine learning with provable generalization, Phys. Rev. Res. 6, 013241 (2024).
  99. M. Rigol and A. Muramatsu, Fermionization in an expanding 1D gas of hard-core bosons, Phys. Rev. Lett. 94, 240403 (2005).
  100. I. Hen and M. Rigol, Strongly interacting atom lasers in three-dimensional optical lattices, Phys. Rev. Lett. 105, 180401 (2010).
  101. M. Jreissaty, J. Carrasquilla, F. A. Wolf, and M. Rigol, Expansion of Bose-Hubbard Mott insulators in optical lattices, Phys. Rev. A 84, 043610 (2011).
  102. A. Jreissaty, J. Carrasquilla, and M. Rigol, Self-trapping in the two-dimensional Bose-Hubbard model, Phys. Rev. A 88, 031606(R) (2013).
  103. J. M. Wilson, N. Malvania, Y. Le, Y. Zhang, M. Rigol, and D. S. Weiss, Observation of dynamical fermionization, Science 367, 1461 (2020).
  104. A. M. Childs, Y. Su, M. C. Tran, N. Wiebe, and S. Zhu, Theory of Trotter error with commutator scaling, Phys. Rev. X 11, 011020 (2021).
  105. S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, and C. Hubig, Time-evolution methods for matrix-product states, Ann. Phys. (NY) 411, 167998 (2019).
  106. A Trotterization of order p is such that the leading term of the error grows with ∼tp+1.
  107. F. Verstraete and J. I. Cirac, Renormalization algorithms for quantum-many body systems in two and higher dimensions, arXiv:cond-mat/0407066.
  108. M. P. Zaletel and F. Pollmann, Isometric tensor network states in two dimensions, Phys. Rev. Lett. 124, 037201 (2020).
  109. M. D'Anna, Y. Zhang, R. Wiersema, M. S. Rudolph, and J. Carrasquilla, Circuit compression for 2D quantum dynamics, arXiv:2507.01883.
  110. J. J. Meyer, M. Mularski, E. Gil-Fuster, A. A. Mele, F. Arzani, A. Wilms, and J. Eisert, Exploiting symmetry in variational quantum machine learning, PRX Quantum 4, 010328 (2023).
  111. Q. T. Nguyen, L. Schatzki, P. Braccia, M. Ragone, P. J. Coles, F. Sauvage, M. Larocca, and M. Cerezo, Theory for equivariant quantum neural networks, PRX Quantum 5, 020328 (2024).
  112. R. Wiersema, A. F. Kemper, B. N. Bakalov, and N. Killoran, Geometric quantum machine learning with horizontal quantum gates, Phys. Rev. Res. 7, 013148 (2025).
  113. M. Malinowski, D. T. C. Allcock, and C. J. Ballance, How to wire a 1000-qubit trapped-ion quantum computer, PRX Quantum 4, 040313 (2023).
  114. Y. Zhang and Y. Zhang, Classical simulability of quantum circuits with shallow magic depth, PRX Quantum 6, 010337 (2025).
  115. https://vectorinstitute.ai/#partners.
  116. M. Horodecki, P. Horodecki, and R. Horodecki, General teleportation channel, singlet fraction, and quasidistillation, Phys. Rev. A 60, 1888 (1999).
  117. C. Schön, E. Solano, F. Verstraete, J. I. Cirac, and M. M. Wolf, Sequential generation of entangled multiqubit states, Phys. Rev. Lett. 95, 110503 (2005).
  118. I. H. Kim, Holographic quantum simulation, arXiv:1702.02093.
  119. J.-G. Liu, Y.-H. Zhang, Y. Wan, and L. Wang, Variational quantum eigensolver with fewer qubits, Phys. Rev. Res. 1, 023025 (2019).
  120. T. Soejima, K. Siva, N. Bultinck, S. Chatterjee, F. Pollmann, and M. P. Zaletel, Isometric tensor network representation of string-net liquids, Phys. Rev. B 101, 085117 (2020).
  121. M. Foss-Feig, D. Hayes, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, J. M. Pino, and A. C. Potter, Holographic quantum algorithms for simulating correlated spin systems, Phys. Rev. Res. 3, 033002 (2021).
  122. S. Anand, J. Hauschild, Y. Zhang, A. C. Potter, and M. P. Zaletel, Holographic quantum simulation of entanglement renormalization circuits, PRX Quantum 4, 030334 (2023).
  123. Y. Zhang, S. Jahanbani, D. Niu, R. Haghshenas, and A. C. Potter, Qubit-efficient simulation of thermal states with quantum tensor networks, Phys. Rev. B 106, 165126 (2022).
  124. S. Singh, R. N. C. Pfeifer, and G. Vidal, Tensor network states and algorithms in the presence of a global U(1) symmetry, Phys. Rev. B 83, 115125 (2011).
  125. T. Jones and S. C. Benjamin, Robust quantum compilation and circuit optimisation via energy minimisation, Quantum 6, 628 (2022).
  126. X.-Z. Luo, D. Luo, and R. G. Melko, Operator learning renormalization group, arXiv:2403.03199.
  127. S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett. 69, 2863 (1992).

Outline

Information

Phys. Rev. Research 8, 023128– Published 7 May, 2026
  • Received 19 November 2024
  • Revised 5 June 2025
  • Accepted 4 February 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation