Anomaly inflow, dualities, and quantum simulation of Abelian lattice gauge theories induced by measurements

Okuda, Takuya; Parayil Mana, Aswin; Sukeno, Hiroki

doi:10.1103/PhysRevResearch.6.043018

Title: Anomaly inflow, dualities, and quantum simulation of Abelian lattice gauge theories induced by measurements

Journal Article · 04 October 2024 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.6.043018 · OSTI ID:2458247

Okuda, Takuya;

; Sukeno, Hiroki

Previous work [] has demonstrated that quantum simulation of Abelian lattice gauge theories (Wegner models including the toric code in a limit) in general dimensions can be achieved by local adaptive measurements on symmetry-protected topological (SPT) states with higher-form generalized global symmetries. The entanglement structure of the resource SPT state reflects the geometric structure of the gauge theory. In this work we explicitly demonstrate the anomaly inflow mechanism between the deconfining phase of the simulated gauge theory on the boundary and the SPT state in the bulk by showing that the anomalous gauge variation of the boundary state obtained by bulk measurement matches that of the bulk theory. Moreover, we construct the resource state and the measurement pattern for the measurement-based quantum simulation of a lattice gauge theory with a matter field (Fradkin-Shenker model), where a simple scheme to protect gauge invariance of the simulated state against errors is proposed. We further consider taking an overlap between the wave function of the resource state for lattice gauge theories and that of a parameterized product state, and we derive precise dualities between partition functions with insertion of defects corresponding to gauging higher-form global symmetries, as well as measurement-induced phases where states induced by a partial overlap possess different (symmetry-protected) topological orders. Measurement-assisted operators to dualize quantum Hamiltonians of lattice gauge theories and their noninvertibility are also presented. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012704

OSTI ID:: 2458247

Journal Information:: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 4 Vol. 6; ISSN PPRHAI; ISSN 2643-1564

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (78)

Ultracold quantum gases and lattice systems: quantum simulation of lattice gauge theories Wiese, U. ‐J. Annalen der Physik, Vol. 525, Issue 10-11 https://doi.org/10.1002/andp.201300104	journal	July 2013
Generalized global symmetries Gaiotto, Davide; Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2015, Issue 2 https://doi.org/10.1007/JHEP02(2015)172	journal	February 2015
Orbifold groupoids Gaiotto, Davide; Kulp, Justin Journal of High Energy Physics, Vol. 2021, Issue 2 https://doi.org/10.1007/JHEP02(2021)132	journal	February 2021
Coupling a QFT to a TQFT and duality Kapustin, Anton; Seiberg, Nathan Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)001	journal	April 2014
Higher Gauging and Non-invertible Condensation Defects Roumpedakis, Konstantinos; Seifnashri, Sahand; Shao, Shu-Heng Communications in Mathematical Physics, Vol. 401, Issue 3 https://doi.org/10.1007/s00220-023-04706-9	journal	May 2023
Symmetry TFTs from String Theory Apruzzi, Fabio; Bonetti, Federico; García Etxebarria, Iñaki Communications in Mathematical Physics, Vol. 402, Issue 1 https://doi.org/10.1007/s00220-023-04737-2	journal	May 2023
Symmetry TFTs for Non-invertible Defects Kaidi, Justin; Ohmori, Kantaro; Zheng, Yunqin Communications in Mathematical Physics, Vol. 404, Issue 2 https://doi.org/10.1007/s00220-023-04859-7	journal	October 2023
Anomalies and fermion zero modes on strings and domain walls Callan, C. G.; Harvey, J. A. Nuclear Physics B, Vol. 250, Issue 1-4 https://doi.org/10.1016/0550-3213(85)90489-4	journal	January 1985
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Cluster-state quantum computation Nielsen, Michael A. Reports on Mathematical Physics, Vol. 57, Issue 1 https://doi.org/10.1016/S0034-4877(06)80014-5	journal	February 2006
A fault-tolerant one-way quantum computer Raussendorf, R.; Harrington, J.; Goyal, K. Annals of Physics, Vol. 321, Issue 9 https://doi.org/10.1016/j.aop.2006.01.012	journal	September 2006
Braiding statistics and link invariants of bosonic/fermionic topological quantum matter in 2+1 and 3+1 dimensions Putrov, Pavel; Wang, Juven; Yau, Shing-Tung Annals of Physics, Vol. 384 https://doi.org/10.1016/j.aop.2017.06.019	journal	September 2017
Topological boundary conditions in abelian Chern–Simons theory Kapustin, Anton; Saulina, Natalia Nuclear Physics B, Vol. 845, Issue 3 https://doi.org/10.1016/j.nuclphysb.2010.12.017	journal	April 2011
Dual gauge field theory of quantum liquid crystals in two dimensions Beekman, Aron J.; Nissinen, Jaakko; Wu, Kai Physics Reports, Vol. 683 https://doi.org/10.1016/j.physrep.2017.03.004	journal	April 2017
Field Theories of Condensed Matter Physics Fradkin, Eduardo Cambridge University Press https://doi.org/10.1017/CBO9781139015509	book	January 2013
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer Martinez, Esteban A.; Muschik, Christine A.; Schindler, Philipp Nature, Vol. 534, Issue 7608 https://doi.org/10.1038/nature18318	journal	June 2016
Measurement-based quantum computation Briegel, H. J.; Browne, D. E.; Dür, W. Nature Physics, Vol. 5, Issue 1 https://doi.org/10.1038/nphys1157	journal	January 2009
Observation of gauge invariance in a 71-site Bose–Hubbard quantum simulator Yang, Bing; Sun, Hui; Ott, Robert Nature, Vol. 587, Issue 7834 https://doi.org/10.1038/s41586-020-2910-8	journal	November 2020
Realistic scheme for quantum simulation of $${{\mathbb{Z}}}_{2}$$ lattice gauge theories with dynamical matter in (2 + 1)D Homeier, Lukas; Bohrdt, Annabelle; Linsel, Simon Communications Physics, Vol. 6, Issue 1 https://doi.org/10.1038/s42005-023-01237-6	journal	June 2023
Topological quantum memory Dennis, Eric; Kitaev, Alexei; Landahl, Andrew Journal of Mathematical Physics, Vol. 43, Issue 9 https://doi.org/10.1063/1.1499754	journal	September 2002
Duality in Generalized Ising Models and Phase Transitions without Local Order Parameters Wegner, Franz J. Journal of Mathematical Physics, Vol. 12, Issue 10 https://doi.org/10.1063/1.1665530	journal	October 1971
Lattice gauge theory simulations in the quantum information era Dalmonte, M.; Montangero, S. Contemporary Physics, Vol. 57, Issue 3 https://doi.org/10.1080/00107514.2016.1151199	journal	March 2016
Quantum spin models for measurement-based quantum computation Wei, Tzu-Chieh Advances in Physics: X, Vol. 3, Issue 1 https://doi.org/10.1080/23746149.2018.1461026	journal	January 2018
Quantum simulations of lattice gauge theories using ultracold atoms in optical lattices Zohar, Erez; Cirac, J. Ignacio; Reznik, Benni Reports on Progress in Physics, Vol. 79, Issue 1 https://doi.org/10.1088/0034-4885/79/1/014401	journal	December 2015
Topological fault-tolerance in cluster state quantum computation Raussendorf, R.; Harrington, J.; Goyal, K. New Journal of Physics, Vol. 9, Issue 6 https://doi.org/10.1088/1367-2630/9/6/199	journal	June 2007
Topological defects on the lattice: I. The Ising model Aasen, David; Mong, Roger S. K.; Fendley, Paul Journal of Physics A: Mathematical and Theoretical, Vol. 49, Issue 35 https://doi.org/10.1088/1751-8113/49/35/354001	journal	August 2016
Non-invertible topological defects in 4-dimensional $\mathbb {Z}_2$ pure lattice gauge theory Koide, Masataka; Nagoya, Yuta; Yamaguchi, Satoshi Progress of Theoretical and Experimental Physics, Vol. 2022, Issue 1 https://doi.org/10.1093/ptep/ptab145	journal	November 2021
Multiple-particle interference and quantum error correction Steane, Andrew Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 452, Issue 1954, p. 2551-2577 https://doi.org/10.1098/rspa.1996.0136	journal	November 1996
Quantum simulation of lattice gauge theories in more than one space dimension—requirements, challenges and methods Zohar, Erez Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 380, Issue 2216 https://doi.org/10.1098/rsta.2021.0069	journal	December 2021
Gauge-Symmetry Protection Using Single-Body Terms Halimeh, Jad C.; Lang, Haifeng; Mildenberger, Julius PRX Quantum, Vol. 2, Issue 4 https://doi.org/10.1103/PRXQuantum.2.040311	journal	October 2021
Measurement as a Shortcut to Long-Range Entangled Quantum Matter Lu, Tsung-Cheng; Lessa, Leonardo A.; Kim, Isaac H. PRX Quantum, Vol. 3, Issue 4 https://doi.org/10.1103/PRXQuantum.3.040337	journal	December 2022
Hierarchy of Topological Order From Finite-Depth Unitaries, Measurement, and Feedforward Tantivasadakarn, Nathanan; Vishwanath, Ashvin; Verresen, Ruben PRX Quantum, Vol. 4, Issue 2 https://doi.org/10.1103/PRXQuantum.4.020339	journal	June 2023
Quantum Simulation for High-Energy Physics Bauer, Christian W.; Davoudi, Zohreh; Balantekin, A. Baha PRX Quantum, Vol. 4, Issue 2 https://doi.org/10.1103/PRXQuantum.4.027001	journal	May 2023
Statistics of the Two-Dimensional Ferromagnet. Part I Kramers, H. A.; Wannier, G. H. Physical Review, Vol. 60, Issue 3 https://doi.org/10.1103/PhysRev.60.252	journal	August 1941
Good quantum error-correcting codes exist Calderbank, A. R.; Shor, Peter W. Physical Review A, Vol. 54, Issue 2 https://doi.org/10.1103/PhysRevA.54.1098	journal	August 1996
Measurement-based quantum computation on cluster states Raussendorf, Robert; Browne, Daniel E.; Briegel, Hans J. Physical Review A, Vol. 68, Issue 2 https://doi.org/10.1103/PhysRevA.68.022312	journal	August 2003
Multiparty entanglement in graph states Hein, M.; Eisert, J.; Briegel, H. J. Physical Review A, Vol. 69, Issue 6 https://doi.org/10.1103/PhysRevA.69.062311	journal	June 2004
Long-range quantum entanglement in noisy cluster states Raussendorf, Robert; Bravyi, Sergey; Harrington, Jim Physical Review A, Vol. 71, Issue 6 https://doi.org/10.1103/PhysRevA.71.062313	journal	June 2005
Anomaly inflow for subsystem symmetries Burnell, Fiona J.; Devakul, Trithep; Gorantla, Pranay Physical Review B, Vol. 106, Issue 8 https://doi.org/10.1103/PhysRevB.106.085113	journal	August 2022
Noninvertible duality transformation between symmetry-protected topological and spontaneous symmetry breaking phases Li, Linhao; Oshikawa, Masaki; Zheng, Yunqin Physical Review B, Vol. 108, Issue 21 https://doi.org/10.1103/PhysRevB.108.214429	journal	December 2023
Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevB.80.155131	journal	October 2009
Entanglement spectrum of a topological phase in one dimension Pollmann, Frank; Turner, Ari M.; Berg, Erez Physical Review B, Vol. 81, Issue 6 https://doi.org/10.1103/PhysRevB.81.064439	journal	February 2010
Topological multicritical point in the phase diagram of the toric code model and three-dimensional lattice gauge Higgs model Tupitsyn, I. S.; Kitaev, A.; Prokof’ev, N. V. Physical Review B, Vol. 82, Issue 8 https://doi.org/10.1103/PhysRevB.82.085114	journal	August 2010
Classification of gapped symmetric phases in one-dimensional spin systems Chen, Xie; Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 83, Issue 3 https://doi.org/10.1103/PhysRevB.83.035107	journal	January 2011
Classifying quantum phases using matrix product states and projected entangled pair states Schuch, Norbert; Pérez-García, David; Cirac, Ignacio Physical Review B, Vol. 84, Issue 16 https://doi.org/10.1103/PhysRevB.84.165139	journal	October 2011
Complete classification of one-dimensional gapped quantum phases in interacting spin systems Chen, Xie; Gu, Zheng-Cheng; Wen, Xiao-Gang Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235128	journal	December 2011
Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations Chen, Xie; Liu, Zheng-Xin; Wen, Xiao-Gang Physical Review B, Vol. 84, Issue 23 https://doi.org/10.1103/PhysRevB.84.235141	journal	December 2011
Symmetry protection of topological phases in one-dimensional quantum spin systems Pollmann, Frank; Berg, Erez; Turner, Ari M. Physical Review B, Vol. 85, Issue 7 https://doi.org/10.1103/PhysRevB.85.075125	journal	February 2012
Symmetry protected topological orders and the group cohomology of their symmetry group Chen, Xie; Gu, Zheng-Cheng; Liu, Zheng-Xin Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155114	journal	April 2013
Topological phases with generalized global symmetries Yoshida, Beni Physical Review B, Vol. 93, Issue 15 https://doi.org/10.1103/PhysRevB.93.155131	journal	April 2016
Realizing anomalous anyonic symmetries at the surfaces of three-dimensional gauge theories Fidkowski, Lukasz; Vishwanath, Ashvin Physical Review B, Vol. 96, Issue 4 https://doi.org/10.1103/PhysRevB.96.045131	journal	July 2017
Quantum Zeno effect and the many-body entanglement transition Li, Yaodong; Chen, Xiao; Fisher, Matthew P. A. Physical Review B, Vol. 98, Issue 20 https://doi.org/10.1103/PhysRevB.98.205136	journal	November 2018
Unitary-projective entanglement dynamics Chan, Amos; Nandkishore, Rahul M.; Pretko, Michael Physical Review B, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevB.99.224307	journal	June 2019
Order and disorder in gauge systems and magnets Fradkin, Eduardo; Susskind, Leonard Physical Review D, Vol. 17, Issue 10 https://doi.org/10.1103/PhysRevD.17.2637	journal	May 1978
Phase diagrams of lattice gauge theories with Higgs fields Fradkin, Eduardo; Shenker, Stephen H. Physical Review D, Vol. 19, Issue 12 https://doi.org/10.1103/PhysRevD.19.3682	journal	June 1979
Wave Function and Strange Correlator of Short-Range Entangled States You, Yi-Zhuang; Bi, Zhen; Rasmussen, Alex Physical Review Letters, Vol. 112, Issue 24 https://doi.org/10.1103/PhysRevLett.112.247202	journal	June 2014
Foliated Quantum Error-Correcting Codes Bolt, A.; Duclos-Cianci, G.; Poulin, D. Physical Review Letters, Vol. 117, Issue 7 https://doi.org/10.1103/PhysRevLett.117.070501	journal	August 2016
Mapping Topological to Conformal Field Theories through strange Correlators Vanhove, Robijn; Bal, Matthias; Williamson, Dominic J. Physical Review Letters, Vol. 121, Issue 17 https://doi.org/10.1103/PhysRevLett.121.177203	journal	October 2018
Reliability of Lattice Gauge Theories Halimeh, Jad C.; Hauke, Philipp Physical Review Letters, Vol. 125, Issue 3 https://doi.org/10.1103/PhysRevLett.125.030503	journal	July 2020
Quantum Circuits Assisted by Local Operations and Classical Communication: Transformations and Phases of Matter Piroli, Lorenzo; Styliaris, Georgios; Cirac, J. Ignacio Physical Review Letters, Vol. 127, Issue 22 https://doi.org/10.1103/PhysRevLett.127.220503	journal	November 2021
A One-Way Quantum Computer Raussendorf, Robert; Briegel, Hans J. Physical Review Letters, Vol. 86, Issue 22 https://doi.org/10.1103/PhysRevLett.86.5188	journal	May 2001
Persistent Entanglement in Arrays of Interacting Particles Briegel, Hans J.; Raussendorf, Robert Physical Review Letters, Vol. 86, Issue 5 https://doi.org/10.1103/PhysRevLett.86.910	journal	January 2001
Topological Entanglement Entropy Kitaev, Alexei; Preskill, John Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110404	journal	March 2006
Detecting Topological Order in a Ground State Wave Function Levin, Michael; Wen, Xiao-Gang Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110405	journal	March 2006
Classical Spin Models and the Quantum-Stabilizer Formalism den Nest, M. Van; Dür, W.; Briegel, H. J. Physical Review Letters, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevLett.98.117207	journal	March 2007
Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions Raussendorf, Robert; Harrington, Jim Physical Review Letters, Vol. 98, Issue 19 https://doi.org/10.1103/PhysRevLett.98.190504	journal	May 2007
Stabilizing lattice gauge theories through simplified local pseudogenerators Halimeh, Jad C.; Homeier, Lukas; Schweizer, Christian Physical Review Research, Vol. 4, Issue 3 https://doi.org/10.1103/PhysRevResearch.4.033120	journal	August 2022
Symmetry-Protected Self-Correcting Quantum Memories Roberts, Sam; Bartlett, Stephen D. Physical Review X, Vol. 10, Issue 3 https://doi.org/10.1103/PhysRevX.10.031041	journal	August 2020
Long-Range Entanglement from Measuring Symmetry-Protected Topological Phases Tantivasadakarn, Nathanan; Thorngren, Ryan; Vishwanath, Ashvin Physical Review X, Vol. 14, Issue 2 https://doi.org/10.1103/PhysRevX.14.021040	journal	June 2024
Measurement-Induced Phase Transitions in the Dynamics of Entanglement Skinner, Brian; Ruhman, Jonathan; Nahum, Adam Physical Review X, Vol. 9, Issue 3 https://doi.org/10.1103/PhysRevX.9.031009	journal	July 2019
An introduction to lattice gauge theory and spin systems Kogut, John B. Reviews of Modern Physics, Vol. 51, Issue 4 https://doi.org/10.1103/RevModPhys.51.659	journal	October 1979
Quantum Algorithms for Quantum Field Theories Jordan, S. P.; Lee, K. S. M.; Preskill, J. Science, Vol. 336, Issue 6085 https://doi.org/10.1126/science.1217069	journal	May 2012
Universal Quantum Simulators Lloyd, S. Science, Vol. 273, Issue 5278 https://doi.org/10.1126/science.273.5278.1073	journal	August 1996
Simulating lattice gauge theories within quantum technologies Bañuls, Mari Carmen; Blatt, Rainer; Catani, Jacopo The European Physical Journal D, Vol. 74, Issue 8 https://doi.org/10.1140/epjd/e2020-100571-8	journal	August 2020
Feynman Lectures on Computation Feynman, Richard P.; Hey, Tony; Allen, Robin W. https://doi.org/10.1201/9780429500442	book	January 2001
Measurement-based quantum simulation of Abelian lattice gauge theories Sukeno, Hiroki; Okuda, Takuya SciPost Physics, Vol. 14, Issue 5 https://doi.org/10.21468/SciPostPhys.14.5.129	journal	May 2023
Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries Seifnashri, Sahand SciPost Physics, Vol. 16, Issue 4 https://doi.org/10.21468/SciPostPhys.16.4.098	journal	April 2024
Paths, Trees, and Flowers Edmonds, Jack Canadian Journal of Mathematics, Vol. 17 https://doi.org/10.4153/CJM-1965-045-4	journal	January 1965

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