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Poboiko I, Gornyi IV, Mirlin AD. Measurement-Induced Phase Transition for Free Fermions above One Dimension. PHYSICAL REVIEW LETTERS 2024; 132:110403. [PMID: 38563946 DOI: 10.1103/physrevlett.132.110403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Revised: 01/10/2024] [Accepted: 02/15/2024] [Indexed: 04/04/2024]
Abstract
A theory of the measurement-induced entanglement phase transition for free-fermion models in d>1 dimensions is developed. The critical point separates a gapless phase with ℓ^{d-1}lnℓ scaling of the second cumulant of the particle number and of the entanglement entropy and an area-law phase with ℓ^{d-1} scaling, where ℓ is a size of the subsystem. The problem is mapped onto an SU(R) replica nonlinear sigma model in d+1 dimensions, with R→1. Using renormalization-group analysis, we calculate critical indices in one-loop approximation justified for d=1+ε with ε≪1. Further, we carry out a numerical study of the transition for a d=2 model on a square lattice, determine numerically the critical point, and estimate the critical index of the correlation length, ν≈1.4.
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Affiliation(s)
- Igor Poboiko
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - Igor V Gornyi
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
| | - Alexander D Mirlin
- Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany
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2
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Iadecola T, Ganeshan S, Pixley JH, Wilson JH. Measurement and Feedback Driven Entanglement Transition in the Probabilistic Control of Chaos. PHYSICAL REVIEW LETTERS 2023; 131:060403. [PMID: 37625043 DOI: 10.1103/physrevlett.131.060403] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/29/2022] [Revised: 02/09/2023] [Accepted: 07/20/2023] [Indexed: 08/27/2023]
Abstract
We uncover a dynamical entanglement transition in a monitored quantum system that is heralded by a local order parameter. Classically, chaotic systems can be stochastically controlled onto unstable periodic orbits and exhibit controlled and uncontrolled phases as a function of the rate at which the control is applied. We show that such control transitions persist in open quantum systems where control is implemented with local measurements and unitary feedback. Starting from a simple classical model with a known control transition, we define a quantum model that exhibits a diffusive transition between a chaotic volume-law entangled phase and a disentangled controlled phase. Unlike other entanglement transitions in monitored quantum circuits, this transition can also be probed by correlation functions without resolving individual quantum trajectories.
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Affiliation(s)
- Thomas Iadecola
- Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
- Ames National Laboratory, Ames, Iowa 50011, USA
| | - Sriram Ganeshan
- Department of Physics, City College, City University of New York, New York, New York 10031, USA
- CUNY Graduate Center, New York, New York 10031, USA
| | - J H Pixley
- Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
- Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010
| | - Justin H Wilson
- Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
- Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
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3
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Moghaddam AG, Pöyhönen K, Ojanen T. Exponential Shortcut to Measurement-Induced Entanglement Phase Transitions. PHYSICAL REVIEW LETTERS 2023; 131:020401. [PMID: 37505948 DOI: 10.1103/physrevlett.131.020401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Revised: 05/19/2023] [Accepted: 06/20/2023] [Indexed: 07/30/2023]
Abstract
Recently discovered measurement-induced entanglement phase transitions in monitored quantum circuits provide a novel example of far-from-equilibrium quantum criticality. Here, we propose a highly efficient strategy for experimentally accessing these transitions through fluctuations. Instead of directly measuring entanglement entropy, which requires an exponential number of measurements in the subsystem size, our method provides a scalable approach to entanglement transitions in the presence of conserved quantities. In analogy to entanglement entropy and mutual information, we illustrate how bipartite and multipartite fluctuations can both be employed to analyze the measurement-induced criticality. Remarkably, the phase transition can be revealed by measuring fluctuations of only a handful of qubits.
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Affiliation(s)
- Ali G Moghaddam
- Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, FI-33014 Tampere, Finland
- Helsinki Institute of Physics, University of Helsinki, Helsinki FI-00014, Finland
- Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
| | - Kim Pöyhönen
- Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, FI-33014 Tampere, Finland
- Helsinki Institute of Physics, University of Helsinki, Helsinki FI-00014, Finland
| | - Teemu Ojanen
- Computational Physics Laboratory, Physics Unit, Faculty of Engineering and Natural Sciences, Tampere University, FI-33014 Tampere, Finland
- Helsinki Institute of Physics, University of Helsinki, Helsinki FI-00014, Finland
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Dehghani H, Lavasani A, Hafezi M, Gullans MJ. Neural-network decoders for measurement induced phase transitions. Nat Commun 2023; 14:2918. [PMID: 37217474 DOI: 10.1038/s41467-023-37902-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/27/2022] [Accepted: 04/05/2023] [Indexed: 05/24/2023] Open
Abstract
Open quantum systems have been shown to host a plethora of exotic dynamical phases. Measurement-induced entanglement phase transitions in monitored quantum systems are a striking example of this phenomena. However, naive realizations of such phase transitions requires an exponential number of repetitions of the experiment which is practically unfeasible on large systems. Recently, it has been proposed that these phase transitions can be probed locally via entangling reference qubits and studying their purification dynamics. In this work, we leverage modern machine learning tools to devise a neural network decoder to determine the state of the reference qubits conditioned on the measurement outcomes. We show that the entanglement phase transition manifests itself as a stark change in the learnability of the decoder function. We study the complexity and scalability of this approach in both Clifford and Haar random circuits and discuss how it can be utilized to detect entanglement phase transitions in generic experiments.
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Affiliation(s)
- Hossein Dehghani
- Joint Quantum Institute, NIST/University of Maryland, College Park, MD, 20742, USA.
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, 20742, USA.
| | - Ali Lavasani
- Joint Quantum Institute, NIST/University of Maryland, College Park, MD, 20742, USA
- Condensed Matter Theory Center, University of Maryland, College Park, MD, 20742, USA
| | - Mohammad Hafezi
- Joint Quantum Institute, NIST/University of Maryland, College Park, MD, 20742, USA
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, 20742, USA
| | - Michael J Gullans
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, MD, 20742, USA
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Sierant P, Turkeshi X. Controlling Entanglement at Absorbing State Phase Transitions in Random Circuits. PHYSICAL REVIEW LETTERS 2023; 130:120402. [PMID: 37027858 DOI: 10.1103/physrevlett.130.120402] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Revised: 02/23/2023] [Accepted: 02/28/2023] [Indexed: 06/19/2023]
Abstract
Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the dynamics toward an absorbing state, we study the entanglement entropy behavior at the absorbing state phase transition. For short-range control operations, we observe a transition between phases with distinct subextensive scalings of entanglement entropy. In contrast, the system undergoes a transition between volume-law and area-law phases for long-range feedback operations. The fluctuations of entanglement entropy and of the order parameter of the absorbing state transition are fully coupled for sufficiently strongly entangling feedback operations. In that case, entanglement entropy inherits the universal dynamics of the absorbing state transition. This is, however, not the case for arbitrary control operations, and the two transitions are generally distinct. We quantitatively support our results by introducing a framework based on stabilizer circuits with classical flag labels. Our results shed new light on the problem of observability of measurement-induced phase transitions.
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Affiliation(s)
- Piotr Sierant
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels (Barcelona), Spain
| | - Xhek Turkeshi
- JEIP, USR 3573 CNRS, Collège de France, PSL Research University, 11 Place Marcelin Berthelot, 75321 Paris Cedex 05, France
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Barratt F, Agrawal U, Potter AC, Gopalakrishnan S, Vasseur R. Transitions in the Learnability of Global Charges from Local Measurements. PHYSICAL REVIEW LETTERS 2022; 129:200602. [PMID: 36461989 DOI: 10.1103/physrevlett.129.200602] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 10/18/2022] [Indexed: 06/17/2023]
Abstract
We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.
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Affiliation(s)
- Fergus Barratt
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Utkarsh Agrawal
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California, USA
| | - Andrew C Potter
- Department of Physics and Astronomy, and Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, Canada V6T 1Z1
| | - Sarang Gopalakrishnan
- Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
- Department of Electrical and Computer Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Romain Vasseur
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
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Stefanov VP, Shatokhin VN, Mogilevtsev DS, Kilin SY. Key for a Hidden Quantum State. PHYSICAL REVIEW LETTERS 2022; 129:083603. [PMID: 36053688 DOI: 10.1103/physrevlett.129.083603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/17/2020] [Revised: 03/05/2022] [Accepted: 07/27/2022] [Indexed: 06/15/2023]
Abstract
Quantum trajectories are crucial to understanding the evolution of open systems. We consider an open cavity mode undergoing up and down multistate quantum jumps due to the emission and absorption of photons. We prove that among all subtrajectories, starting simultaneously from different photon number states, only one survives a long single-run evolution. A random Fock state terminating the subtrajectory becomes known for the ergodic case via the key-the processed record of the input and output photocounts, and the trajectory duration. Based on this result, we propose a robust protocol to infer the Fock state, a valuable resource for quantum applications.
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Affiliation(s)
- V P Stefanov
- B.I.Stepanov Institute of Physics of NAS of Belarus, Nezavisimosti Ave. 68, 220072, Minsk, Belarus
| | - V N Shatokhin
- Physikalisches Institut and EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - D S Mogilevtsev
- B.I.Stepanov Institute of Physics of NAS of Belarus, Nezavisimosti Ave. 68, 220072, Minsk, Belarus
| | - S Ya Kilin
- B.I.Stepanov Institute of Physics of NAS of Belarus, Nezavisimosti Ave. 68, 220072, Minsk, Belarus
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Abbasi M, Chen W, Naghiloo M, Joglekar YN, Murch KW. Topological Quantum State Control through Exceptional-Point Proximity. PHYSICAL REVIEW LETTERS 2022; 128:160401. [PMID: 35522514 DOI: 10.1103/physrevlett.128.160401] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 01/12/2022] [Accepted: 03/22/2022] [Indexed: 06/14/2023]
Abstract
We study the quantum evolution of a non-Hermitian qubit realized as a submanifold of a dissipative superconducting transmon circuit. Real-time tuning of the system parameters to encircle an exceptional point results in nonreciprocal quantum state transfer. We further observe chiral geometric phases accumulated under state transport, verifying the quantum coherent nature of the evolution in the complex energy landscape and distinguishing between coherent and incoherent effects associated with exceptional point encircling. Our work demonstrates an entirely new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled through dynamical non-Hermitian control.
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Affiliation(s)
- Maryam Abbasi
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
| | - Weijian Chen
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Center for Quantum Sensors, Washington University, St. Louis, Missouri 63130, USA
| | - Mahdi Naghiloo
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Research Laboratory of Electronics, MIT, Cambridge, Massachusetts 02139, USA
| | - Yogesh N Joglekar
- Department of Physics, Indiana University Purdue University Indianapolis (IUPUI), Indianapolis, Indiana 46202, USA
| | - Kater W Murch
- Department of Physics, Washington University, St. Louis, Missouri 63130, USA
- Center for Quantum Sensors, Washington University, St. Louis, Missouri 63130, USA
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Lavasani A, Alavirad Y, Barkeshli M. Topological Order and Criticality in (2+1)D Monitored Random Quantum Circuits. PHYSICAL REVIEW LETTERS 2021; 127:235701. [PMID: 34936777 DOI: 10.1103/physrevlett.127.235701] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/05/2021] [Accepted: 11/08/2021] [Indexed: 06/14/2023]
Abstract
It has recently been discovered that random quantum circuits provide an avenue to realize rich entanglement phase diagrams, which are hidden to standard expectation values of operators. Here we study (2+1)D random circuits with random Clifford unitary gates and measurements designed to stabilize trivial area law and topologically ordered phases. With competing single qubit Pauli-Z and toric code stabilizer measurements, in addition to random Clifford unitaries, we find a phase diagram involving a tricritical point that maps to (2+1)D percolation, a possibly stable critical phase, topologically ordered, trivial, and volume law phases, and lines of critical points separating them. With Pauli-Y single qubit measurements instead, we find an anisotropic self-dual tricritical point, with dynamical exponent z≈1.46, exhibiting logarithmic violation of the area law and an anomalous exponent for the topological entanglement entropy, which thus appears distinct from any known percolation fixed point. The phase diagram also hosts a measurement-induced volume law entangled phase in the absence of unitary dynamics.
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Affiliation(s)
- Ali Lavasani
- Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
| | - Yahya Alavirad
- Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
- Department of Physics, University of California at San Diego, La Jolla, California 92093, USA
| | - Maissam Barkeshli
- Condensed Matter Theory Center, University of Maryland, College Park, Maryland 20742, USA
- Joint Quantum Institute, University of Maryland, College Park, Maryland 20742, USA
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