Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2003.12721 · Physical review. B./Physical review. B

Conformal invariance and quantum nonlocality in critical hybrid circuits

Yaodong Li, Xiao Chen, Andreas W. W. Ludwig, Matthew P. A. Fisher

Published Sep 14, 2021• 140 citations
arXivHTMLPDF

Abstract

Local measurements in random quantum circuits lead to a new class of ``entanglement phase transitions''. Through extensive calculations at the critical point of ``stabilizer'' circuits --- organized by a mapping from the finite rectangular geometry to the semi-infinite plane --- the authors find here an emergent conformal field theory description of the entanglement dynamics, whose critical exponents are beyond any known theory. As we show, conformal symmetry implies a measurement-induced Bell-like nonlocality, where distant qubits become entangled with an infinite speed.

DOI
10.1103/physrevb.104.104305

Related papers

Conformal invariance and quantum non-locality in hybrid quantum circuits

Yaodong Li, Xiaohong Chen, Andreas W. W. Ludwig +1 more

We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition, by revealing space-time conformal covariance of entanglement entropies and mutual information for various subregions at different circuit depths. While the evolution takes place in real time, the spacetime manifold of the circuit appears to host a Euclidean field theory with imaginary time. Throughout the paper we investigate circuits with several different boundary conditions by injecting physical qubits at the spatial and/or temporal boundaries, all giving consistent characterizations of the underlying Clifford We emphasize (super)universal results that are consequences solely of the conformal invariance and do not depend crucially on the precise nature of the CFT. Among these are the infinite entangling speed as a consequence of measurement-induced quantum non-locality, and the critical purification dynamics of a mixed initial state.

•Mar 28, 2020•33 citations

Measurement-Induced Transition in Long-Range Interacting Quantum Circuits

Maxwell Block, Yimu Bao, Soonwon Choi +2 more

The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power law, we demonstrate that long-range interactions give rise to a continuum of nonconformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power law.

arXiv:2104.13372•Physical Review Letters•Jan 5, 2022•192 citations

Entanglement phase transitions in random stabilizer tensor networks

Zhi-Cheng Yang, Yaodong Li, Matthew P. A. Fisher +1 more

The authors explore a class of random tensor network models with stabilizer local tensors and study the entanglement phase transitions in these models. They find that an entanglement phase transition can be induced by randomly breaking bulk tensor legs and they extract a set of universal data characterizing the conformal invariance at the critical points. The results clearly demonstrate regimes where a geometric bond percolation picture does or does not apply at the transitions. This work may open new connections to holographic quantum error correcting codes, built from tensor networks.

arXiv:2107.12376•Physical review. B./Physical review. B•Mar 10, 2022•48 citations

Entanglement transition in the projective transverse field Ising model

Nicolai Lang, Hans Peter Büchler

Random quantum circuits have emerged as useful toy models for entanglement transitions in quantum many-body systems. Here, the authors study a projective version of the transverse-field Ising model without unitary dynamics where the competition between two noncommuting measurements drives an entanglement transition. The authors identify a nonlocal classical process that captures the entanglement dynamics and relate the model to bond percolation in space-time. This leads to a conformal field theory description of the system at criticality which they verify numerically for large systems.

arXiv:2006.09748•Physical review. B./Physical review. B•Sep 23, 2020•139 citations

Infinitely fast critical dynamics: Teleportation through temporal rare regions in monitored quantum circuits

Gal Shkolnik, Sarang Gopalakrishnan, David A. Huse +2 more

We consider measurement-induced phase transitions in monitored quantum circuits with a measurement rate that fluctuates in time, remaining spatially uniform at each time. The spatially correlated fluctuations in the measurement rate disrupt the volume-law phase for low measurement rates; at a critical measurement rate, they give rise to an entanglement phase transition with ``ultrafast'' dynamics, i.e., spacetime ($x,t$) scaling $\log x \sim t^{ψ_τ}$. The ultrafast dynamics at the critical point can be viewed as a spacetime-rotated version of an infinite-randomness critical point; despite the spatial locality of the dynamics, ultrafast information propagation is possible because of measurement-induced quantum teleportation. We identify temporal Griffiths phases on either side of this critical point. We provide a physical interpretation of these phases, and support it with extensive numerical simulations of information propagation and entanglement dynamics in stabilizer circuits. The implications of our results on the general stability of phase transitions and ordered phases to such temporal randomness are discussed.

arXiv:2411.03442•Nov 5, 2024•0 citations

Structure of Measurement-Induced Entanglement in Infinite-Randomness Critical States

Oliver Breach

The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent $(3-\sqrt{5})/2$ in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.

cond-mat.stat-mechCross-listedarXiv:2609.17670•Sep 17, 2026•0 citations
Local measurements in random quantum circuits lead to a new class of entanglement phase transitions''. Through extensive calculations at the critical point of stabilizer'' circuits --- organized by a mapping from the finite rectangular geometry to the semi-infinite plane --- the authors find here an emergent conformal field theory description of the entanglement dynamics, whose critical exponents are beyond any known theory. As we show, conformal symmetry implies a measurement-induced Bell-like nonlocality, where distant qubits become entangled with an infinite speed.
We establish the emergence of a conformal field theory (CFT) in a (1+1)-dimensional hybrid quantum circuit right at the measurement-driven entanglement transition, by revealing space-time conformal covariance of entanglement entropies and mutual information for various subregions at different circuit depths. While the evolution takes place in real time, the spacetime manifold of the circuit appears to host a Euclidean field theory with imaginary time. Throughout the paper we investigate circuits with several different boundary conditions by injecting physical qubits at the spatial and/or temporal boundaries, all giving consistent characterizations of the underlying Clifford We emphasize (super)universal results that are consequences solely of the conformal invariance and do not depend crucially on the precise nature of the CFT. Among these are the infinite entangling speed as a consequence of measurement-induced quantum non-locality, and the critical purification dynamics of a mixed initial state.
The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power law, we demonstrate that long-range interactions give rise to a continuum of nonconformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power law.
The authors explore a class of random tensor network models with stabilizer local tensors and study the entanglement phase transitions in these models. They find that an entanglement phase transition can be induced by randomly breaking bulk tensor legs and they extract a set of universal data characterizing the conformal invariance at the critical points. The results clearly demonstrate regimes where a geometric bond percolation picture does or does not apply at the transitions. This work may open new connections to holographic quantum error correcting codes, built from tensor networks.
Random quantum circuits have emerged as useful toy models for entanglement transitions in quantum many-body systems. Here, the authors study a projective version of the transverse-field Ising model without unitary dynamics where the competition between two noncommuting measurements drives an entanglement transition. The authors identify a nonlocal classical process that captures the entanglement dynamics and relate the model to bond percolation in space-time. This leads to a conformal field theory description of the system at criticality which they verify numerically for large systems.
We consider measurement-induced phase transitions in monitored quantum circuits with a measurement rate that fluctuates in time, remaining spatially uniform at each time. The spatially correlated fluctuations in the measurement rate disrupt the volume-law phase for low measurement rates; at a critical measurement rate, they give rise to an entanglement phase transition with ``ultrafast'' dynamics, i.e., spacetime (x,tx,tx,t) scaling log⁡x∼tψτ\log x \sim t^{ψ_τ}logx∼tψτ​. The ultrafast dynamics at the critical point can be viewed as a spacetime-rotated version of an infinite-randomness critical point; despite the spatial locality of the dynamics, ultrafast information propagation is possible because of measurement-induced quantum teleportation. We identify temporal Griffiths phases on either side of this critical point. We provide a physical interpretation of these phases, and support it with extensive numerical simulations of information propagation and entanglement dynamics in stabilizer circuits. The implications of our results on the general stability of phase transitions and ordered phases to such temporal randomness are discussed.
The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent (3−5)/2(3-\sqrt{5})/2(3−5​)/2 in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.