The evolution of entanglement entropy in quantum circuits composed of Haar-random gates and projective measurements shows versatile behavior, with connections to phase transitions and complexity theory. We reformulate the problem in terms of a classical Markov process for the dynamics of bipartition purities and establish a probabilistic cellular-automaton algorithm to compute entanglement entropy in monitored random circuits on arbitrary graphs. In one dimension, we further relate the evolution of the entropy to a simple classical spin model that naturally generalizes a two-dimensional lattice percolation problem. We also establish a Markov model for the evolution of the zeroth Rényi entropy and demonstrate that, in one dimension and in the limit of large local dimension, it coincides with the corresponding second-Rényi-entropy model. Finally, we extend the Markovian description to a more general setting that incorporates continuous-time dynamics, defined by stochastic Hamiltonians and weak local measurements continuously monitoring the system.
Monitored quantum dynamics reveal quantum state trajectories which exhibit a rich phenomenology of entanglement structures, including a transition from a weakly-monitored volume law entangled phase to a strongly-monitored area law phase. For one-dimensional hybrid circuits with both random unitary dynamics and interspersed measurements, we combine analytic mappings to an effective statistical mechanics model with extensive numerical simulations on hybrid Clifford circuits to demonstrate that the universal entanglement properties of the volume law phase can be quantitatively described by a fluc…
Generic many-body systems coupled to an environment lose their quantum entanglement due to decoherence and evolve to a mixed state with only classical correlations. Here, we show that measurements can stabilize quantum entanglement within open quantum systems. Specifically, in random unitary circuits with dephasing at the boundary, we find both numerically and analytically that projective measurements performed at a small nonvanishing rate results in a steady state with an $L^{1/3}$ power-law scaling entanglement negativity within the system. Using an analytical mapping to a statistical mechan…
Fractal structure of multipartite entanglement in monitored quantum circuits
Smalley-Curl Institute, Rice University（莱斯大学斯马利-柯尔研究所）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文系）；Laboratory of Atomic and Solid State Physics, Cornell University（康奈尔大学原子与固态物理实验室）
Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, disti…
We study a (1+1)-dimensional quantum circuit consisting of Haar-random unitary gates and projective measurements that conserve a total $U(1)$ charge and thus have $U(1)$ symmetry. In addition to a measurement-induced entanglement transition between a volume-law and an area-law entangled phase, we find a phase transition between two phases characterized by bipartite charge fluctuation growing with the subsystem size or staying constant. At this charge-fluctuation transition, steady-state quantities obtained by evolving an initial state with a definitive total charge exhibit critical scaling beh…
Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
University of Tokyo（东京大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先锋研究本部）；University of Warwick（华威大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心）；RIKEN（理化学研究所）；Ritsumeikan University（立命馆大学）
Infinitely fast critical dynamics: Teleportation through temporal rare regions in monitored quantum circuits
Racah Institute of Physics, The Hebrew University of Jerusalem（拉卡物理学研究所，耶路撒冷希伯来大学）；Department of Electrical and Computer Engineering, Princeton University（电气与计算机工程系，普林斯顿大学）；Department of Physics, Princeton University（物理系，普林斯顿大学）；The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem（分子动力学弗里茨·哈伯研究中心，耶路撒冷希伯来大学）；Department of Physics and Astronomy, Center for Materials Theory, Rutgers University（物理与天文学系，材料理论中心，罗格斯大学）；Center for Computational Quantum Physics, Flatiron Institute（计算量子物理中心，平顿研究所）
Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp …
Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California（南加州大学明思海电气与计算机工程系）；Department of Electrical and Computer Engineering, Princeton University（普林斯顿大学电气与计算机工程系）；Department of Physics and Astronomy, University of Southern California（南加州大学物理与天文学系）
Random quantum circuit is a minimally structured model to study the entanglement dynamics of many-body quantum systems. In this paper, we considered a one-dimensional quantum circuit with noisy Haar-random unitary gates using density matrix operator and tensor contraction methods. It is shown that the entanglement evolution of the random quantum circuits is properly characterized by the logarithmic entanglement negativity. By performing exact numerical calculations, we found that, as the physical error rate is decreased below a critical value $p_c\approx 0.056$, the logarithmic entanglement ne…
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 …
Flow to Nishimori universality in weakly monitored quantum circuits with qubit loss
University of Cologne（科隆大学）；University of Geneva（日内瓦大学）；University of California, Santa Barbara（加州大学圣塔芭芭拉分校）；The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））
Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
RIKEN Center for Quantum Computing (RQC)（理化学研究所量子计算中心）；RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；RIKEN Center for Emergent Matter Science (CEMS)（理化学研究所新物质科学中心）；RIKEN Cluster for Pioneering Research (CPR)（理化学研究所先锋研究集群）
No measurement induced phase transition in the entanglement dynamics of monitored non-interacting one-dimensional fermions in a disordered or quasiperiodic potential
Shanghai Center for Complex Physics, School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院复杂物理中心）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）
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 sub-extensive 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…
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We encounter two phase transitions with increasing projection rate: The first is the volume-to-area law transition observed in quantum circuits with projective measurements; The second separates the pure Poisson level statistics phase at large projective measurement rates from a regime of residual level repulsion in the entanglement spectrum within the area-law phase,…
We study a class of (1+1)D symmetric random quantum circuits with two competing types of measurements in addition to random unitary dynamics. The circuit exhibits a rich phase diagram involving robust symmetry-protected topological (SPT), trivial, and volume law entangled phases, where the transitions are hidden to expectation values of operators and can only be accessed through the entanglement entropy averaged over quantum trajectories. In the absence of unitary dynamics, we find a purely measurement-induced critical point with logarithmic scaling of the entanglement entropy, which we map ex…
We address entanglement transitions in monitored random quantum circuits of non-interacting fermions, in particular, the question of whether Born-rule and forced measurements yield the same universality class. For a generic circuit with no symmetry other than fermion parity, acting on a one-dimensional Majorana chain, we numerically obtain several critical exponents, providing clear evidence that the two transitions with Born-rule and forced measurements are in different universality classes. We provide a theoretical understanding for our numerical results by identifying the underlying statist…
We develop solvable models of large-$N$ hybrid quantum circuits on qubits and fermions with long-range power-law interactions and continuous local monitoring, which provide analytical access to the entanglement phase diagram and error-correcting properties of many-body entangled non-equilibrium states generated by such dynamics. In one dimension, the long-range coupling is irrelevant for $α>3/2$, where $α$ is the power-law exponent, and the models exhibit a conventional measurement-induced phase transition between volume- and area-law entangled phases. For $1/2<α<3/2$ the long-range coupling b…
A quantum many-body system whose dynamics includes local measurements at a nonzero rate can be in distinct dynamical phases, with differing entanglement properties. We introduce theoretical approaches to measurement-induced phase transitions (MPT) and also to entanglement transitions in random tensor networks. Many of our results are for "all-to-all" quantum circuits with unitaries and measurements, in which any qubit can couple to any other, and related settings where some of the complications of low-dimensional models are reduced. We also propose field theory descriptions for spatially local…
