Triviality of quantum trajectories close to a directed percolation transition

Abstract

We study quantum circuits consisting of unitary gates, projective measurements, and control operations that steer the system towards a pure absorbing state. Two types of phase transition occur as the rate of these control operations is increased: a measurement-induced entanglement transition, and a directed percolation transition into the absorbing state (taken here to be a product state). In this work we show analytically that these transitions are generically distinct, with the quantum trajectories becoming disentangled before the absorbing state transition is reached, and we analyze their critical properties. We introduce a simple class of models where the measurements in each quantum trajectory define an Effective Tensor Network (ETN) -- a subgraph of the initial spacetime graph where nontrivial time evolution takes place. By analyzing the entanglement properties of the ETN, we show that the entanglement and absorbing-state transitions coincide only in the limit of infinite local Hilbert-space dimension. Focusing on a Clifford model which allows numerical simulations for large system sizes, we verify our predictions and study the finite-size crossover between the two transitions at large local Hilbert space dimension. We give evidence that the entanglement transition is governed by the same fixed point as in hybrid circuits without feedback.

arXiv comment18 pages, 9 figures; v2: Appendix added, minor revision

References in corpus (55)

• Persistent entanglement in arrays of interacting particles
• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Improved Simulation of Stabilizer Circuits
• A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound
• Operator Spreading in Random Unitary Circuits
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Measurement-driven entanglement transition in hybrid quantum circuits
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Random Quantum Circuits
• Holographic duality from random tensor networks
• Unitary-projective entanglement dynamics
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• Dynamical purification phase transitions induced by quantum measurements
• Random Quantum Circuits are Approximate 2-designs
• Universal scaling behavior of non-equilibrium phase transitions
• Emergent statistical mechanics of entanglement in random unitary circuits
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Entanglement Transitions from Holographic Random Tensor Networks
• Statistical mechanics of quantum error correcting codes
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Low-density series expansions for directed percolation I: A new efficient algorithm with applications to the square lattice
• The Field Theory Approach to Percolation Processes
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Fault-Tolerant Quantum Computation with Higher-Dimensional Systems
• The entanglement membrane in chaotic many-body systems
• Entanglement and dynamics of diffusion-annihilation processes with Majorana defects
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Efficient Generation of Generic Entanglement
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Foliated Quantum Codes
• Measurement-induced steering of quantum systems
• Measurement-induced phase transitions in quantum automaton circuits
• Absorbing state phase transition with competing quantum and classical fluctuations
• Measurements conspire nonlocally to restructure critical quantum states
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Controlling entanglement at absorbing state phase transitions in random circuits
• Transitions in the learnability of global charges from local measurements
• Neural-Network Decoders for Measurement Induced Phase Transitions
• Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems
• Phases and dynamics of ultracold bosons in a tilted optical lattice
• Directed Percolation and Systems with Absorbing States: Impact of Boundaries
• Measurement-induced phase transition in a classical, chaotic many-body system
• Non-equilibrium absorbing state phase transitions in discrete-time quantum dynamics
• Bridging the gap between classical and quantum many-body information dynamics
• Using (1 + 1)D Quantum Cellular Automata for Exploring Collective Effects in Large Scale Quantum Neural Networks
• Dissipative generation of pure steady states and a gambler's ruin problem
• Asynchronism and nonequilibrium phase transitions in $(1+1)$D quantum cellular automata
• Reaction-diffusion dynamics in a Fibonacci chain: Interplay between classical and quantum behavior

Cited by in corpus (36)

• Universality in driven open quantum matter
• Purification Timescales in Monitored Fermions
• Probing post-measurement entanglement without post-selection
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Many-Body Open Quantum Systems
• Boundary transfer matrix spectrum of measurement-induced transitions
• Random-matrix models of monitored quantum circuits
• Field theory of monitored, interacting fermion dynamics with charge conservation
• An architecture for two-qubit encoding in neutral ytterbium-171 atoms
• Measurement-induced phase transitions in monitored infinite-range interacting systems
• Monitored long-range interacting systems: spin-wave theory for quantum trajectories
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Steering-induced phase transition in measurement-only quantum circuits
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Principal component analysis of absorbing state phase transitions
• Local and nonlocal stochastic control of quantum chaos: Measurement- and control-induced criticality
• Breakdown of Measurement-Induced Phase Transitions Under Information Loss
• Statistical Mechanics of Stochastic Quantum Control: $d$-adic Rényi Circuits
• Free fermions under adaptive quantum dynamics
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Efficient post-selection in light-cone correlations of monitored quantum circuits
• Random Quantum Circuits with Time-Reversal Symmetry
• Monitored Fluctuating Hydrodynamics
• Telling different unravelings apart via nonlinear quantum-trajectory averages
• Absorbing State Phase Transition with Clifford Circuits
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Emergent deterministic entanglement dynamics in monitored infinite-range bosonic systems
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor
• Control-driven critical fluctuations across quantum trajectories
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation