Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions

Abstract

We investigate the structure of many-body wave functions of 1D quantum circuits with local measurements employing the participation entropies. The leading term in system size dependence of participation entropy indicates a model dependent multifractal scaling of the wave-functions at any non-zero measurement rate. The sub-leading term contains universal information about measurement-induced phase transitions and plays the role of an order parameter, being constant non-zero in the error correcting phase and vanishing in the quantum Zeno phase. We provide robust numerical evidence investigating a variety of quantum many-body systems, and provide an analytical interpretation of this behavior expressing the participation entropy in terms of partition functions of classical statistical models in 2D.

4+16 pages, added new results on universality and extended discussions, comments welcome

References in corpus (67)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Anderson Transitions
• Strong quantum computational advantage using a superconducting quantum processor
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Quantum trajectories and open many-body quantum systems
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• High-fidelity projective readout of a solid-state spin quantum register
• Stim: a fast stabilizer circuit simulator
• Critical properties of the measurement-induced transition in random quantum circuits
• Evenly distributed unitaries: on the structure of unitary designs
• Observation of quantum jumps in a superconducting artificial atom
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Ergodicity breaking in a model showing many-body localization
• Ground state entanglement and geometric entropy in the Kitaev's model
• Entanglement phase transitions in measurement-only dynamics
• Coherent many-body spin dynamics in a long-range interacting Ising chain
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
• Statistical mechanics of quantum error correcting codes
• Measurement Protected Quantum Phases
• Measurement and entanglement phase transitions in all-to-all quantum circuits, on quantum trees, and in Landau-Ginsburg theory
• Postselection-free entanglement dynamics via spacetime duality
• Measurement-induced quantum criticality under continuous monitoring
• Self-Organized Error Correction in Random Unitary Circuits with Measurement
• Measurement-induced criticality in (2+1)-d hybrid quantum circuits
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Entanglement Transition in the Projective Transverse Field Ising Model
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Fate of measurement-induced phase transition in long-range interactions
• Symmetry enriched phases of quantum circuits
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
• Measurement-induced entanglement transitions in many-body localized systems
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Spacetime duality between localization transitions and measurement-induced transitions
• Measurement-induced dynamics of many-body systems at quantum criticality
• Hadamard-free circuits expose the structure of the Clifford group
• Measurement-induced transitions of the entanglement scaling law in ultracold gases with controllable dissipation
• Entanglement Negativity at Measurement-Induced Criticality
• Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
• Rényi entropy of a line in two-dimensional Ising models
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• How Dynamical Quantum Memories Forget
• Mean-field entanglement transitions in random tree tensor networks
• Quantum criticality in the nonunitary dynamics of $(2+1)$-dimensional free fermions
• Chaos and ergodicity across the energy spectrum of interacting bosons
• Participation spectroscopy and entanglement Hamiltonian of quantum spin models
• Engineered dissipation induced entanglement transition in quantum spin chains: from logarithmic growth to area law
• Improving entanglement and thermodynamic Rényi entropy measurements in quantum Monte Carlo
• Quantum Zeno effect appears in stages
• Simulating a measurement-induced phase transition for trapped ion circuits
• Yang-Lee edge singularity triggered entanglement transition
• A pulsed ion microscope to probe quantum gases
• Multifractality and self-averaging at the many-body localization transition
• Efficient Quantum Tensor Product Expanders and k-designs
• Classical Models of Entanglement in Monitored Random Circuits
• Multifractality in non-unitary random dynamics
• Criticality and entanglement in non-unitary quantum circuits and tensor networks of non-interacting fermions
• Entanglement transitions from restricted Boltzmann machines
• A simple method for sampling random Clifford operators

Cited by in corpus (83)

• Random Quantum Circuits
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Many-Body Localization in the Age of Classical Computing
• Quantifying nonstabilizerness of matrix product states
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Monitored Open Fermion Dynamics: Exploring the Interplay of Measurement, Decoherence, and Free Hamiltonian Evolution
• Controlling entanglement at absorbing state phase transitions in random circuits
• Measuring nonstabilizerness via multifractal flatness
• Transitions in the learnability of global charges from local measurements
• Disordered monitored free fermions
• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Efficient quantum algorithms for stabilizer entropies
• Measurement-induced criticality as a data-structure transition
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Stability of many-body localization in Floquet systems
• Purification Timescales in Monitored Fermions
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Localization properties in disordered quantum many-body dynamics under continuous measurement
• Universality in Anderson localization on random graphs with varying connectivity
• Entanglement-magic separation in hybrid quantum circuits
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Entanglement phases, localization and multifractality of monitored free fermions in two dimensions
• Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
• Entanglement transitions and quantum bifurcations under continuous long-range monitoring
• Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
• Entanglement phase transitions in non-Hermitian quasicrystals
• Interactions and integrability in weakly monitored Hamiltonian systems
• Hilbert space delocalization under random unitary circuits
• KPZ physics and phase transition in a classical single random walker under continuous measurement
• Entanglement Growth and Minimal Membranes in $(d+1)$ Random Unitary Circuits
• Measurement-induced symmetry restoration and quantum Mpemba effect
• Renormalization group for measurement and entanglement phase transitions
• Enhanced Entanglement in the Measurement-Altered Quantum Ising Chain
• Chaos and magic in the dissipative quantum kicked top
• Measurement-Induced Quantum Synchronization and Multiplexing
• Anticoncentration and state design of random tensor networks
• Hilbert-space correlations beyond multifractality and bipartite entanglement in many-body localised systems
• The impact of different unravelings in a monitored system of free fermions
• Monitored long-range interacting systems: spin-wave theory for quantum trajectories
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Many-body entropies and entanglement from polynomially-many local measurements
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Magic transition in measurement-only circuits
• Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
• Multifractality of many-body non-Hermitian skin effect
• Stabilizer Rényi Entropy and Conformal Field Theory
• Nonstabilizerness of a Boundary Time Crystal
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• An analysis of localization transitions using non-parametric unsupervised learning
• Multifractality in the interacting disordered Tavis-Cummings model
• The non-stabilizerness of fermionic Gaussian states
• Fermionic Magic Resources of Quantum Many-Body Systems
• Measurement-Induced Spectral Transition
• Unconventional Scalings of Quantum Entropies in Long-Range Heisenberg Chains
• Emergent multifractality in power-law decaying eigenstates
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Phase transitions induced by standard and predetermined measurements in transmon arrays
• Multipartite entanglement structure of monitored quantum circuits
• Probing prethermal nonergodicity through measurement outcomes of monitored quantum dynamics
• Multifractality in monitored single-particle dynamics
• Monitored Fluctuating Hydrodynamics
• Measurement-induced phase transition in periodically driven free-fermionic systems
• Random Quantum Circuits with Time-Reversal Symmetry
• Telling different unravelings apart via nonlinear quantum-trajectory averages
• Multifractality and excited-state quantum phase transition in ferromagnetic spin-$1$ Bose-Einstein condensates
• Absorption to Fluctuating Bunching States in Non-Unitary Boson Dynamics
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Detecting Measurement-Induced Entanglement Transitions With Unitary Mirror Circuits
• Entanglement phases and phase transitions in monitored free fermion system due to localizations
• Entanglement behavior and localization properties in monitored fermion systems
• Measurement-induced criticality in extended and long-range unitary circuits
• Transitions of the Lyapunov spectrum and entanglement entropy in monitored quantum dynamics with homogeneous unitary gates
• Anticoncentration in Clifford Circuits and Beyond: From Random Tensor Networks to Pseudo-Magic States
• Entanglement transition and suppression of critical phase of thermofield double state in monitored quantum circuit with unitary $R$ matrix gates
• Noisy Monitored Quantum Circuits
• Information Bounds on phase transitions in disordered systems