How Dynamical Quantum Memories Forget

Abstract

Motivated by recent work showing that a quantum error correcting code can be generated by hybrid dynamics of unitaries and measurements, we study the long time behavior of such systems. We demonstrate that even in the "mixed" phase, a maximally mixed initial density matrix is purified on a time scale equal to the Hilbert space dimension (i.e., exponential in system size), albeit with noisy dynamics at intermediate times which we connect to Dyson Brownian motion. In contrast, we show that free fermion systems -- i.e., ones where the unitaries are generated by quadratic Hamiltonians and the measurements are of fermion bilinears -- purify in a time quadratic in the system size. In particular, a volume law phase for the entanglement entropy cannot be sustained in a free fermion system.

24 pages, 2 figures (v3) expanding the proof of Lemma 3

References in corpus (4)

• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Statistical mechanics of quantum error correcting codes
• Emergent conformal symmetry in non-unitary random dynamics of free fermions
• Random Unitaries Give Quantum Expanders

Cited by in corpus (80)

• Random Quantum Circuits
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions
• Postselection-free entanglement dynamics via spacetime duality
• Dynamically Generated Logical Qubits
• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Entanglement and purification transitions in non-Hermitian quantum mechanics
• Fate of measurement-induced phase transition in long-range interactions
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Topological order and criticality in (2+1)D monitored random quantum circuits
• Spacetime duality between localization transitions and measurement-induced transitions
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Measurement-induced criticality and entanglement clusters: a study of 1D and 2D Clifford circuits
• Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
• Topological transitions with continuously monitored free fermions
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Nonlinear sigma models for monitored dynamics of free fermions
• Entanglement Domain Walls in Monitored Quantum Circuits and the Directed Polymer in a Random Environment
• Controlling entanglement at absorbing state phase transitions in random circuits
• Quantum coding with low-depth random circuits
• Disordered monitored free fermions
• Enhanced entanglement negativity in boundary driven monitored fermionic chains
• Entanglement transitions with free fermions
• Continuous Gaussian Measurements of the Free Boson CFT: A model for Exactly Solvable and Detectable Measurement-Induced Dynamics
• Entanglement phase transitions in random stabilizer tensor networks
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Universal Entanglement Transitions of Free Fermions with Long-range Non-unitary Dynamics
• Purification Timescales in Monitored Fermions
• Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit
• Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition
• Many-body Dynamics in Monitored Atomic Gases Without Post-Selection Barrier
• Measurement-induced phase transitions on dynamical quantum trees
• Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
• Entanglement transitions and quantum bifurcations under continuous long-range monitoring
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Measurement-induced phase transitions in sparse nonlocal scramblers
• Monitored fermions with conserved $\mathrm{U}(1)$ charge
• Learnability transitions in monitored quantum dynamics via eavesdropper's classical shadows
• Interactions and integrability in weakly monitored Hamiltonian systems
• Surface codes, quantum circuits, and entanglement phases
• Entanglement dynamics with string measurement operators
• Absence of measurement-induced entanglement transition due to feedback-induced skin effect
• Density and current statistics in boundary-driven monitored fermionic chains
• Ultrafast Entanglement Dynamics in Monitored Quantum Circuits
• Random-matrix models of monitored quantum circuits
• Field theory of monitored, interacting fermion dynamics with charge conservation
• Chaos and magic in the dissipative quantum kicked top
• The impact of different unravelings in a monitored system of free fermions
• Topological Defects in Floquet Circuits
• Entanglement Transition due to particle losses in a monitored fermionic chain
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
• Nonstabilizerness in the unitary and monitored quantum dynamics of XXZ-staggered and SYK models
• Quantum simulation using noisy unitary circuits and measurements
• Decoding the Projective Transverse Field Ising Model
• Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Temporal Entanglement Barriers in Dual-Unitary Clifford Circuits with Measurements
• Measurement-induced Lévy flights of quantum information
• Protect Measurement-Induced Phase Transition from Noise
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Measurement-Induced Phase Transition in State Estimation of Chaotic Systems and the Directed Polymer
• Charge and Spin Sharpening Transitions on Dynamical Quantum Trees
• Topological Modes in Monitored Quantum Dynamics
• Driven Non-Unitary Dynamics of Quantum Critical Systems
• Measurement Induced Chirality II: Diffusion and Disorder
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Entanglement transitions from restricted Boltzmann machines
• Multifractality in monitored single-particle dynamics
• Rise and fall of nonstabilizerness via random measurements
• Coherent Information Phase Transition in a Noisy Quantum Circuit
• Efficient circular Dyson Brownian motion algorithm
• Observable Measurement-Induced Transitions
• Entanglement transition in unitary system-bath dynamics
• Absence of measurement- and unraveling-induced entanglement transitions in continuously monitored one-dimensional free fermions
• Symmetry and Topology of Monitored Quantum Dynamics
• Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain