Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics

Abstract

Quantum information is typically fragile under measurements and environmental coupling. Remarkably, we find that its lifetime can scale exponentially with system size when the environment is continuously monitored via mid-circuit measurements -- regardless of bath size. Starting from a maximally entangled state with a reference, we analytically prove this exponential scaling for typical Haar random unitaries and confirm it through numerical simulations in both random unitary circuits and chaotic Hamiltonian systems. In the absence of bath monitoring, the lifetime exhibits a markedly different scaling: it grows at most linearly -- or remains constant -- with system size and decays inversely with the bath size. We further extend our findings numerically to a broad class of initial states. In the intermediate regime of partial monitoring, we identify and prove a two-scale transition, where the QMI decays logarithmically at microscopic time scales but linearly at macroscopic time scales.} We discuss implications for {monitored quantum circuits in the weak measurement limit, quantum algorithms such as quantum diffusion models and quantum reservoir computing, and quantum communication. Finally, we experimentally verify the gap of persisted information on IBM Quantum hardwares.

20+32 pages, 14+16 figures

References in corpus (34)

• Good Quantum Error-Correcting Codes Exist
• Black holes as mirrors: quantum information in random subsystems
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum error correction below the surface code threshold
• Quantum Entanglement Growth Under Random Unitary Dynamics
• Measurement-driven entanglement transition in hybrid quantum circuits
• Quantum Many-Body Scars and Weak Breaking of Ergodicity
• The randomized measurement toolbox
• Harnessing disordered quantum dynamics for machine learning
• Measuring Gaussian quantum information and correlations using the Renyi entropy of order 2
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Non-Abelian Topological Order and Anyons on a Trapped-Ion Processor
• Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states
• Boosting computational power through spatial multiplexing in quantum reservoir computing
• TensorCircuit: a Quantum Software Framework for the NISQ Era
• Exact emergent quantum state designs from quantum chaotic dynamics
• Temporal Information Processing on Noisy Quantum Computers
• Efficient Long-Range Entanglement using Dynamic Circuits
• Time Series Quantum Reservoir Computing with Weak and Projective Measurements
• Cross Entropy Benchmark for Measurement-Induced Phase Transitions
• Solvable model of deep thermalization with distinct design times
• Minimal Model for Fast Scrambling
• Generative quantum machine learning via denoising diffusion probabilistic models
• Generating random quantum channels
• Constant-depth preparation of matrix product states with adaptive quantum circuits
• Approximating many-body quantum states with quantum circuits and measurements
• Feedback-driven quantum reservoir computing for time-series analysis
• State preparation by shallow circuits using feed forward
• Quantum reservoir computing in finite dimensions
• Noise-induced phase transitions in hybrid quantum circuits
• Overcoming the Coherence Time Barrier in Quantum Machine Learning on Temporal Data
• Mutual information and spontaneous symmetry breaking
• Holographic deep thermalization for secure and efficient quantum random state generation
• Measurement-driven quantum advantages in shallow circuits