Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics

TL;DR

This paper demonstrates that continuous monitoring of quantum systems can exponentially extend the lifetime of quantum information, contrasting with the limited scaling without monitoring, and verifies these findings experimentally on IBM Quantum hardware.

Contribution

It analytically and numerically establishes exponential quantum information lifetime scaling under continuous monitoring, a significant advancement over prior linear or constant scaling.

Findings

Exponential scaling of quantum information lifetime with system size under monitoring.

Linear or constant lifetime scaling without bath monitoring.

Experimental verification of information persistence gap on IBM Quantum hardware.

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.