Random-matrix models of monitored quantum circuits

Abstract

We study the competition between Haar-random unitary dynamics and measurements for unstructured systems of qubits. For projective measurements, we derive various properties of the statistical ensemble of Kraus operators analytically, including the purification time and the distribution of Born probabilities. The latter generalizes the Porter-Thomas distribution for random unitary circuits to the monitored setting and is log-normal at long times. We also consider weak measurements that interpolate between identity quantum channels and projective measurements. In this setting, we derive an exactly solvable Fokker-Planck equation for the joint distribution of singular values of Kraus operators, analogous to the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation modelling disordered quantum wires. We expect that the statistical properties of Kraus operators we have established for these simple systems will serve as a model for the entangling phase of monitored quantum systems more generally.

v2: minor revisions, references added, 35+3 pages, 3 figures

References in corpus (13)

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Cited by in corpus (13)

• Hilbert space delocalization under random unitary circuits
• Zero-temperature entanglement membranes in quantum circuits
• A Dyson Brownian motion model for weak measurements in chaotic quantum systems
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Measurement-Induced Spectral Transition
• Measurement-induced entanglement and complexity in random constant-depth 2D quantum circuits
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Deviations from the Porter-Thomas Distribution due to Nonstatistical $\gamma$ Decay below the ${}^{150}$Nd Neutron Separation Threshold
• Efficient circular Dyson Brownian motion algorithm
• Observable Measurement-Induced Transitions
• Symmetry and Topology of Monitored Quantum Dynamics
• Monitored quantum transport: full counting statistics of a quantum Hall interferometer
• Entropy and singular-value moments of products of truncated random unitary matrices