Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems

Abstract

We introduce a model of non-unitary quantum dynamics that exhibits infinitely long-lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. Ergodicity is evaded by combining a sequence of projective measurements with a local feedback rule that is inspired by Toom's `North-East-Center' classical cellular automaton. The measurements in question only partially collapse the wavefunction of the system, allowing some quantum coherence to persist. We demonstrate our claims using numerical simulations of a Clifford circuit in two spatial dimensions which allows access to large system sizes, and also present results for more generic dynamics on modest system sizes. We also devise explicit experimental protocols realising this dynamics using one- and two-qubit gates that are available on present-day quantum computing platforms.

6+7 pages, 2+6 figures

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• Postselection-free learning of measurement-induced quantum dynamics
• Holographic dissipative space-time supersolids
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Experimental observation of a time rondeau crystal: Temporal Disorder in Spatiotemporal Order
• Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
• Universal Stochastic Equations of Monitored Quantum Dynamics
• Sensing with discrete time crystals
• Absolutely stable time crystals at finite temperature
• Space-time symmetry breaking in nonequilibrium frustrated magnetism
• Feedback-induced interactive dynamics: unitary but dissipative evolution
• Prolonging a discrete time crystal by quantum-classical feedback
• Robust Oscillations and Edge Modes in Nonunitary Floquet Systems
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Measurement-invisible quantum correlations in scrambling dynamics
• Exact, Average, and Broken Symmetries in a Simple Adaptive Monitored Circuit
• Noise resilience in adaptive and symmetric monitored quantum circuits
• Exploring the Landscape of Non-Equilibrium Memories with Neural Cellular Automata
• Apparent bistability from weak long-range interactions