State estimation with quantum extreme learning machines beyond the scrambling time

Abstract

Quantum extreme learning machines (QELMs) leverage untrained quantum dynamics to efficiently process information encoded in input quantum states, avoiding the high computational cost of training more complicated nonlinear models. On the other hand, quantum information scrambling (QIS) quantifies how the spread of quantum information into correlations makes it irretrievable from local measurements. Here, we explore the tight relation between QIS and the predictive power of QELMs. In particular, we show efficient state estimation is possible even beyond the scrambling time, for many different types of dynamics -- in fact, we show that in all the cases we studied, the reconstruction efficiency at long interaction times matches the optimal one offered by random global unitary dynamics. These results offer promising venues for robust experimental QELM-based state estimation protocols, as well as providing novel insights into the nature of QIS from a state estimation perspective.

References in corpus (29)

• Black holes as mirrors: quantum information in random subsystems
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Opportunities in Quantum Reservoir Computing and Extreme Learning Machines
• Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
• Quantum reservoir computing with a single nonlinear oscillator
• Dynamical phase transitions in quantum reservoir computing
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Time Series Quantum Reservoir Computing with Weak and Projective Measurements
• Information Scrambling and Chaos in Open Quantum Systems
• Information Processing Capacity of Spin-Based Quantum Reservoir Computing Systems
• Scrambling and Complexity in Phase Space
• Reconstructing quantum states with quantum reservoir networks
• Potential and limitations of quantum extreme learning machines
• Scalable photonic platform for real-time quantum reservoir computing
• Realising and compressing quantum circuits with quantum reservoir computing
• Quasiprobabilities in quantum thermodynamics and many-body systems
• Experimental property-reconstruction in a photonic quantum extreme learning machine
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• The Reservoir Learning Power across Quantum Many-Boby Localization Transition
• Quantum scrambling and the growth of mutual information
• Creating and concentrating quantum resource states in noisy environments using a quantum neural network
• Quantum reservoir computing in finite dimensions
• Shadow tomography on general measurement frames
• Solving the time-complexity problem and tuning the performance of quantum reservoir computing by artificial memory restriction
• Information scrambling -- a quantum thermodynamic perspective
• Measurable Krylov Spaces and Eigenenergy Count in Quantum State Dynamics
• Quantum scrambling via accessible tripartite information
• Phase-transition-like behavior in information retrieval of a quantum scrambled random circuit system
• An operational definition of quantum information scrambling

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• Practical Quantum Reservoir Computing in Rydberg Atom Arrays
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