Role of scrambling and noise in temporal information processing with quantum systems

arXiv:2505.10080 · quant-ph, cond-mat.dis-nn, cs.LG, cs.NE, stat.ML · Submitted 2025-05-15 · Read on arXiv

quant-ph, cond-mat.dis-nn, cs.LG, cs.NE, stat.ML

Submitted: 2025-05-15

Updated: 2026-09-23

Comments: v3: Extensively revised, notably with new results for widely used physical reservoirs, connecting phases of matter to the emergence of exponential concentration. 23 + 52 pages, 9 + 12 figures, 2 + 1 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Reservoir Computing — 46× in this paper
• Trace — 16× in this paper · explained in 2 episodes
• Echo State Property — 10× in this paper
• Fading Memory Property — 8× in this paper
• Memory Decay — 7× in this paper · explained in 3 episodes
• Quantum Circuits — 6× in this paper · explained in 2 episodes
• Generalization — 5× in this paper · explained in 13 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Echo State Network — 2× in this paper
• Phase Transitions — 2× in this paper · explained in 2 episodes
• Temporal Correlations — 2× in this paper · explained in 2 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Adaptability — 1× in this paper · explained in 1 episode
• Additivity — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Chaotic Dynamics — 1× in this paper · explained in 2 episodes
• Combinatorial Optimization — 1× in this paper · explained in 2 episodes
• Core — 1× in this paper · explained in 2 episodes
• Entanglement — 1× in this paper · explained in 4 episodes
• Fidelity — 1× in this paper · explained in 2 episodes
• Homogenization — 1× in this paper · explained in 2 episodes
• Loss Function — 1× in this paper · explained in 2 episodes
• No-Go Theorem — 1× in this paper · explained in 2 episodes
• Non-Markovianity — 1× in this paper · explained in 3 episodes
• Sample Complexity — 1× in this paper · explained in 15 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Large-scale quantum reservoir learning with an analog quantum computer
• Quantum Reservoir Computing Implementations for Classical and Quantum Problems
• Memory-Augmented Hybrid Quantum Reservoir Computing
• Efficient Unitary T-designs from Random Sums
• Quantum reservoir computing with repeated measurements on superconducting devices
• Physical reservoir computing using finitely-sampled quantum systems
• Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction
• Exponential concentration and symmetries in Quantum Reservoir Computing
• Non-Markovianity and memory enhancement in Quantum Reservoir Computing
• Input-dependence in quantum reservoir computing
• Non-unital noise in a superconducting quantum computer as a computational resource for reservoir computing
• Quantum Refrigerator
• Noise-induced shallow circuits and absence of barren plateaus
• Simulating quantum circuits with arbitrary local noise using Pauli Propagation
• Classically estimating observables of noiseless quantum circuits
• Optimal quantum reservoir computing for market forecasting: An application to fight food price crises
• Quantum reservoir probing: an inverse paradigm of quantum reservoir computing for exploring quantum many-body physics
• Quantum reservoir probing of quantum phase transitions
• Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't
• Does provable absence of barren plateaus imply classical simulability?

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