Optimal Stabilizer Testing and Learning with Limited Quantum Memory
arXiv:2607. 02444v1 Announce Type: cross Abstract: We study stabilizer state testing and learning with limited coherent quantum memory.
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arXiv:2607. 02444v1 Announce Type: cross Abstract: We study stabilizer state testing and learning with limited coherent quantum memory.
We study stabilizer state testing and learning with limited coherent quantum memory. Here an algorithm sequentially receives copies of an unknown $n$-qubit state, but may keep only $k$ qubits of coherent quantum memory between measurements.
The paper investigates quantum reservoir computing using highly scrambling quantum systems modeled by high‑order unitary designs. It shows that in noiseless settings, measurement readouts become exponentially concentrated as the reservoir size grows, but this concentration does not worsen with repeated iterations, while memory of early inputs decays exponentially with both reservoir size and iterations. In noisy environments, memory also decays exponentially over time for local noisy channels, and the study introduces new proof techniques for bounding concentration in temporal quantum models. Numerical results indicate that even physical reservoirs, such as an Ising model in a quantum‑chaotic phase, can exhibit exponential concentration, whereas reservoirs in a many‑body localized phase or at the edge of chaos do not.
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