Moment-Selective Quantum Designs in Aperiodic Temporal Ensembles

Abstract:We introduce a general mechanism for engineering moment-selective temporal designs with hierarchically structured aperiodic drives. At special control settings where the driven dynamics is constrained by a finite symmetry group, lower-order moments can already reproduce Haar statistics while a selected higher-order deviation remains nonzero. A small static detuning from such a setting generically produces an exponentially long lifetime whose exponent scales inversely with the square of the detuning. We illustrate this mechanism in qubit systems through exact Fibonacci and silver-mean constructions with tetrahedral and icosahedral resonances, for which the first retained non-Haar moments occur at orders $3$ and $6$, respectively. We further show that stochastic control fluctuations produce a qualitatively different cutoff from coherent detuning. Finally, we propose a finite-time signature of the long-lived moment that can be measured without requiring observations over exponentially long times.

Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)

arXiv:2609.13371 [quant-ph]

(or arXiv:2609.13371v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.13371 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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