Ramanujan-modulated multitone control for high-fidelity quantum state preparation
Phys. Rev. A 113, 042605 – Published 9 April, 2026
DOI: https://doi.org/10.1103/xwvv-9hsf
Abstract
Closed quantum systems with degenerate spectra or sparse couplings often trap conventional Lyapunov or gradient controllers on invariant sets, yielding low final fidelities. We propose a hybrid control strategy that uses a number-theoretic exploration phase followed by a Lyapunov refinement. In the low-fidelity regime, the control signal is a bounded, aperiodic drive formed by a Littlewood-Ramanujan modulation multiplied by a bandwidth-limited multitone comb built from divisors of a highly composite number. This prime-driven signal provides persistent excitation across Bohr gaps without phase locking and activates the noncommuting directions needed to escape degenerate subspaces. Once a preset fidelity threshold is reached, the controller switches to a Lyapunov law with logarithmic shaping, ensuring monotonic fidelity increase under amplitude constraints. We prove finite hitting time to the threshold and asymptotic convergence under bounded-input, detectability, and persistence-of-excitation conditions, and provide practical tuning rules. Simulations on multilevel systems show high-fidelity state preparation and consistent improvements over standard Lyapunov control.
