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We present a theoretical proposal for preparing and manipulating a state of asingle continuous-variable degree of freedom confined to a nonharmonicpotential. By utilizing optimally controlled modulation of the potential'sposition and depth, we demonstrate the generation of non-Gaussian states,including Fock, Gottesman-Kitaev-Preskill, multi-legged-cat, and cubic-phasestates, as well as the implementation of arbitrary unitaries within a selectedtwo-level subspace. Additionally, we propose protocols for single-shotorthogonal state discrimination and algorithmic cooling and analyze therobustness of this control scheme against noise. Since all the presentedprotocols rely solely on the precise modulation of the effective nonharmonicpotential landscape, they are relevant to several experiments withcontinuous-variable systems, including the motion of a single particle in anoptical tweezer or lattice, or current in circuit quantum electrodynamics.

Quantum control of continuous systems via nonharmonic potential modulation