Quantitative compilation of hybrid qubit–rotor controls

Determine finite-window synthesis bounds for the controlled shift, momentum-selective qubit rotation, and momentum-controlled target-operation gates in hybrid qubit–rotor systems, including their circuit lengths and control times, and establish whether the logical compression of cross-register Fourier phases persists when spectral selectivity and small interaction angles are assigned physical costs.

Background

The paper proves universal control only as strong-operator density on the infinite-dimensional hybrid Hilbert space. This is an existence result and does not provide quantitative estimates for approximating a target unitary on a finite momentum window.

The Fourier constructions likewise report logical instruction counts that assign unit cost to MQR, CShift, conditional-phase, CPHS, and Hadamard operations. The unresolved issue is to convert these logical resources into physically meaningful synthesis bounds involving circuit length, control time, spectral selectivity, interaction strength, phase resolution, and leakage, while determining whether the apparent reduction in cross-register Fourier-phase instructions survives that cost model.