Near-optimal synthesis of non-Gaussian phase gates via qubit-oscillator Rabi control

Non-Gaussian gates remain a key bottleneck for universal continuous-variable (CV) quantum computation because the nonlinearities they require are difficult to engineer. To address this challenge, we develop an efficient qubit-oscillator Rabi synthesis scheme for polynomial phase gates, with a total interaction time that scales polylogarithmically with the inverse target error (\varepsilon). Specifically, for a class of readily preparable initial states, we show that a degree-(R) phase gate can be approximated by an analytically constructed Rabi sequence with total time (O(\log^{(R-1)/2+o(1)}(1/\varepsilon))). This construction requires no numerical optimization and therefore extends naturally to arbitrarily large multimode systems. We further establish a total-time lower bound of (Ω(\log^{(R-1)/2}(1/\varepsilon))), showing that the synthesis is near optimal. As applications, we use this scheme to simulate representative CV quantum dynamics and implement a CV quantum algorithm for solving linear partial differential equations. These results establish qubit-oscillator Rabi control as an efficient, analytically compilable, and near-optimal primitive for CV quantum information processing.

Source: arXiv:2609.09132v1 - http://arxiv.org/abs/2609.09132v1 PDF: https://arxiv.org/pdf/2609.09132v1 Original Link: http://arxiv.org/abs/2609.09132v1