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

Abstract: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 \(\Omega(\log^{(R-1)/2}(1/\varepsilon))\), 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.

arXiv:2609.09132 [quant-ph]

(or arXiv:2609.09132v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.09132 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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