通过量子比特-振荡器拉比控制实现非高斯相位门的近最优合成
Near-optimal synthesis of non-Gaussian phase gates via qubit-oscillator Rabi control
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- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学基础与前沿研究院）
- Yangtze Delta Industrial Innovation Center of Quantum Science and Technology（长三角量子科技产业创新中心）
- Yau Mathematical Sciences Center, Tsinghua University（清华大学丘成桐数学科学中心）
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中文总结 AI 辅助
本文提出一种无需数值优化的量子比特-振荡器拉比控制方案，以近最优时间合成非高斯相位门，并应用于模拟CV量子动力学和求解线性偏微分方程。
中文摘要 AI 辅助
非高斯门仍然是通用连续变量（CV）量子计算的关键瓶颈，因为它们所需的非线性难以工程实现。为了应对这一挑战，我们开发了一种高效的量子比特-振荡器拉比合成方案，用于多项式相位门，其总相互作用时间随目标误差ε的倒数呈多对数增长。具体而言，对于一类易于制备的初始态，我们证明了一个R次相位门可以通过解析构造的拉比序列来近似，总时间为O(log^{(R-1)/2+o(1)}(1/ε))。该构造无需数值优化，因此自然扩展到任意大的多模系统。我们进一步建立了总时间的下界Ω(log^{(R-1)/2}(1/ε))，表明该合成是近最优的。作为应用，我们使用该方案模拟了代表性的CV量子动力学，并实现了一个用于求解线性偏微分方程的CV量子算法。这些结果确立了量子比特-振荡器拉比控制作为CV量子信息处理中一种高效、可解析编译且近最优的基本操作。
英文摘要
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.
