首个多参数连续变量门高效学习算法,精度高且实验可行。
Efficient learning of bosonic Gaussian unitaries
- 用相干/压缩光探针+线性光学+探测,实现快速学习
- 误差随模式数和精度要求多项式增长,能量约束下最优
- 适合量子光学与纠错研究者,实验资源要求低
玻色高斯酉算符是量子光学干涉仪和玻色纠错方案等核心连续变量量子技术的基础单元。本文提出首个时间高效的玻色高斯酉算符学习算法,并给出严格分析。该算法在能量约束钻石距离下,以小的最坏情况误差估计未知酉算符。其运行时间和查询复杂度关于模式数、目标精度倒数及输入能量和输出能量增长的自然能量参数呈多项式关系。协议仅需实验友好的光子资源:相干态和压缩态探针、被动线性光学元件以及异相/同相探测。随后采用高效的经典后处理方法,通过辛正则化步骤将矩阵估计投影至辛群。在输入能量无界极限下,仅需2m+2次查询即可达到任意高精度,其中m为模式数。据我们所知,这是首个对多参数连续变量酉算符族具有严格效率保证的学习算法。
原文摘要 · Abstract (English)
Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient algorithm for learning bosonic Gaussian unitaries with a rigorous analysis. Our algorithm produces an estimate of the unknown unitary that is accurate to small worst-case error, measured by the physically motivated energy-constrained diamond distance. Its runtime and query complexity scale polynomially with the number of modes, the inverse target accuracy, and natural energy parameters quantifying the allowed input energy and the unitary's output-energy growth. The protocol uses only experimentally friendly photonic resources: coherent and squeezed probes, passive linear optics, and heterodyne/homodyne detection. We then employ an efficient classical post-processing routine that leverages a symplectic regularization step to project matrix estimates onto the symplectic group. In the limit of unbounded input energy, our procedure attains arbitrarily high precision using only $2m+2$ queries, where $m$ is the number of modes. To our knowledge, this is the first provably efficient learning algorithm for a multiparameter family of continuous-variable unitaries.
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