论文标题
gibbs在量子计算机上的连续电势抽样
Gibbs Sampling of Continuous Potentials on a Quantum Computer
论文作者
论文摘要
连续实现的功能中的吉布斯采样是机器学习中兴趣的挑战性问题。在这里，我们利用量子傅里叶变换来构建函数周期性时为此任务构建量子算法。我们使用量子算法来求解线性的普通微分方程来求解fokker-planck方程并准备编码Gibbs分布的量子状态。我们表明，这些函数在量子计算机上的插值和分化的效率取决于该函数傅立叶变换的傅立叶系数的衰减速率。我们将此特性视为傅立叶域中的度量集中，还为其提供了功能分析条件。我们的算法将命令查询归零，以对函数的量子甲骨文进行零。尽管遇到了长期的混合时间，但该算法允许在采样中取得指数提高的精度，而在一般情况下，尤其是在几何条件下，在平均估计中，多项式量子加速速度，我们确定了能量函数的关键点。
Gibbs sampling from continuous real-valued functions is a challenging problem of interest in machine learning. Here we leverage quantum Fourier transforms to build a quantum algorithm for this task when the function is periodic. We use the quantum algorithms for solving linear ordinary differential equations to solve the Fokker--Planck equation and prepare a quantum state encoding the Gibbs distribution. We show that the efficiency of interpolation and differentiation of these functions on a quantum computer depends on the rate of decay of the Fourier coefficients of the Fourier transform of the function. We view this property as a concentration of measure in the Fourier domain, and also provide functional analytic conditions for it. Our algorithm makes zeroeth order queries to a quantum oracle of the function. Despite suffering from an exponentially long mixing time, this algorithm allows for exponentially improved precision in sampling, and polynomial quantum speedups in mean estimation in the general case, and particularly under geometric conditions we identify for the critical points of the energy function.
