Multidimensional Quantum Generative Modeling by Quantum Hartley Transform

IF 4.4 Q1 OPTICS
Hsin-Yu Wu, Vincent E. Elfving, Oleksandr Kyriienko
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引用次数: 0

Abstract

An approach for building quantum models based on the exponentially growing orthonormal basis of Hartley kernel functions is developed. First, a differentiable Hartley feature map parameterized by real-valued argument that enables quantum models suitable for solving stochastic differential equations and regression problems is designed. Unlike the naturally complex Fourier encoding, the proposed Hartley feature map circuit leads to quantum states with real-valued amplitudes, introducing an inductive bias and natural regularization. Next, a quantum Hartley transform circuit is proposed as a map between computational and Hartley basis. The developed paradigm is applied to generative modeling from solutions of stochastic differential equations, and utilize the quantum Hartley transform for fine sampling from parameterized distributions through an extended register. Finally, the capability of multivariate quantum generative modeling is demonstrated for both correlated and uncorrelated distributions. As a result, the developed quantum Hartley-based generative models (QHGMs) offer a distinct quantum approach to generative AI at increasing scale.

Abstract Image

基于量子Hartley变换的多维量子生成建模
提出了一种基于Hartley核函数的指数增长正交基构建量子模型的方法。首先,设计了一个实值参数化的可微Hartley特征映射,使量子模型适用于求解随机微分方程和回归问题。与自然复杂的傅立叶编码不同,所提出的Hartley特征映射电路导致具有实值振幅的量子态,引入归纳偏置和自然正则化。其次,提出了一个量子哈特利变换电路作为计算基和哈特利基之间的映射。开发的范例应用于随机微分方程解的生成建模,并利用量子哈特利变换通过扩展寄存器从参数化分布中进行精细采样。最后,对相关分布和不相关分布证明了多元量子生成建模的能力。因此,开发的基于哈特利的量子生成模型(qhgm)为越来越大规模的生成人工智能提供了一种独特的量子方法。
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CiteScore
7.90
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0.00%
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