Dimension reduction with structure-aware quantum circuits for hybrid machine learning

• URL: http://arxiv.org/abs/2508.00048v1
• Date: Thu, 31 Jul 2025 17:18:43 GMT
• Title: Dimension reduction with structure-aware quantum circuits for hybrid machine learning
• Authors: Ammar Daskin,
• Abstract summary: Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form.<n>We show that quantum circuits designed on a value $k$ can approximate the reduced-form representations of entire datasets.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Schmidt decomposition of a vector can be understood as writing the singular value decomposition (SVD) in vector form. A vector can be written as a linear combination of tensor product of two dimensional vectors by recursively applying Schmidt decompositions via SVD to all subsystems. Given a vector expressed as a linear combination of tensor products, using only the $k$ principal terms yields a $k$-rank approximation of the vector. Therefore, writing a vector in this reduced form allows to retain most important parts of the vector while removing small noises from it, analogous to SVD-based denoising. In this paper, we show that quantum circuits designed based on a value $k$ (determined from the tensor network decomposition of the mean vector of the training sample) can approximate the reduced-form representations of entire datasets. We then employ this circuit ansatz with a classical neural network head to construct a hybrid machine learning model. Since the output of the quantum circuit for an $2^n$ dimensional vector is an $n$ dimensional probability vector, this provides an exponential compression of the input and potentially can reduce the number of learnable parameters for training large-scale models. We use datasets provided in the Python scikit-learn module for the experiments. The results confirm the quantum circuit is able to compress data successfully to provide effective $k$-rank approximations to the classical processing component.

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