Superposed parameterised quantum circuits

2025/06/10 by Viktoria Patapovich, Periyasamy, Maniraman, Patapovich, Viktoria +4
Computer Science · Materials Science · Physics and Astronomy · #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #FOS: Physical sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Neural and Evolutionary Computing (cs.NE) #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2506.08749

openalex publication_date 2025/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Quantum machine learning has shown promise for high-dimensional data analysis, yet many existing approaches rely on linear unitary operations and shared trainable parameters across outputs. These constraints limit expressivity and scalability relative to the multi-layered, non-linear architectures of classical deep networks. We introduce superposed parameterised quantum circuits to overcome these limitations. By combining flip-flop quantum random-access memory with repeat-until-success protocols, a superposed parameterised quantum circuit embeds an exponential number of parameterised sub-models in a single circuit and induces polynomial activation functions through amplitude transformations and post-selection. We provide an analytic description of the architecture, showing how multiple parameter sets are trained in parallel while non-linear amplitude transformations broaden representational power beyond conventional quantum kernels. Numerical experiments underscore these advantages: on a 1D step-function regression a two-qubit superposed parameterised quantum circuit cuts the mean-squared error by three orders of magnitude versus a parameter-matched variational baseline; on a 2D star-shaped two-dimensional classification task, introducing a quadratic activation lifts accuracy to 81.4% and reduces run-to-run variance three-fold. These results position superposed parameterised quantum circuits as a hardware-efficient route toward deeper, more versatile parameterised quantum circuits capable of learning complex decision boundaries.

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