Superposed Parameterised Quantum Circuits

• URL: http://arxiv.org/abs/2506.08749v1
• Date: Tue, 10 Jun 2025 12:44:11 GMT
• Title: Superposed Parameterised Quantum Circuits
• Authors: Viktoria Patapovich, Mo Kordzanganeh, Alexey Melnikov,
• Abstract summary: We introduce superposed parameterised quantum circuits to overcome limitations of existing approaches.<n>A superposed parameterised quantum circuit embeds an exponential number of parameterised sub-models in a single circuit.<n>We show how multiple parameter sets are trained in parallel while non-linear transformations broaden power beyond conventional quantum kernels.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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