Superposed parameterised quantum circuits

TL;DR

This paper introduces superposed parameterised quantum circuits that embed multiple sub-models simultaneously, enhancing expressivity and non-linearity, and demonstrating significant improvements in quantum machine learning tasks.

Contribution

It presents a novel architecture combining superposition and amplitude transformations, enabling parallel training of multiple parameter sets and increased representational power in quantum circuits.

Findings

Three orders of magnitude error reduction in 1D regression

81.4% accuracy in 2D classification task

Reduced run-to-run variance three-fold

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.