Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification

TL;DR

The paper introduces Variational Phasor Circuits (VPC), a novel phase-native architecture inspired by quantum circuits, enabling efficient brain-computer interface classification with fewer parameters and competitive accuracy.

Contribution

VPC is a new deterministic classical architecture operating on the complex unit circle, offering a unified, phase-based approach for brain signal classification.

Findings

VPC achieves competitive accuracy on synthetic BCI benchmarks.

VPC uses fewer trainable parameters than Euclidean baselines.

VPC demonstrates potential as a quantum-inspired classification method.

Abstract

We present the \textbf{Variational Phasor Circuit (VPC)}, a deterministic classical learning architecture operating on the continuous $S^1$ unit circle manifold. Inspired by variational quantum circuits, VPC replaces dense real-valued weight matrices with trainable phase shifts, local unitary mixing, and structured interference in the ambient complex space. This phase-native design provides a unified method for both binary and multi-class classification of spatially distributed signals. A single VPC block supports compact phase-based decision boundaries, while stacked VPC compositions extend the model to deeper circuits through inter-block pull-back normalization. Using synthetic brain-computer interface benchmarks, we show that VPC can decode difficult mental-state classification tasks with competitive accuracy and substantially fewer trainable parameters than standard Euclidean baselines. These results position unit-circle phase interference as a practical and mathematically principled alternative to dense neural computation, and motivate VPC as both a standalone classifier and a front-end encoding layer for future hybrid phasor-quantum systems.