variational-phasor-circuits-bci

name	variational-phasor-circuits-bci
description	Variational Phasor Circuits (VPC) for phase-native Brain-Computer Interface classification using continuous S1 unit circle manifold with trainable phase shifts and unitary mixing
authors	["Dibakar Sigdel"]
arxiv_id	2603.18078
published	2026-06-15T00:00:00.000Z
categories	["cs.LG","q-bio.NC"]
tags	["bci","phase-native","variational-circuits","unitary-mixing","complex-space"]
score	8
status	novel

Variational Phasor Circuits for Phase-Native BCI Classification

Paper: Variational Phasor Circuits for Phase-Native Brain-Computer Interface Classification
arXiv: 2603.18078
Authors: Dibakar Sigdel
Published: 2026-06-15

Summary

Variational Phasor Circuit (VPC) is a deterministic classical learning architecture operating on the continuous S1 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.

Core Methodology

Phase-Native Architecture

1. S1 Unit Circle Manifold

   • Continuous circular topology for phase-based representations
   • Avoids Euclidean weight matrices
   • Compact parameter space

2. Trainable Phase Shifts

   • Replace dense weight matrices with phase rotations
   • Local unitary mixing operations
   • Structured interference in complex space

3. VPC Block Design

   • Single blocks: compact phase-based decision boundaries
   • Stacked compositions: deeper circuits via pull-back normalization
   • Inter-block normalization for stability

Key Features

• Parameter Efficiency: Substantially fewer trainable parameters than Euclidean baselines
• Competitive Accuracy: Matches standard approaches on BCI tasks
• Phase-Native: Natural encoding of oscillatory neural signals

Applications

Brain-Computer Interface

• Mental-state classification tasks
• EEG signal decoding
• Phase-based neural signal processing

Advantages vs Euclidean Methods

Metric	VPC	Standard Euclidean
Parameters	Compact	Dense matrices
Accuracy	Competitive	Baseline
Phase encoding	Native	Requires transformation

Implementation Insights

Phase Shift Operations