PhasorFlow: A Python Library for Unit Circle Based Computing

2026-03-16

AI Summary

提出PhasorFlow库，基于单位圆和复数相量，通过酉波干涉门和变分相量电路实现轻量、确定性的经典机器学习方法。

Technology Category

Machine Learning: Quantum Machine LearningComputer Vision: Other Foundations of Computer VisionReasoning under Uncertainty: Probabilistic Programming

Application Category

Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSecurity and Privacy: Large-scale security measurements

Abstract

We present PhasorFlow, an open-source Python library introducing a computational paradigm operating on the $S^1$ unit circle. Inputs are encoded as complex phasors $z = e^{iθ}$ on the $N$-Torus ($\mathbb{T}^N$). As computation proceeds via unitary wave interference gates, global norm is preserved while individual components drift into $\mathbb{C}^N$, allowing algorithms to natively leverage continuous geometric gradients for predictive learning. PhasorFlow provides three core contributions. First, we formalize the Phasor Circuit model ($N$ unit circle threads, $M$ gates) and introduce a 22-gate library covering Standard Unitary, Non-Linear, Neuromorphic, and Encoding operations with full matrix algebra simulation. Second, we present the Variational Phasor Circuit (VPC), analogous to Variational Quantum Circuits (VQC), enabling optimization of continuous phase parameters for classical machine learning tasks. Third, we introduce the Phasor Transformer, replacing expensive $QK^TV$ attention with a parameter-free, DFT-based token mixing layer inspired by FNet. We validate PhasorFlow on non-linear spatial classification, time-series prediction, financial volatility detection, and neuromorphic tasks including neural binding and oscillatory associative memory. Our results establish unit circle computing as a deterministic, lightweight, and mathematically principled alternative to classical neural networks and quantum circuits. It operates on classical hardware while sharing quantum mechanics' unitary foundations. PhasorFlow is available at https://github.com/mindverse-computing/phasorflow.

Problem

• unit circle computing
• phasor representation
• classical alternative to quantum circuits
• predictive learning
• neuromorphic computing