PhasorFlow: A Python Library for Unit Circle Based Computing
This introduces a novel paradigm for machine learning researchers seeking efficient, mathematically principled methods, though it is incremental in building on quantum-inspired concepts.
The authors tackled the problem of developing a new computational paradigm based on unit circle operations, resulting in PhasorFlow, a Python library that provides deterministic and lightweight alternatives to neural networks and quantum circuits, validated on tasks like classification and time-series prediction.
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.