This paper introduces PhasorFlow, an open-source Python library for computing on the $S^1$ unit circle. Inputs are encoded as complex phasors $z=e^{i\phi}$ on the $N$-torus ($\mathbb{T}^N$); as computation proceeds through unitary wave-interference gates, global norm is preserved while components drift into $\mathbb{C}^N$, allowing algorithms to leverage continuous geometric gradients.
PhasorFlow makes three significant contributions. First, we formalize the Phasor Circuit model ($N$ threads, $M$ gates) with a 22-gate library that spans standard-unitary, non-linear, neuromorphic, and encoding operations under full matrix-algebra simulation.
Second, we introduce the Variational Phasor Circuit (VPC), a trainable phase-native classifier analogous to variational quantum circuits. Third, we present the Phasor Transformer block and Large Phasor Model (LPM), replacing $QK^TV$ attention with a parameter-free DFT token-mixing layer.
We validate the framework on applications unique to the library, including financial volatility detection, neuromorphic associative memory, neural binding, period finding, and algorithmic logic. This positions unit-circle computing as a deterministic, lightweight paradigm on classical hardware. Available at PhasorFlow GitHub.
Blogger's Review: The emergence of PhasorFlow offers a fresh perspective on unit circle computing, combining the flexibility of quantum circuits with the stability of classical computation. Its potential applications in finance and neuromorphic computing are particularly promising, warranting deeper exploration by developers.