PhasorFlow: A Python Library for Unit Circle Based Computing

2026-07-11 · Source: cs.AI updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Software Development & Engineering, Emerging Technologies & Innovation · Depth: Expert, extended

Summary

PhasorFlow is an open-source Python library introducing unit circle based computing, a paradigm operating on the S^1 unit circle. It encodes inputs as complex phasors z=e^iθ on the N-Torus (T^N), utilizing unitary wave interference for predictive learning. The library formalizes the Phasor Circuit model with a 22-gate library, introduces Variational Phasor Circuits (VPC) for classical machine learning, and presents the Phasor Transformer, which replaces QK^TV attention with a parameter-free, DFT-based token mixing layer. Validated on non-linear spatial classification, time-series prediction, financial volatility detection, and neuromorphic tasks, PhasorFlow offers a deterministic, lightweight, and mathematically principled alternative to classical neural networks and quantum circuits, operating on classical hardware.

Key takeaway

For Machine Learning Engineers developing models for oscillatory or spatio-temporal data, PhasorFlow offers a compelling alternative to traditional neural networks. You should explore Variational Phasor Circuits for tasks requiring high parameter efficiency, such as non-linear classification, or consider Phasor Transformers for sequence prediction to significantly reduce computational complexity compared to self-attention mechanisms. This framework provides deterministic, interpretable results on classical hardware.

Key insights

Unit circle computing offers a deterministic, parameter-efficient alternative to neural networks and quantum circuits for phase-based dynamics.

Principles

• Unitary operations preserve global norm, allowing individual components to drift into C^N.
• Phase coherence provides a parameter-free measure of internal state structure.
• DFT gates enable parameter-free global mixing, reducing complexity.

Method

PhasorFlow defines a circuit model with 22 gates (Standard Unitary, Non-Linear, Neuromorphic, Encoding). VPCs encode data as phases, apply parameterized gates, and extract predictions via phase-to-probability mappings. Phasor Transformers use DFT for token mixing.

In practice

• Use VPCs for non-linear classification with minimal parameters.
• Apply Phasor Transformers for efficient time-series prediction.
• Monitor phase coherence for unsupervised anomaly detection in oscillatory data.

Topics

• Unit Circle Computing
• Phasor Circuits
• Variational Phasor Circuits
• Phasor Transformer
• Discrete Fourier Transform
• Neuromorphic Computing

Code references

• mindverse-computing/phasorflow
• Qiskit/qiskit

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.AI updates on arXiv.org.