Pauli Algebra & Commutator Skill

High-efficiency, zero-dependency Python implementation of Pauli Group Algebra and Commutation Operator Relations.

Features

• Pauli Basis Representation: Full support for (\sigma_0, \sigma_x, \sigma_y, \sigma_z) matrix representations.
• Commutator Algebra: Evaluates Lie bracket ([A, B] = AB - BA) ensuring foundational quantum algebra compliance ([\sigma_j, \sigma_k] = 2i\epsilon_{jkl}\sigma_l).
• Zero External Dependencies: Pure Python standard library.
• Native MCP Protocol: JSON-RPC 2.0 stdio server compatible with Claude Desktop, Cursor, and Windsurf.

Architecture

graph TD
    OpA["Pauli Matrix A"] & OpB["Pauli Matrix B"] --> AB["Compute Matrix Product AB"]
    OpA & OpB --> BA["Compute Matrix Product BA"]
    AB & BA --> Sub["Subtract: AB - BA"]
    Sub --> Commutator["Lie Bracket Commutator [A, B]"]