Physics

Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

Quantum mechanics simulations and analysis using QuTiP (Quantum Toolbox in Python). Use when working with quantum systems including: (1) quantum states (kets, bras, density matrices), (2) quantum operators and gates, (3) time evolution and dynamics (Schrödinger, master equations, Monte Carlo), (4) open quantum systems with dissipation, (5) quantum measurements and entanglement, (6) visualization (Bloch sphere, Wigner functions), (7) steady states and correlation functions, or (8) advanced methods (Floquet theory, HEOM, stochastic solvers). Handles both closed and open quantum systems across various domains including quantum optics, quantum computing, and condensed matter physics.

Comprehensive quantum computing toolkit for building, optimizing, and executing quantum circuits. Use when working with quantum algorithms, simulations, or quantum hardware including (1) Building quantum circuits with gates and measurements, (2) Running quantum algorithms (VQE, QAOA, Grover), (3) Transpiling/optimizing circuits for hardware, (4) Executing on IBM Quantum or other providers, (5) Quantum chemistry and materials science, (6) Quantum machine learning, (7) Visualizing circuits and results, or (8) Any quantum computing development task.