What problem does it solve? Approximating the quantum time-evolution operator e^{-iHt} requires a controllable, error-bounded method; this Skill implements Taylor series truncation with time-slicing and Linear Combination of Unitaries (LCU) circuit construction, returning both approximate and exact evolution matrices with a Frobenius error metric. ## Core Features & Use Cases - Adaptive truncation: Automatically computes the number of time slices r and Taylor degree K from the spectral norm of H, evolution time t, and target error, with the degree hard-capped at 15. - LCU circuit construction: Decomposes the Hamiltonian into Pauli strings, builds the truncated series via dynamic programming, elevates it to the r-th power, and assembles a single LCU circuit. - Validation against exact evolution: Compares the approximation against scipy.linalg.expm and reports the Frobenius norm of the error. - Use Case: A researcher comparing Hamiltonian simulation methods runs the Taylor algorithm on a 2x2 Hermitian matrix with t=1.0 and degree=15, then sweeps degree and t to study how slicing and truncation order affect accuracy versus Trotter or QSP approaches. ## Quick Start Ask the assistant to run Taylor Hamiltonian simulation on a 2x2 Hermitian matrix H=[[2,1],[1,3]] with t=1.0, error 1e-8, and degree 15, then report the Frobenius error.
