What problem does it solve? Building a correct Quantum Fourier Transform circuit requires precise gate ordering, controlled-phase angles, and bit-reversal swaps, and small convention mistakes silently produce wrong results. This Skill provides a verified UnitaryLab implementation of QFT and inverse QFT with NumPy FFT-based validation, debugging guidance, and a documented parameter contract. ## Core Features & Use Cases - QFT/IQFT Circuit Construction: Builds the transform with Hadamard gates, multi-controlled phase rotations, and final SWAP gates, using qft.dagger() for the inverse. - Numerical Verification: Compares simulator output against NumPy ifft(state) * sqrt(2^n) (QFT) or fft(state) / sqrt(2^n) (IQFT) and reports an L2 verification error. - Debugging and Reimplementation Support: Documents common failure modes such as missing bit-reversal swaps, normalization mistakes, and FFT convention mismatches. - Use Case: A quantum computing student needs to run a 3-qubit QFT on a basis state, confirm the output matches the classical discrete Fourier transform, and then verify that QFT followed by IQFT recovers the original state with near-machine-precision fidelity. ## Quick Start Ask the assistant to run the quantum-fourier-transform skill to apply a 3-qubit QFT to a given state vector and report the verification error against NumPy.
