10.1 Quantum Fourier Transform
The Quantum Fourier Transform (QFT) is widely used in quantum computing. We need it in this chapter to estimate eigenvalues via the function order and period finding algorithm in section 10.5. We then use that in Shor’s factoring algorithm in section 10.7. If that weren’t enough, the Hadamard H is the 1-qubit QFT, and we’ve seen many examples of its use. algorithm$Quantum Fourier Transform Quantum Fourier Transform
Other applications of the QFT include quantum Monte Carlo, 77 and the Harrow-Hassidim-Loyd (HHL) algorithm for solving systems of linear equations under restrictive conditions. 105 63 algorithm$Monte Carlo Monte Carlo algorithm algorithm$Harrow-Hassidim-Loyd Harrow-Hassidim-Loyd algorithm algorithm$HHL HHL algorithm
Most treatments of the QFT start by comparing it to the classical Discrete Fourier Transform and then the Fast Fourier Transform. If you don’t know either of these, don’t worry...
