Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Quantum computation and quantum information
Quantum computation and quantum information
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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We present the detailed process of converting the classical Fourier Transform algorithm into the quantum one by using QR decomposition. This provides an example of a technique for building quantum algorithms using classical ones. The Quantum Fourier Transform is one of the most important quantum subroutines known at present, used in most algorithms that have exponential speed-up compared to the classical ones. We briefly review Fast Fourier Transform and then make explicit all the steps that led to the quantum formulation of the algorithm, generalizing Coppersmith's work.