The universality of the quantum Fourier transform in forming the basis of quantum computing algorithms Academic Article uri icon


  • The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P (), both of which are 2 2 unitary matrices as operators on the two-dimensional 1-qubit space. In this paper, we show that H and P() suffice to generate the unitary group U(2) and, consequently, through controlled-U operations and their concatenations, the entire unitary group U (2n) on n qubits can be generated. Since any quantum computing algorithm in an n-qubit quantum computer is based on operations by matrices in U(2n), in this sense we have the universality of the QFT. 2002 Elsevier Science (USA). All rights reserved.

published proceedings


author list (cited authors)

  • Bowden, C. M., Chen, G., Diao, Z. J., & Klappenecker, A.

citation count

  • 5

complete list of authors

  • Bowden, CM||Chen, G||Diao, ZJ||Klappenecker, A

publication date

  • October 2002