The Universality of the Quantum Fourier Transform in Forming the Basis of Quantum Computing Algorithms
| dc.creator | Bowden, Charles M. | |
| dc.creator | Chen, Goong | |
| dc.creator | Diao, Zijian | |
| dc.creator | Klappenecker, Andreas | |
| dc.date | 2000-07-31 | |
| dc.date.accessioned | 2026-07-07T06:00:32Z | |
| dc.date.available | 2026-07-07T06:00:32Z | |
| dc.description | 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 2x2 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(2^n) 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(2^n), in this sense we have the universality of the QFT. | |
| dc.description | 12 pages, 3 figures, submitted to SIAM Journal on Computing | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0007122 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0007122 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/88997 | |
| dc.subject | Quantum Physics | |
| dc.title | The Universality of the Quantum Fourier Transform in Forming the Basis of Quantum Computing Algorithms | |
| dc.type | text |