dorsal/arxiv
View SchemaThe Universality of the Quantum Fourier Transform in Forming the Basis of Quantum Computing Algorithms
| Authors | Charles M. Bowden, Goong Chen, Zijian Diao, Andreas Klappenecker |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0007122 |
| URL | https://arxiv.org/abs/quant-ph/0007122 |
Abstract
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.
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"abstract": "The quantum Fourier transform (QFT) is a powerful tool in quantum computing.\nThe main ingredients of QFT are formed by the Walsh-Hadamard transform H and\nphase shifts P(.), both of which are 2x2 unitary matrices as operators on the\ntwo-dimensional 1-qubit space. In this paper, we show that H and P(.) suffice\nto generate the unitary group U(2) and, consequently, through controlled-U\noperations and their concatenations, the entire unitary group U(2^n) on\nn-qubits can be generated. Since any quantum computing algorithm in an n-qubit\nquantum computer is based on operations by matrices in U(2^n), in this sense we\nhave the universality of the QFT.",
"arxiv_id": "quant-ph/0007122",
"authors": [
"Charles M. Bowden",
"Goong Chen",
"Zijian Diao",
"Andreas Klappenecker"
],
"categories": [
"quant-ph"
],
"title": "The Universality of the Quantum Fourier Transform in Forming the Basis of Quantum Computing Algorithms",
"url": "https://arxiv.org/abs/quant-ph/0007122"
},
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