An improved quantum Fourier transform algorithm and applications

Hales, Lisa; Hallgren, Sean

doi:10.1109/sfcs.2000.892139

Cited by 104 publications

(85 citation statements)

References 11 publications

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“…It is a known phenomenon from classical signal processing, that the peaks for this Fourier spectrum approximate the peaks for the spectrum which would have been obtained by computing the DFT for the right length. The works [73][74][75][76] contain a detailed analysis of this tradeoff between length of the DFT and sharpness of the resulting spectral peaks.…”

Section: Quantum Signal Transformsmentioning

confidence: 99%

Quantum algorithms: A survey of some recent results

Rötteler

2006

Informatik Forsch. Entw.

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Quantum algorithms are a field of growing interest within the theoretical computer science as well as the physics community. Surprisingly, although the number of researchers working on the subject is ever-increasing, the number of quantum algorithms found so far is quite small. In fact, the task of designing new quantum algorithms has been proven to be extremely difficult. In this paper we give an overview of the known quantum algorithms and briefly describe the underlying ideas. Roughly, the algorithms presented are divided into hidden subgroup type algorithms and in amplitude amplification type algorithms. While the former deal with problems of group-theoretical nature and have the promise to yield strong separations of classical and quantum algorithms, the latter have been proved to be a prolific source of algorithms in which a polynomial speed-up as compared to classical algorithms can be achieved. We also discuss quantum algorithms which do not fall under these two categories and give a survey of techniques of general interest in quantum computing such as adiabatic computing, lower bounds for quantum algorithms, and quantum interactive proofs.

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Section: Quantum Signal Transformsmentioning

confidence: 99%

Quantum algorithms: A survey of some recent results

Rötteler

2006

Informatik Forsch. Entw.

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“…We have demonstrated how to reduce the number of operations required when performing a QFT on the qubus quantum computer to 7N − 6 per QFT. This is linear in the number of qubits N, compared with O(N 2 ) for the simple gate sequence, and O(N log N) for the best known gate sequence [9]. This suggests that continuous-variable ancillas could be equivalent to the quantum circuit model with unbounded fan-out, and measurement-based quantum computing [10].…”

Section: Application To the Qftmentioning

confidence: 99%

Qubus ancilla-driven quantum computation

Brown¹,

De²,

Kendon³

et al. 2014

AIP Conference Proceedings

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“…Technologies that support arbitrary single qubit rotations do not need to utilize any of the synthesis techniques developed to approximate them, saving a polynomial time overhead. Arbitrary controlled rotation (a two qubit operation) is useful, particularly for the quantum Fourier transform (QFT) at the heart of Shor's algorithm [Shor 1994;Hales and Hallgren 2000;Barenco et al 1996].…”

Section: Time and Gate Characteristicsmentioning

confidence: 99%

Architectural implications of quantum computing technologies

Meter

Oskin

2006

J. Emerg. Technol. Comput. Syst.

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In this article we present a classification scheme for quantum computing technologies that is based on the characteristics most relevant to computer systems architecture. The engineering trade-offs of execution speed, decoherence of the quantum states, and size of systems are described. Concurrency, storage capacity, and interconnection network topology influence algorithmic efficiency, while quantum error correction and necessary quantum state measurement are the ultimate drivers of logical clock speed. We discuss several proposed technologies. Finally, we use our taxonomy to explore architectural implications for common arithmetic circuits, examine the implementation of quantum error correction, and discuss cluster-state quantum computation.

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An improved quantum Fourier transform algorithm and applications

Cited by 104 publications

References 11 publications

Quantum algorithms: A survey of some recent results

Quantum algorithms: A survey of some recent results

Qubus ancilla-driven quantum computation

Architectural implications of quantum computing technologies

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