On the power of quantum computation

Simon, Damien

doi:10.1109/sfcs.1994.365701

Cited by 588 publications

(646 citation statements)

References 13 publications

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“…A recent work that examined the theoretical feasibility of an optimally-constructed adiabatic algorithm for Simon's problem [34], which shares many similarities with, and in fact provided the motivation for, Shor's algorithm, has introduced a somewhat-novel approach for constructing quantum adiabatic algorithms [32]. Within this approach, which will be discussed in more detail next, a multitude of adiabatic evolutions is executed simultaneously in parallel and a single measurement at the end of the run, performed on the entire system, is used to extract valuable information.…”

Section: Introductionmentioning

confidence: 99%

Fourier-transforming with quantum annealers

Hen

2014

Front. Phys.

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We introduce a set of quantum adiabatic evolutions that we argue may be used as "building blocks," or subroutines, in the construction of an adiabatic algorithm that executes Quantum Fourier Transform (QFT) with the same complexity and resources as its gate-model counterpart. One implication of the above construction is the theoretical feasibility of implementing Shor's algorithm for integer factorization in an optimal manner, and any other algorithm that makes use of QFT, on quantum annealing devices. We discuss the possible advantages, as well as the limitations, of the proposed approach as well as its relation to traditional adiabatic quantum computation.Keywords: adiabatic quantum computing, quantum adiabatic algorithm, quantum fourier transform, integer factorization, Shor's algorithm

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Section: Introductionmentioning

confidence: 99%

Fourier-transforming with quantum annealers

Hen

2014

Front. Phys.

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“…The algorithm of Simon [5] finds the "period" of a function. This algorithm finds the hidden string s in Simon's Problem.…”

Section: Introductionmentioning

confidence: 99%

A Hybrid Architecture Approach for Quantum Algorithms

Aghaei¹,

Zukarnain²,

Mamat³

et al. 2009

J. of Computer Science

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Problem statement:In this study, a general plan of hybrid architecture for quantum algorithms is proposed. Approach: Analysis of the quantum algorithms shows that these algorithms were hybrid with two parts. First, the relationship of classical and quantum parts of the hybrid algorithms was extracted. Then a general plan of hybrid structure was designed. Results: This plan was illustrated the hybrid architecture and the relationship of classical and quantum parts of the algorithms. This general plan was used to increase implementation performance of quantum algorithms. Conclusion/Recommendations: Moreover, simulation results of quantum algorithms on the hybrid architecture proved that quantum algorithms can be implemented on the general plan as well.

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“…Later, D. R. Simon defined a problem that is in the class BQP ψ but not in BPP ψ (Simon 1997). This problem, called Simon's problem, can be defined as follows:…”

Section: Introductionmentioning

confidence: 99%

Deterministic polynomial-time quantum algorithms for Simon?s problem

Mihara

Sung

2003

comput. complex.

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D. R. Simon stated a problem, so-called Simon's problem, whose computational complexity is in the class BQP ψ but not in BPP ψ , where ψ is the function or oracle given in the problem. This result indicates that BPP may be strictly included in its quantum counterpart, BQP. Later, G. Brassard and P. Høyer showed that Simon's problem and its extended version can be solved by a deterministic polynomial time quantum algorithm. That is, these problems are in the class EQP ψ . In this paper, we show that Simon's problem and its extended version can be deterministically solved in a simpler and more concrete way than that proposed by G. Brassard and P. Høyer.

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On the power of quantum computation

Cited by 588 publications

References 13 publications

Fourier-transforming with quantum annealers

Fourier-transforming with quantum annealers

A Hybrid Architecture Approach for Quantum Algorithms

Deterministic polynomial-time quantum algorithms for Simon?s problem

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