Quantum fast Fourier transform and quantum computation by linear optics

Barak, Ronen; Ben‐Aryeh, Y.

doi:10.1364/josab.24.000231

Cited by 62 publications

(61 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Depending on the dimension of the qFFT, a final relabeling of the output modes is necessary to recover the unitary [2,10].…”

Section: Fast Quantum Hadamard and Fourier Transformsmentioning

confidence: 99%

“…As an example (Fig. 1), the 8-dimensional qFFT can be obtained within the generalized fast architecture by setting all beamsplitters to be 50:50 ð Again, a final relabeling of the output modes is necessary to retrieve the correct form of the qFFT [10,13].…”

Section: Generalized Fast Quantum Transformmentioning

confidence: 99%

“…However, the high versatility of this decomposition comes at the cost of requiring, in general, more elements than those really sufficient for a specific transformation [9]. A new algorithm has been recently developed by Barak and Ben-Aryeh (BB) [10] which, following the famous classical algorithm of Cooley and Tukey [11], minimizes the number of beamsplitters and phase shifters for implementing the 2 n -dimensional quantum Fourier transform (QFT) over the optical modes. Indeed, the BB construction of the m-mode Fast Quantum Fourier Transform (qFFT) reduces the optical elements to only Oðm log mÞ, to be compared with the Oðm 2 Þ elements necessary in the more general decomposition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Quantum Fast Transformations via Femtosecond Laser Writing Technique

Flamini

Viggianiello

Bentivegna

et al. 2017

IIS

View full text Add to dashboard Cite

Quantum computers promise to be able to solve tasks beyond the reach of standard computational platforms. Among the others, photonic quantum walks prove to be great candidates for their implementation, since single photon sources, passive linear optics and photo-detectors are sufficient for universal quantum computation. To this aim, a device performing the quantum Fourier transform represents a fundamental building block for quantum algorithms, whose applications are not limited to the field of quantum computation. Recently, an algorithm has been developed to efficiently realize a quantum Fourier transform of an input photonic state by using a quantum walk on elementary linear-optical components. Here we provide a simple operative description of the algorithm, introducing a whole class of quantum transformations achievable through a generalization of this procedure. We finally discuss how femtosecond laser writing technology well represents an efficient and scalable platform for the implementation of this class of photonic quantum walks.

show abstract

“…Depending on the dimension of the qFFT, a final relabeling of the output modes is necessary to recover the unitary [2,10].…”

Section: Fast Quantum Hadamard and Fourier Transformsmentioning

confidence: 99%

Section: Generalized Fast Quantum Transformmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Quantum Fast Transformations via Femtosecond Laser Writing Technique

Flamini

Viggianiello

Bentivegna

et al. 2017

IIS

View full text Add to dashboard Cite

show abstract

“…Barak and Ben-Aryeh 10 have described a QTF implementation with linear optics, following closely an Cooley-Tukey FFT based matrix decomposition to reduce the required number of optical components required. 50:50 beamsplitters and pure phase shifters are shown to be the only linear optical components required to implement the FFT structure, and an arrangement of these is shown for the proposed implementation of the 3 qubit QTF considered in detail in the paper.…”

Section: Coherent Optical Implementation Of the Quantum Fourier Transmentioning

confidence: 99%

Coherent optical implementations of the fast Fourier transform and their comparison to the optical implementation of the quantum Fourier transform

2013

View full text Add to dashboard Cite

Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar.

show abstract

“…In particular, the logic gates based upon ferroelectric liquid crystals [24], liquid-crystalline cells [25,26], silicon micro-ring resonators [27,28] and local nonlinear Mach-Zehnder interferometer [29] have been proposed. Today the main attention is focused on quantum logic gates and quantum computing [30][31][32][33][34][35][36][37][38][39][40][41]. This is because the quantum logic gates have minimal sizes.…”

mentioning

confidence: 99%