scholarly journals Linear depth stabilizer and quantum Fourier transformation circuits with no auxiliary qubits in finite-neighbor quantum architectures

2007 ◽  
Vol 76 (5) ◽  
Author(s):  
Dmitri Maslov
Keyword(s):  
Fourier Transformation ◽  
Quantum Fourier Transformation

QUANTUM SINGULAR VALUE DECOMPOSITION BASED APPROXIMATION ALGORITHM

2010 ◽  
Vol 19 (06) ◽  
pp. 1141-1162 ◽  
Author(s):  
LASZLO GYONGYOSI ◽  
SANDOR IMRE
Keyword(s):  
Singular Value Decomposition ◽  
Fourier Transformation ◽  
Singular Value ◽  
Fourier Domain ◽  
Complex Matrix ◽  
Orthogonal Matrices ◽  
Novel Approach ◽  
Value Decomposition ◽  
Quantum Fourier Transformation ◽  
Ordinary Quantum

Singular Value Decomposition (SVD) is one of the most useful techniques for analyzing data in linear algebra. SVD decomposes a rectangular real or complex matrix into two orthogonal matrices and one diagonal matrix. The proposed Quantum-SVD algorithm interpolates the non-uniform angles in the Fourier domain. The error of the Quantum-SVD approach is some orders lower than the error given by ordinary Quantum Fourier Transformation. Our Quantum-SVD algorithm is a fundamentally novel approach for the computation of the Quantum Fourier Transformation (QFT) of non-uniform states. The presented Quantum-SVD algorithm is based on the singular value decomposition mechanism, and the computation of Quantum Fourier Transformation of non-uniform angles of a quantum system. The Quantum-SVD approach provides advantages in terms of computational structure, being based on QFT and multiplications.

scholarly journals An Image Encryption Method Based on Quantum Fourier Transformation

2018 ◽  
Vol 08 (03) ◽  
pp. 75-87
Author(s):  
Ying Liu ◽  
Bing Zhou ◽  
Zijing Li ◽  
Jiangnan Deng ◽  
Zhengying Cai
Keyword(s):  
Image Encryption ◽  
Fourier Transformation ◽  
Encryption Method ◽  
Quantum Fourier Transformation

(t,n) Threshold d-level QSS based on QFT

2020 ◽  
Vol 20 (11&12) ◽  
pp. 957-968
Author(s):  
Sarbani Roy ◽  
Sourav Mukhopadhyay
Keyword(s):  
Quantum Computation ◽  
Secret Sharing ◽  
Fourier Transformation ◽  
Quantum Secret Sharing ◽  
Communication Security ◽  
Local Measurement ◽  
Classical Communication ◽  
Quantum Fourier Transformation ◽  
Important Branch ◽  
Threshold Schemes

Quantum secret sharing (QSS) is an important branch of secure multiparty quantum computation. Several schemes for (n, n) threshold QSS based on quantum Fourier transformation (QFT) have been proposed. Inspired by the flexibility of (t, n) threshold schemes, Song {\it et al.} (Scientific Reports, 2017) have proposed a (t, n) threshold QSS utilizing QFT. Later, Kao and Hwang (arXiv:1803.00216) have identified a {loophole} in the scheme but have not suggested any remedy. In this present study, we have proposed a (t, n)threshold QSS scheme to share a d dimensional classical secret. This scheme can be implemented using local operations (such as QFT, generalized Pauli operators and local measurement) and classical communication. Security of the proposed scheme is described against outsider and participants' eavesdropping.

STABILITY OF THE QUANTUM FOURIER TRANSFORMATION ON THE ISING QUANTUM COMPUTER

2005 ◽  
Vol 03 (03) ◽  
pp. 441-462 ◽  
Author(s):  
GIUSEPPE LUCA CELARDO ◽  
CARLOS PINEDA ◽  
MARKO ŽNIDARIČ
Keyword(s):  
Quantum Computation ◽  
Fourier Transformation ◽  
Quantum Computer ◽  
External Perturbation ◽  
Systematic Errors ◽  
Physical Parameters ◽  
System Parameters ◽  
Transformation Algorithm ◽  
Resonant Transitions ◽  
Quantum Fourier Transformation

We analyze the influence of errors on the implementation of the quantum Fourier transformation. Two kinds of errors are studied: (i) systematic errors due to off-resonant transitions and (ii) errors due to an external perturbation. The scaling of errors with system parameters and the number of qubits is analyzed. To suppress off-resonant transitions, we use correcting pulses while in order to suppress errors due to an external perturbation, we use an improved quantum Fourier transformation algorithm. As a result, the fidelity of quantum computation is increased by several orders of magnitude and is thus stable in a much wider range of physical parameters.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

Zur Anwendung der harmonischen Analyse bei der Funktionsszintigraphie des Herzens

1979 ◽  
Vol 18 (04) ◽  
pp. 167-171 ◽  
Author(s):  
R. Knopp ◽  
H.-P. Breuel ◽  
P. Fischer
Keyword(s):  
Fourier Transformation

ZusammenfassungDie nach Gleichverteilung von 99mTc-Serumalbumin szintigraphisch gewonnenen Volumenkurven des linken Ventrikels werden zur Gewinnung aussagefähiger Ergebnisse einer harmonischen Analyse unterzogen. Es ergibt sich hierdurch die Möglichkeit der quantitativen Analyse der Volumenkurve in geschlossener Form. Die Resynthese nach Fourier-Transformation stellt für den vorliegenden Funktionstyp ein gut geeignetes Glättungsverfahren dar, so daß die aus den Volumenkurven berechneten Parameter Ejektionsfraktion, maximale Austreibungs- und Füllungsgeschwindigkeit mit großer Genauigkeit erfaßt werden.

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