scholarly journals Quantum operation, quantum Fourier transform and semi-definite programming

2004 ◽  
Vol 323 (1-2) ◽  
pp. 48-56 ◽  
Author(s):  
Runyao Duan ◽  
Zhengfeng Ji ◽  
Yuan Feng ◽  
Mingsheng Ying
Keyword(s):  
Fourier Transform ◽  
Quantum Operation ◽  
Quantum Fourier Transform

Quantum expanders from any classical Cayley graph expander

2008 ◽  
Vol 8 (8&9) ◽  
pp. 715-721 ◽  
Author(s):  
A.W. Harrow
Keyword(s):  
Fourier Transform ◽  
Spectral Gap ◽  
Expander Graphs ◽  
Quantum Operation ◽  
Quantum Fourier Transform ◽  
Density Matrices ◽  
Constant Degree ◽  
Carry Over ◽  
Kraus Operators ◽  
Classical Constant

We give a simple recipe for translating walks on Cayley graphs of a group G into a quantum operation on any irrep of G. Most properties of the classical walk carry over to the quantum operation: degree becomes the number of Kraus operators, the spectral gap becomes the gap of the quantum operation (viewed as a linear map on density matrices), and the quantum operation is efficient whenever the classical walk and the quantum Fourier transform on G are efficient. This means that using classical constant-degree constant-gap families of Cayley expander graphs on e.g. the symmetric group, we can construct efficient families of quantum expanders.

Optical simulator of the quantum Fourier transform

2016 ◽  
Vol 114 (2) ◽  
pp. 20004 ◽  
Author(s):  
Y. S. Nam ◽  
R. Blümel
Keyword(s):  
Fourier Transform ◽  
Quantum Fourier Transform

A watermark strategy for quantum images based on quantum fourier transform

2012 ◽  
Vol 12 (2) ◽  
pp. 793-803 ◽  
Author(s):  
Wei-Wei Zhang ◽  
Fei Gao ◽  
Bin Liu ◽  
Qiao-Yan Wen ◽  
Hui Chen
Keyword(s):  
Fourier Transform ◽  
Quantum Fourier Transform ◽  
Quantum Images

scholarly journals Implementation of the quantum Fourier transform on a hybrid qubit–qutrit NMR quantum emulator

2015 ◽  
Vol 13 (07) ◽  
pp. 1550059 ◽  
Author(s):  
Shruti Dogra ◽  
Arvind Dorai ◽  
Kavita Dorai
Keyword(s):  
Fourier Transform ◽  
Quantum Algorithms ◽  
Quantum Computers ◽  
Quantum Fourier Transform ◽  
Specific Implementation ◽  
Circuit Decomposition

The quantum Fourier transform (QFT) is a key ingredient of several quantum algorithms and a qudit-specific implementation of the QFT is hence an important step toward the realization of qudit-based quantum computers. This work develops a circuit decomposition of the QFT for hybrid qudits based on generalized Hadamard and generalized controlled-phase gates, which can be implemented using selective rotations in NMR. We experimentally implement the hybrid qudit QFT on an NMR quantum emulator, which uses four qubits to emulate a single qutrit coupled to two qubits.

Quantum Teleportation of Multiple Qubits Based on Quantum Fourier Transform

2018 ◽  
Vol 22 (12) ◽  
pp. 2427-2430 ◽  
Author(s):  
Dan Song ◽  
Chen He ◽  
Zhengwen Cao ◽  
Geng Chai
Keyword(s):  
Fourier Transform ◽  
Quantum Teleportation ◽  
Quantum Fourier Transform

scholarly journals The quantum Fourier transform based on quantum vision representation

2018 ◽  
Vol 17 (12) ◽  
Author(s):  
Hai-Sheng Li ◽  
Ping Fan ◽  
Hai-ying Xia ◽  
Shuxiang Song ◽  
Xiangjian He
Keyword(s):  
Fourier Transform ◽  
Quantum Fourier Transform
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