The quantum Fourier transform on a linear nearest neighbor architecture

2007 ◽  
Vol 7 (4) ◽  
pp. 383-391
Author(s):  
Y. Takahashi ◽  
N. Kunihiro ◽  
K. Ohta
Keyword(s):  
Fourier Transform ◽  
Nearest Neighbor ◽  
Quantum Circuit ◽  
Quantum Fourier Transform ◽  
Factoring Algorithm

We show how to construct an efficient quantum circuit for computing a good approximation of the quantum Fourier transform on a linear nearest neighbor architecture. The constructed circuit uses no ancillary qubits and its depth and size are $O(n)$ and $O(n\log n)$, respectively, where $n$ is the length of the input. The circuit is useful for decreasing the size of Fowler et al.'s quantum circuit for Shor's factoring algorithm on a linear nearest neighbor architecture.

Protocol and quantum circuit for implementing theN-bit discrete quantum Fourier transform in cavity QED

2010 ◽  
Vol 43 (6) ◽  
pp. 065503 ◽  
Author(s):  
Hong-Fu Wang ◽  
Xiao-Qiang Shao ◽  
Yong-Fang Zhao ◽  
Shou Zhang ◽  
Kyu-Hwang Yeon
Keyword(s):  
Fourier Transform ◽  
Cavity Qed ◽  
Quantum Circuit ◽  
Quantum Fourier Transform

Synthesis of quantum circuits for $d$-level systems by using cosine-sine

2009 ◽  
Vol 9 (5&6) ◽  
pp. 423-443
Author(s):  
Y. Nakajima ◽  
Y. Kawano ◽  
H. Sekigawa ◽  
M. Nakanishi ◽  
S. Yamashita ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Quantum Circuit ◽  
Previous Method ◽  
Quantum Circuits ◽  
Divide And Conquer ◽  
Synthesis Methods ◽  
Quantum Fourier Transform ◽  
Asymptotically Optimal ◽  
Polynomial Size

We study the problem of designing minimal quantum circuits for any operations on $n$ qudits by means of the cosine-sine decomposition. Our method is based on a divide-and-conquer strategy. In that strategy, the size of the produced quantum circuit depends on whether the partitioning is balanced. We provide a new cosine-sine decomposition based on a balanced partitioning for $d$-level systems. The produced circuit is not asymptotically optimal except when $d$ is a power of two, but, when the number of qudits $n$ is small, our method can produce the smallest quantum circuit compared to the circuits produced by other synthesis methods. For example, when $d=3$ (three-level systems) and $n=2$ (two qudits), then the number of two-qudit operations called CINC, which is a generalized versions of CNOT, is 36 whereas the previous method needs 156 CINC gates. Moreover, we show that our method is useful for designing a polynomial-size quantum circuit for the radix-$d$ quantum Fourier transform.

scholarly journals A Quantum Cellular Automata Type Architecture with Quantum Teleportation for Quantum Computing

Entropy ◽  
2019 ◽  
Vol 21 (12) ◽  
pp. 1235
Author(s):  
Dimitrios Ntalaperas ◽  
Konstantinos Giannakis ◽  
Nikos Konofaos
Keyword(s):  
Fourier Transform ◽  
Cellular Automata ◽  
Quantum Teleportation ◽  
Nearest Neighbor ◽  
Input Pulse ◽  
Quantum Gate ◽  
Quantum Cellular Automata ◽  
Quantum Fourier Transform ◽  
Single Qubit ◽  
Qubit Operations

We propose an architecture based on Quantum Cellular Automata which allows the use of only one type of quantum gate per computational step, using nearest neighbor interactions. The model is built in partial steps, each one of them analyzed using nearest neighbor interactions, starting with single-qubit operations and continuing with two-qubit ones. A demonstration of the model is given, by analyzing how the techniques can be used to design a circuit implementing the Quantum Fourier Transform. Since the model uses only one type of quantum gate at each phase of the computation, physical implementation can be easier since at each step only one kind of input pulse needs to be applied to the apparatus.

Bilinear interpolation method for quantum images based on quantum Fourier transform

2018 ◽  
Vol 16 (04) ◽  
pp. 1850031 ◽  
Author(s):  
Panchi Li ◽  
Xiande Liu
Keyword(s):  
Image Processing ◽  
Fourier Transform ◽  
Nearest Neighbor ◽  
Interpolation Method ◽  
New Method ◽  
Basic Operation ◽  
Quantum Fourier Transform ◽  
Bilinear Interpolation ◽  
Image Scaling ◽  
Bicubic Interpolation

Image scaling is the basic operation that is widely used in classic image processing, including nearest-neighbor interpolation, bilinear interpolation, and bicubic interpolation. In quantum image processing (QIP), the research on image scaling is focused on nearest-neighbor interpolation, while the related research of bilinear interpolation is very rare, and that of bicubic interpolation has not been reported yet. In this study, a new method based on quantum Fourier transform (QFT) is designed for bilinear interpolation of images. Firstly, some basic functional modules are constructed, in which the new method based on QFT is adopted for the design of two core modules (i.e. addition and multiplication), and then these modules are used to design quantum circuits for the bilinear interpolation of images, including scaling-up and down. Finally, the complexity analysis of the scaling circuits based on the elementary gates is deduced. Simulation results show that the scaling image using bilinear interpolation is clearer than that using the nearest-neighbor interpolation.

scholarly journals Entanglement and its role in Shor's algorithm

2006 ◽  
Vol 6 (7) ◽  
pp. 630-640
Author(s):  
V.M. Kendon ◽  
W.J. Munro
Keyword(s):  
Numerical Simulation ◽  
Fourier Transform ◽  
Quantum Information ◽  
Quantum Information Processing ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Quantum Fourier Transform ◽  
Shor's Algorithm ◽  
Critical Resource ◽  
Factoring Algorithm

Entanglement has been termed a critical resource for quantum information processing and is thought to be the reason that certain quantum algorithms, such as Shor's factoring algorithm, can achieve exponentially better performance than their classical counterparts. The nature of this resource is still not fully understood: here we use numerical simulation to investigate how entanglement between register qubits varies as Shor's algorithm is run on a quantum computer. The shifting patterns in the entanglement are found to relate to the choice of basis for the quantum Fourier transform.

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
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