scholarly journals Quantum Fourier analysis

2020 ◽  
Vol 117 (20) ◽  
pp. 10715-10720
Author(s):  
Arthur Jaffe ◽  
Chunlan Jiang ◽  
Zhengwei Liu ◽  
Yunxiang Ren ◽  
Jinsong Wu
Keyword(s):  
Fourier Transform ◽  
Quantum Information ◽  
Fourier Analysis ◽  
Relative Entropy ◽  
Uncertainty Principle ◽  
Category Theory ◽  
Quantum Fourier Transform ◽  
Open Problems ◽  
Quantum Symmetry

Quantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory) with analytic estimates. This provides interesting tools to investigate phenomena such as quantum symmetry. We establish bounds on the quantum Fourier transform F, as a map between suitably defined Lp spaces, leading to an uncertainty principle for relative entropy. We cite several applications of quantum Fourier analysis in subfactor theory, in category theory, and in quantum information. We suggest a topological inequality, and we outline several open problems.

Performance scaling of the quantum Fourier transform with defective rotation gates

2015 ◽  
Vol 15 (9&10) ◽  
pp. 721-736
Author(s):  
Yun Seong Nam ◽  
Reinhold Blume
Keyword(s):  
Fourier Transform ◽  
Quantum Information ◽  
Numerical Simulations ◽  
Scaling Laws ◽  
Analytical Formula ◽  
Unexpected Result ◽  
Quantum Fourier Transform ◽  
Processor Performance ◽  
Performance Scaling ◽  
Random Defects

Addressing Landauer's question concerning the influence of static gate defects on quantum information processor performance, we investigate analytically and numerically the case of the quantum Fourier transform (QFT) with defective controlled rotation (CROT) gates. Two types of defects are studied, separately and in combination: systematic and random. Analytical scaling laws of QFT performance are derived with respect to the number of qubits $n$, the size $\delta$ of systematic defects, and the size $\epsilon$ of random defects. The analytical results are in excellent agreement with numerical simulations. In addition, we present an unexpected result: The performance of the defective QFT does not deteriorate with increasing $n$, but approaches a constant that scales in $\epsilon$. We derive an analytical formula that accurately reproduces the $\epsilon$ scaling of the performance plateaus. Overall, we observe that the CROT gates may exhibit static and random defects of the order of 30\% and larger, and still result in satisfactory QFT performance. Thus we answer Landauer's question in the case of the QFT: far from being lethal, the QFT can tolerate tremendous static gate defects and still perform its function. The extraordinary robustness of the QFT with respect to static gate defects displayed in our numerical and analytical calculations should be a welcome boon for laboratory and industrial realizations of quantum circuitry.

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.

scholarly journals EFFICIENT IMPLEMENTATIONS OF THE QUANTUM FOURIER TRANSFORM: AN EXPERIMENTAL PERSPECTIVE

2005 ◽  
Vol 03 (02) ◽  
pp. 413-424 ◽  
Author(s):  
KAVITA DORAI ◽  
DIETER SUTER
Keyword(s):  
Fourier Transform ◽  
Quantum Computing ◽  
Quantum Information ◽  
Quantum Algorithms ◽  
Point Of View ◽  
Quantum Fourier Transform ◽  
Density Matrices ◽  
Standard Quantum ◽  
Hadamard Transformation ◽  
State Tomography

The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the implementation. We focus here on an interesting decomposition of the QFT as a product of the non-selective Hadamard transformation followed by multiqubit gates corresponding to square- and higher-roots of controlled-NOT gates. This decomposition requires only O(n) operations and is thus linear in the number of qubits n. The schemes were implemented on a two-qubit NMR quantum information processor and the resultant density matrices reconstructed using standard quantum state tomography techniques. Their experimental fidelities have been measured and compared.

Secure Cloud Quantum Computing with Verification Based on Quantum Interactive Proof

Impact ◽  
2019 ◽  
Vol 2019 (10) ◽  
pp. 30-32
Author(s):  
Tomoyuki Morimae
Keyword(s):  
Quantum Computing ◽  
Quantum Information ◽  
Theoretical Physics ◽  
View Point ◽  
Research Subjects ◽  
Interactive Proof ◽  
Open Problems ◽  
Main Research ◽  
Proof Systems ◽  
Information Group

In cloud quantum computing, a classical client delegate quantum computing to a remote quantum server. An important property of cloud quantum computing is the verifiability: the client can check the integrity of the server. Whether such a classical verification of quantum computing is possible or not is one of the most important open problems in quantum computing. We tackle this problem from the view point of quantum interactive proof systems. Dr Tomoyuki Morimae is part of the Quantum Information Group at the Yukawa Institute for Theoretical Physics at Kyoto University, Japan. He leads a team which is concerned with two main research subjects: quantum supremacy and the verification of quantum computing.

scholarly journals Aspects of quantum information in finite density field theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Lucas Daguerre ◽  
Raimel Medina ◽  
Mario Solís ◽  
Gonzalo Torroba
Keyword(s):  
Field Theory ◽  
Quantum Information ◽  
Mutual Information ◽  
Fermi Surface ◽  
Relative Entropy ◽  
Chemical Potential ◽  
Operator Product ◽  
Dirac Fermions ◽  
Long Distance ◽  
Finite Density

Abstract We study different aspects of quantum field theory at finite density using methods from quantum information theory. For simplicity we focus on massive Dirac fermions with nonzero chemical potential, and work in 1 + 1 space-time dimensions. Using the entanglement entropy on an interval, we construct an entropic c-function that is finite. Unlike what happens in Lorentz-invariant theories, this c-function exhibits a strong violation of monotonicity; it also encodes the creation of long-range entanglement from the Fermi surface. Motivated by previous works on lattice models, we next calculate numerically the Renyi entropies and find Friedel-type oscillations; these are understood in terms of a defect operator product expansion. Furthermore, we consider the mutual information as a measure of correlation functions between different regions. Using a long-distance expansion previously developed by Cardy, we argue that the mutual information detects Fermi surface correlations already at leading order in the expansion. We also analyze the relative entropy and its Renyi generalizations in order to distinguish states with different charge and/or mass. In particular, we show that states in different superselection sectors give rise to a super-extensive behavior in the relative entropy. Finally, we discuss possible extensions to interacting theories, and argue for the relevance of some of these measures for probing non-Fermi liquids.

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.

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