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In this work, we present a rigorous accuracy analysis of the quantum Fourier transform (QFT), that identifies three natural sources of accuracy degeneracy: (i) discretization accuracy inherited from classical sampling theory, (ii) accuracy…

Quantum Physics · Physics 2025-02-18 Marina O. Lisnichenko , Oleg M. Kiselev

The results of quantum process tomography on a three-qubit nuclear magnetic resonance quantum information processor are presented, and shown to be consistent with a detailed model of the system-plus-apparatus used for the experiments. The…

Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…

Quantum Physics · Physics 2012-02-13 James M. Chappell , Max A. Lohe , Lorenz von Smekal , Azhar Iqbal , Derek Abbott

An enduring challenge in computer science is reducing the runtime required to solve computational problems. Quantum computing has attracted significant attention due to its potential to deliver asymptotically faster solutions to certain…

Quantum Physics · Physics 2025-03-25 Mischa P. Woods

Algorithms to compute the quantum Fourier transform over a cyclic group are fundamental to many quantum algorithms. This paper describes such an algorithm and gives a proof of its correctness, tightening some claimed performance bounds…

Quantum Physics · Physics 2007-05-23 Chris Lomont

It has previously been established that the logarithmic-depth approximate quantum Fourier transform (AQFT) provides a suitable replacement for the regular QFT in many quantum algorithms. Since the AQFT is less accurate by definition,…

Quantum Physics · Physics 2007-05-23 Donny Cheung

Quantum state estimation is an important task of many quantum information protocols. We consider two families of unitary evolution operators, one with a one-parameter and the other with a two-parameter, which enable the estimation of a…

Quantum Physics · Physics 2023-01-27 Cristian A. Galvis Florez , J. Martínez-Cifuentes , K. M. Fonseca-Romero

The quantum Fourier transform (QFT) brings efficiency in many respects, especially usage of resource, for most operations on quantum computers. In this study, the existing QFT-based and non-QFT-based quantum arithmetic operations are…

Information Theory · Computer Science 2020-10-09 Engin Şahin

In this paper, an algorithm for Quantum Inverse Fast Fourier Transform (QIFFT) is developed to work for quantum data. Analogous to a classical discrete signal, a quantum signal can be represented in Dirac notation, application of QIFFT is a…

Quantum Physics · Physics 2024-09-13 Mayank Roy , Devi Maheswaran

Quantum computing with qudits, quantum systems with $d > 2$ levels, offers a powerful extension beyond qubits, expanding the computational possibilities of quantum systems, allowing the simplification of the implementation of several…

Quantum Physics · Physics 2024-10-10 Francesco Pudda , Mario Chizzini , Luca Crippa

The conventional Quantum Fourier Transform, with exponential speedup compared to the classical Fast Fourier Transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, the…

Quantum Physics · Physics 2017-04-03 S. S. Zhou , T. Loke , J. A. Izaac , J. B. Wang

Quantum process tomography (QPT) methods aim at identifying a given quantum process. The present paper focuses on the estimation of a unitary process. This class is of particular interest because quantum mechanics postulates that the…

Quantum Physics · Physics 2024-01-23 François Verdeil , Yannick Deville

Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…

Numerical Analysis · Mathematics 2023-05-05 Benjamin Kenwright

This paper is concerned with the phase estimation algorithm in quantum computing algorithms, especially the scenarios where (1) the input vector is not an eigenvector; (2) the unitary operator is not exactly implemented; (3) random…

Quantum Physics · Physics 2022-08-10 Xiantao Li

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…

Machine Learning · Computer Science 2020-08-31 Yong-chan Park , Jun-Gi Jang , U Kang

For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements.…

Quantum Physics · Physics 2025-12-23 Michael Lubasch , Yuta Kikuchi , Lewis Wright , Conor Mc Keever

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits as…

Quantum Physics · Physics 2016-08-31 M. Müller , A. Rivas , E. A. Martínez , D. Nigg , P. Schindler , T. Monz , R. Blatt , M. A. Martin-Delgado

It is called blind quantum computation(BQC) that a client who has limited quantum technologies can delegate her quantum computing to a server who has fully-advanced quantum computers. But the privacy of the client's quantum inputs,…

Quantum Physics · Physics 2019-08-27 Xiaoqian Zhang

Quantum tomography is the main method used to assess the quality of quantum information processing devices, but its complexity presents a major obstacle for the characterization of even moderately large systems. The number of experimental…

Quantum Physics · Physics 2015-03-19 Marcus P. da Silva , Olivier Landon-Cardinal , David Poulin

The quantum Fourier transform (QFT) is a powerful tool in quantum computing. The main ingredients of QFT are formed by the Walsh-Hadamard transform H and phase shifts P(.), both of which are 2x2 unitary matrices as operators on the…

Quantum Physics · Physics 2007-05-23 Charles M. Bowden , Goong Chen , Zijian Diao , Andreas Klappenecker