Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Experimental and Theoretical Physics Letters

Pulse sequences for realizing the quantum Fourier transform on multilevel systems

V. E. Zobov, Alexander S. Ermilov

Published Jul 1, 2006• 2 citations
Publisher

Abstract

Sequences of selective pulses of an RF magnetic field for realizing the quantum Fourier transform by NMR methods on systems with four, six, and eight nonequidistant levels are found using the virtual spin formalism. The results can be applied to other quantum systems when laser pulses are used.
DOI
10.1134/s0021364006100092

Related papers

Realization of quantum discrete Fourier transform with NMR

Ximing, Fang, Xiwen +6 more

The pulse sequences of the logic operations used in quantum discrete Fourier transform are designed for the experiment of nuclear magnetic resonance(NMR), and 2-qubit discrete Fourier transforms are implemented experimentally with NMR. The experimental errors are examined and methods for reducing the errors are proposed.

中国科学通报：英文版•Jan 1, 2000•0 citations

Experimental Realization of Discrete Fourier Transformation on NMR Quantum Computer

Liping Fu, Jun Luo, Li Xiao +1 more

We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be realized on any L-bit quantum number in principle.

arXiv:quant-ph/9905083•May 25, 1999•5 citations

Theory of selective excitation of multiple-quantum transitions

W. S. Warren, D. P. Weitekamp, Alexander Pines

The question of whether a molecule can be made to absorb and emit photons only in groups of n is treated. Pulse sequences are introduced which in effect selectively induce the absorption of only groups of n photons. This causes only n-quantum transitions even when many other transitions might be resonant. The technique involves repeated phase shifts of 2π/n in the radiation to build up the selected coherences and cancel all other coherences, and is applicable to a wide range of spectroscopic systems. Coherent averaging theory is extended to describe selective sequences and demonstrates that n-quantum selectivity is possible to arbitrarily high order in the average Hamiltonian expansion. High-order selectivity requires many phase shifts, however, and for this reason the residual nonselective effects of sequences which are selective to only a finite order are calculated. Selective sequences are applied to the multiple-quantum NMR of oriented molecules, where in combination with time reversal sequences they produce a much more efficient transfer of the population differences into selected coherences than is obtainable by normal wideband pumping. For example, the 10-quantum transition in a 10-spin system can be enhanced by more than four orders of magnitude. Experiments on selective excitaiton of the 4-quantum transitions in oriented benzene verify the expected enhancement.

The Journal of Chemical Physics•Sep 1, 1980•193 citations

Fourier Synthesis Methods for Control of Inhomogeneous Quantum Systems

Brent Pryor, Navin Khaneja

Finding control laws (pulse sequences) that can compensate for dispersions in parameters which govern the evolution of a quantum system is an important problem in the fields of coherent spectroscopy, imaging, and quantum information processing. The use of composite pulse techniques for such tasks has a long and widely known history. In this paper, we introduce the method of Fourier synthesis control law design for compensating dispersions in quantum system dynamics. We focus on system models arising in NMR spectroscopy and NMR imaging applications.

arXiv:0705.2566•May 17, 2007•0 citations

Implementation of the Quantum Fourier Transform

Yaakov S. Weinstein, Marco A. Pravia, Evan M. Fortunato +2 more

A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.

arXiv:quant-ph/9906059•Physical Review Letters•Feb 26, 2001•289 citations

Representation of the quantum Fourier transform on multilevel basic elements by a sequence of selective rotation operators

Alexander S. Ermilov, V. E. Zobov

To experimentally realize quantum computations on d -level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3–10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.

Optics and Spectroscopy•Dec 1, 2007•8 citations
The question of whether a molecule can be made to absorb and emit photons only in groups of n is treated. Pulse sequences are introduced which in effect selectively induce the absorption of only groups of n photons. This causes only n-quantum transitions even when many other transitions might be resonant. The technique involves repeated phase shifts of 2π/n in the radiation to build up the selected coherences and cancel all other coherences, and is applicable to a wide range of spectroscopic systems. Coherent averaging theory is extended to describe selective sequences and demonstrates that n-quantum selectivity is possible to arbitrarily high order in the average Hamiltonian expansion. High-order selectivity requires many phase shifts, however, and for this reason the residual nonselective effects of sequences which are selective to only a finite order are calculated. Selective sequences are applied to the multiple-quantum NMR of oriented molecules, where in combination with time reversal sequences they produce a much more efficient transfer of the population differences into selected coherences than is obtainable by normal wideband pumping. For example, the 10-quantum transition in a 10-spin system can be enhanced by more than four orders of magnitude. Experiments on selective excitaiton of the 4-quantum transitions in oriented benzene verify the expected enhancement.
Finding control laws (pulse sequences) that can compensate for dispersions in parameters which govern the evolution of a quantum system is an important problem in the fields of coherent spectroscopy, imaging, and quantum information processing. The use of composite pulse techniques for such tasks has a long and widely known history. In this paper, we introduce the method of Fourier synthesis control law design for compensating dispersions in quantum system dynamics. We focus on system models arising in NMR spectroscopy and NMR imaging applications.
A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.
To experimentally realize quantum computations on d -level basic elements (qudits) at d > 2, it is necessary to develop schemes for the technical realization of elementary logical operators. We have found sequences of selective rotation operators that represent the operators of the quantum Fourier transform (Walsh-Hadamard matrices) for d = 3–10. For the prime numbers 3, 5, and 7, the well-known method of linear algebra is applied, whereas, for the factorable numbers 6, 9, and 10, the representation of virtual spins is used (which we previously applied for d = 4, 8). Selective rotations can be realized, for example, by means of pulses of an RF magnetic field for systems of quadrupole nuclei or laser pulses for atoms and ions in traps.