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 Mathematical Physics

Comment on “On the universality of almost every quantum logic gate” [J. Math. Phys. 41, 240 (2000)]

Nik Weaver

Published May 1, 2000• 0 citations
Publisher
DOI
10.1063/1.533308

Related papers

Comment on “Adiabatically implementing quantum gates” [J. Appl. Phys. 115, 224901 (2014)]

Richard H. Warren

Journal of Applied Physics•Apr 20, 2015•1 citation

Reply to comment on ‘control landscapes are almost always trap free: a geometric assessment’

Benjamin Russell, Re-Bing Wu, HERSCHEL A. RABITZ

Abstract This paper is a rebuttal of the comment by Zhdanov (2018 J. Phys. A: Math. Theor .) with regard to our paper (Russell et al 2017 J. Phys. A: Math. Theor . 50 205302). Parts of the comment either misrepresent the original claims in Russell et al (2017 J. Phys. A: Math. Theor . 50 205302) or consider issues that go beyond the scope of Russell et al (2017 J. Phys. A: Math. Theor . 50 205302). We address all of these points in the rebuttal. A remaining item about the prospect of an accumulation of null sets was already considered in a prior work (Russell et al 2018 J. Phys. A: Math. Theor . 51 335103). Importantly, the comment fails to consider the vast and continually growing set of successful quantum control tests under well-defined conditions, which serves as foundational evidence for the results in Russell et al (2017 J. Phys. A: Math. Theor . 50 205302). In summary, the remarks in the comment either misconstrue the claims of Russell et al (2017 J. Phys. A: Math. Theor . 50 205302) or raise points that are irrelevant to the goal of the original work. Thus, we conclude that the primary claim of the original paper stands: almost all closed finite dimensional quantum systems are trap free given adequate control resources.

Journal of Physics A Mathematical and Theoretical•Oct 31, 2018•12 citations

Deciding universality of quantum gates

Gábor Ivanyos

arXiv:quant-ph/0603009•Journal of Algebra•Oct 24, 2006•1 citation

On the universality of almost every quantum logic gate

Nik Weaver

Lloyd [Phys. Rev. Lett. 75, 346 (1995)] showed that almost every quantum logic gate is universal in the sense that it can be used to approximate any unitary transformation. The argument relied on a more general fact whose proof was not given in detail. We give a complete proof of this more general fact.

Journal of Mathematical Physics•Jan 1, 2000•27 citations

SOME UNSOLVED PROBLEMS IN QUANTUM LOGICS

Stanley Gudder

Elsevier eBooks•Jan 1, 1978•13 citations

Response to “Comment on ‘Quantization of the damped harmonic oscillator’” [J. Math. Phys. 60, 094101 (2019)]

M. Serhan, M. Abusini, Ahmed Al-Jamel +2 more

This is a response to a recently reported comment [F. M. Fernández, J. Math. Phys. 60, 094101 (2019)] on paper [M. Serhan et al., J. Math. Phys. 59, 082105 (2018)] regarding the quantization of the damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be first achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. The canonical quantization on the resulted Hermitian Hamiltonian yields the real energy eigenvalues as exactly given by Eq. (35) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)].

arXiv:1903.00352•Journal of Mathematical Physics•Sep 1, 2019•4 citations
Abstract This paper is a rebuttal of the comment by Zhdanov (2018 J. Phys. A: Math. Theor .) with regard to our paper (Russell et al 2017 J. Phys. A: Math. Theor . 50 205302). Parts of the comment either misrepresent the original claims in Russell et al (2017 J. Phys. A: Math. Theor . 50 205302) or consider issues that go beyond the scope of Russell et al (2017 J. Phys. A: Math. Theor . 50 205302). We address all of these points in the rebuttal. A remaining item about the prospect of an accumulation of null sets was already considered in a prior work (Russell et al 2018 J. Phys. A: Math. Theor . 51 335103). Importantly, the comment fails to consider the vast and continually growing set of successful quantum control tests under well-defined conditions, which serves as foundational evidence for the results in Russell et al (2017 J. Phys. A: Math. Theor . 50 205302). In summary, the remarks in the comment either misconstrue the claims of Russell et al (2017 J. Phys. A: Math. Theor . 50 205302) or raise points that are irrelevant to the goal of the original work. Thus, we conclude that the primary claim of the original paper stands: almost all closed finite dimensional quantum systems are trap free given adequate control resources.
This is a response to a recently reported comment [F. M. Fernández, J. Math. Phys. 60, 094101 (2019)] on paper [M. Serhan et al., J. Math. Phys. 59, 082105 (2018)] regarding the quantization of the damped harmonic oscillator using a non-Hermitian Hamiltonian with real energy eigenvalues. We assert here that the calculation of Eq. (29) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)] is incorrect, and thus the subsequent steps via the Nikiforov-Uvarov method are affected, and the energy eigenvalues should have been complex. However, we show here that the Hermiticity of the Hamiltonian should be first achieved to make the correct transition from classical Hamiltonian to quantum counterpart, and this can be reached using the symmetrization rule. The canonical quantization on the resulted Hermitian Hamiltonian yields the real energy eigenvalues as exactly given by Eq. (35) of Serhan et al. [J. Math. Phys. 59, 082105 (2018)].