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

CRC Press eBooks

Quantum Gates, Scattering Theory, Noise in Schrodinger and Dirac's Equations

Harish Parthasarathy

Published Jul 29, 2021• 0 citations
Publisher

Abstract

[ 41] The performance of quantum gates in the presence of classical and quantum noise.
DOI
10.1201/9781003221432-5

Related papers

Performance analysis of quantum unitary gates in presence of noise in the field of quantum communication

Navneet Sharma, Tarun Kumar Rawat, Harish Parthasarathy +1 more

This paper presents the performance analysis of unitary quantum gate in presence of noise, using the time dependent Schrödinger dynamics of system Hamiltonian. The perturbed Hamiltonian is expressed as the sum of unperturbed Hamiltonian and perturbation of any real valued controllable function. The basic idea is to maintain the unitarity for corresponding time evolutionary system after time T and it is achieved after solving the time-dependent Schrodinger equation along with Dyson series expansion. This work presents the behaviour of time evolutionary process of quantum system, first without noise and then in the presence of noise. The aim of this paper is to provide a simple mathematical approach for realizing the approximate unitary quantum gates when noise is having its appearance in corresponding quantum control field.

India International Conference on Power Electronics (IICPE)•Nov 1, 2016•0 citations

Schrödinger Equation and Quantum Gates

Hiu Yung Wong

Springer eBooks•Jan 1, 2025•0 citations

How Does Noise Affect a Quantum State?

Joseph H. Eberly, Ting Yu

Springer eBooks•Dec 15, 2011•0 citations

Quantum Mechanics

Harish Parthasarathy

This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.

CRC Press eBooks•Jul 29, 2021•0 citations

Lecture Notes on Quantum Mechanics

Samuel D Lindenbaum

Failure of the classical theories wave packets wave functions and probability Schrodinger's Equation quantum mechanical operators Schrodinger's Equation with forces continuous spectrum Eigensolutions the harmonic oscillator three-dimensional problems matrices matrices in different representations approximate methods I applications of WKB method alpha decay approximate methods II continuous spectrum perturbation approximate methods III spin and spinors fine structure of the hydrogen atom anomalous Zeeman effect assemblages of identical particles the Dirac Equation non-relativistic limits of the Dirac Equation Dirac operator and wave function transformations negative energy solutions - positron theory relativistic theory of Coulomb scattering Compton scattering.

WORLD SCIENTIFIC eBooks•Apr 1, 1999•57 citations

White Noise Approach to Quantum Stochastic Integrals(White Noise Analysis and Quantum Probability)

Nobuaki Obata

数理解析研究所講究録•Jun 1, 1994•0 citations
This paper presents the performance analysis of unitary quantum gate in presence of noise, using the time dependent Schrödinger dynamics of system Hamiltonian. The perturbed Hamiltonian is expressed as the sum of unperturbed Hamiltonian and perturbation of any real valued controllable function. The basic idea is to maintain the unitarity for corresponding time evolutionary system after time T and it is achieved after solving the time-dependent Schrodinger equation along with Dyson series expansion. This work presents the behaviour of time evolutionary process of quantum system, first without noise and then in the presence of noise. The aim of this paper is to provide a simple mathematical approach for realizing the approximate unitary quantum gates when noise is having its appearance in corresponding quantum control field.
This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
Failure of the classical theories wave packets wave functions and probability Schrodinger's Equation quantum mechanical operators Schrodinger's Equation with forces continuous spectrum Eigensolutions the harmonic oscillator three-dimensional problems matrices matrices in different representations approximate methods I applications of WKB method alpha decay approximate methods II continuous spectrum perturbation approximate methods III spin and spinors fine structure of the hydrogen atom anomalous Zeeman effect assemblages of identical particles the Dirac Equation non-relativistic limits of the Dirac Equation Dirac operator and wave function transformations negative energy solutions - positron theory relativistic theory of Coulomb scattering Compton scattering.