Computation Methods on Quantum Systems

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 6529

Special Issue Editor


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Guest Editor
Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México. Cuernavaca, Morelos 62210, Mexico
Interests: quantum optics; discrete systems; group theoretical methods; computational algorithms; time-dependent quantum and classical systems

Special Issue Information

Dear Colleagues,

Since the birth of the quantum theory as a framework to deal with the microscopic, their philosophical and mathematical nature has been a disruptive pathway that permeates on a lot of fields that appear to be disconnected. Nowadays, we recognize the mathematical methods and analytical facts of quantum mechanics as a set of rules, procedures, and understandings, thus helping us to solve problems regarding true quantum systems and analogues that seem to follow a similar nature and dynamical rules.

This Special Issue, entitled "Computation on Quantum Systems", is intended to be a collection of wide-range results which report on the use of mathematical procedures and methods which aim to unravel the evolution and interactions of quantum systems, as well as similar analogues.

The topics of which we expect works are regarded, but not limited to, solutions on dynamical equations; time-dependent and independent systems; operational approaches to quantum, classical, and hybrid systems; algebraic structures; group theoretical methods; and numerical analysis.

We hope you find this proposal as a correct and exciting place to share your work.

Dr. Alejandro R. Urzúa
Guest Editor

Manuscript Submission Information

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Keywords

  • mathematical methods
  • quantum systems
  • analytical computation
  • numerical computation
  • algebraic structures

Published Papers (3 papers)

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Research

18 pages, 12816 KiB  
Article
Spectral Problem of the Hamiltonian in Quantum Mechanics without Reference to a Potential Function
by Ibraheem F. Al-Yousef, Moayad Ekhwan, H. Bahlouli and A. D. Alhaidari
Axioms 2023, 12(4), 334; https://doi.org/10.3390/axioms12040334 - 29 Mar 2023
Viewed by 1530
Abstract
Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the series are energy orthogonal polynomials that contain all spectral information about [...] Read more.
Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the series are energy orthogonal polynomials that contain all spectral information about the system. We exploit the properties of these polynomials to introduce physical systems with rich and highly nontrivial energy spectra. In this approach, no reference is made at all to the usual potential energy function. We consider, in this new approach, a few representative problems at the level of undergraduate students who took at least two courses in quantum mechanics and are familiar with the basics of orthogonal polynomials. Our aim is to expose students to quantum systems with rich energy spectra that goes beyond the very limited textbook examples of systems with very simple energy spectra (e.g., the harmonic oscillator, Coulomb, Morse, Pöschl–Teller, etc.) illustrating the physical significance of these energy polynomials in the description of a quantum system. To assist students, partial solutions are given in an appendix as tables and figures. Full article
(This article belongs to the Special Issue Computation Methods on Quantum Systems)
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15 pages, 810 KiB  
Article
An IND-CPA Analysis of a Cryptosystem Based on Bivariate Polynomial Reconstruction Problem
by Siti Nabilah Yusof, Muhammad Rezal Kamel Ariffin, Terry Shue Chien Lau, Nur Raidah Salim, Sook-Chin Yip and Timothy Tzen Vun Yap
Axioms 2023, 12(3), 304; https://doi.org/10.3390/axioms12030304 - 17 Mar 2023
Cited by 2 | Viewed by 1205
Abstract
The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in [...] Read more.
The Polynomial Reconstruction Problem (PRP) was introduced in 1999 as a new hard problem in post-quantum cryptography. Augot and Finiasz were the first to design a cryptographic system based on a univariate PRP, which was published at Eurocrypt 2003 and was broken in 2004. In 2013, a bivariate PRP was proposed. The design is a modified version of Augot and Finiasz’s design. Our strategic method, comprising the modified Berlekamp–Welch algorithm and Coron strategies, allowed us to obtain certain secret parameters of the bivariate PRP. This finding resulted in us concluding that the bivariate PRP is not secure against Indistinguishable Chosen-Plaintext Attack (IND-CPA). Full article
(This article belongs to the Special Issue Computation Methods on Quantum Systems)
18 pages, 859 KiB  
Article
Entanglement Dynamics Governed by Time-Dependent Quantum Generators
by Artur Czerwinski
Axioms 2022, 11(11), 589; https://doi.org/10.3390/axioms11110589 - 25 Oct 2022
Cited by 7 | Viewed by 2182
Abstract
In the article, we investigate entanglement dynamics defined by time-dependent linear generators. We consider multilevel quantum systems coupled to an environment that induces decoherence and dissipation, such that the relaxation rates depend on time. By applying the condition of partial commutativity, one can [...] Read more.
In the article, we investigate entanglement dynamics defined by time-dependent linear generators. We consider multilevel quantum systems coupled to an environment that induces decoherence and dissipation, such that the relaxation rates depend on time. By applying the condition of partial commutativity, one can precisely describe the dynamics of selected subsystems. More specifically, we investigate the dynamics of entangled states. The concurrence is used to quantify the amount of two-qubit entanglement in the time domain. The framework appears to be an efficient tool for investigating quantum evolution of entangled states driven by time-local generators. In particular, non-Markovian effects can be included to observe the restoration of entanglement in time. Full article
(This article belongs to the Special Issue Computation Methods on Quantum Systems)
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