Modeling the Properties of Magnetostrictive Elements Using Quantum Emulators
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe manuscript titled "Modeling the properties of magnetostrictive elements of small spacecraft using quantum emulators" explores mathematical and numerical methods for modeling magnetostrictive multielectronic systems based on a combination of quantum and classical methods. Overall, the manuscript is well-written and the research is conducted meticulously. However, there are a few points that need to be addressed before considering it for publication:
1. The research topic of the study is magnetostrictive elements of small spacecraft. In the introduction, it is required to supplement the performance improvements or negative impacts of researching magnetostrictive elements on small spacecraft.
2. The author proposes the QCNM algorithm, which actually involves quantum simulation calculations on classical computers. Is this idea original to the author? If not, relevant references should be added in the introduction.
3. In the Materials and Methods section, it is required to provide a description of the structure of small spacecraft and its magnetostrictive elements. This will help readers understand why the subsequent content involves numerical modeling of multi-atomic systems.
4. The specific physical meaning of Formula (8) is not specified.
5. Figures 7 and 8 need to be compared. It is advisable to use the same scale for both axes to make the results more intuitive.
Since the variate of Figure 7 is magnetic fields of different intensity, this should be indicated in the caption of Figure 7.
6. The simulation results of Figure 7 are not explained in the main text.
7. How were the deviations of 5% and 7% obtained? If these values were calculated at specific points, they should be listed accordingly.
Author Response
Спасибо за внимание к этой работе.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsIn this manuscript, the authors presented a framework of hybrid quantum-classical simulations called QCNM. The module is specifically focused on solving the time-dependent Schrodinger equation. The authors applied this framework to an alloy system and presented the results in the paper.
Although the overall quality of the paper is ok, I have a few comments and questions that I want the authors to address.
First, I’m confused about the motivation of this paper. If the motivation is to understand the alloy system better, why do we need hybrid quantum-classical methods? What is the advantage? Also, wouldn’t pure quantum many-body simulations, for example, density-functional calculations, work?
Second, the methodology in this paper looks to be pretty straightforward. The idea is based on a direct time evolution of the time-dependent Schrodinger equation. I think there should be some other work appearing in the literature before and the authors at least should cite some of them. Also, the citations to other hybrid quantum-classical methods are missing.
Thirdly, in the results part the authors show a few plots of the results of the alloy system. To be honest, I don’t know what the plots are at all as there are no explanations for how the physical quantities are calculated. This part is completely missing.
Author Response
Thank you for your attention to this paper.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsI do not have further comments.
Author Response
Comment 1: [First, I’m confused about the motivation of this paper. If the motivation is to understand the alloy system better, why do we need hybrid quantum-classical methods? What is the advantage? Also, wouldn’t pure quantum many-body simulations, for example, density-functional calculations, work?]
Response 1: [At the moment, the authors are only at the beginning of the path of research and creation of a combined quantum-classical approach for modeling and synthesis of magnetostrictive materials and devices. More extensive research in this and related fields is planned in the future. Our considerations, which led us to the need to use a combined quantum-classical approach, we have tried to set out below.]
The article was written with the support of a grant from the Russian Science Foundation (project № 23-29-00207), https://rscf.ru/project/23-29-00207/) «Mathematical modeling and synthesis of magnetostrictive materials and devices» and reflects some of the results obtained during the work of the team of authors on this topic. The main scientific problem of the project is to create a methodology for modeling and synthesizing new effective and durable magnetostrictive materials (MM) with strictly specified properties that ensure technological safety and economic efficiency of various industries.
Such a task should be solved taking into account a variety of environmental criteria and physical principles, operational (magnetic, deformation, etc.) characteristics of materials, indicators of structure and properties of materials, accounting for formulation and production technology, cost, etc., so magnetostrictive material must be considered systematically as a complex technical system experiencing a complex of influences and having a number of controllable parameters. Such an approach requires generalization of the scientific and methodological foundations of MM and multicriteria synthesis of magnetostrictive materials, the development of a mathematical apparatus for the analysis and synthesis of MM, problem-oriented software complexes and the creation of magnetostrictive materials with specified properties on their basis.
It is known that the magnetostrictive effect itself consists in the simultaneous change of three components: deformation of the alloy wire + a change in the magnetic field + a change in the electric current. This effect is inherent only in certain two- or multi-component alloys with certain charges, certain atomic sizes and certain types of atomic lattices. Such alloys have a deformed and stressed atomic lattice. It is believed that a magnetic or electric field affects parts of the atomic lattice that consist of different atoms and are called domains, which are oriented along magnetic (electric) lines of force and make a slight turn, which collectively along the length of the magnetostrictive element causes its deformation. Currently, the theory and practice of electro-magnetic phenomena and devices are well studied, and the theory and practice of deformations of various materials are also well studied, but the authors do not know a full-fledged theory of magnetostrictive interaction. There are many local studies and solutions on various effects, materials or structures in which the magnetostrictive effect manifests itself to a greater or lesser extent.
The operational properties of MM are usually described by distributed nonlinear dynamic models, while the mathematical description of the macrostructure and macro properties of a magnetostrictive composite is performed by linear kinetic models, thus there is a problem of transition from nonlinear microlevel models to linear macrolevel models of a magnetostrictive composite.
Density functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure (or nuclear structure) (principally the ground state) of many-body systems, in particular atoms, molecules, and the condensed phases. Using this theory, the properties of a many-electron system can be determined by using functionals, i.e. functions of another function. In the case of DFT, these are functionals of the spatially dependent electron density. Although the method has disadvantages: difficulties in determining potentials, the requirement of large computing resources, the need to compare calculations with reference systems, etc.
You are absolutely right that if we just needed to explore a new material and determine its properties, then using the DFT method and the like would be more justified. But the article solves other problems, namely, it considers an approach to creating a methodology that will simultaneously and collectively: mathematically describe with acceptable accuracy the parameters of the structure of composite alloys, their electro-magnetic and deformative properties, which will allow to obtain an information model of a magnetostrictive material and the magnetostrictive effect that is inherent in this particular material (alloy). This is necessary in order to perform a multi-criteria synthesis of magnetostrictive materials or devices with specified structure parameters and magnetostrictive properties according to the information model. According to the authors, the Schrodinger equations (SE) (as a special case, the Dirac equation system) allows us to mathematically describe the structure parameters of a magnetostrictive composite in a general way, as well as link all three components of the magnetostrictive effect into a single equation system. Numerical algorithms for solving the SE are currently being actively developed. Such methods are based on a quantum approach in the mathematical description of the structure and properties of the atomic lattice, when the Rutherford model is conditionally replaced by a quantum model in which 1 dimensional element of a magnetostrictive alloy is given by 1 qubit. The authors propose a combined algorithm in which the structural and magnetostrictive properties are set at the quantum level in the form of qubits of information, and the solution of such an information model is performed on a conventional computer using a quantum emulator inside the computer memory. It is for these reasons that the authors abandoned the use of the DFT method and decided to develop methods and algorithms of quantum classical numerical methods (QCNM) designed to be performed on a classical computer in a standard software environment equipped with a classical computing module and a module for emulating quantum computing, with the possibility of data exchange between them.]
Thank you for paying attention to this. The authors agree with this comment. [No additional changes were made to reflect the additional motivation for writing the article. The authors set out the motives and prerequisites for writing the article in the Introduction, pp. 1-2.].
Comment 2: [Second, the methodology in this paper looks to be pretty straightforward. The idea is based on a direct time evolution of the time-dependent Schrodinger equation. I think there should be some other work appearing in the literature before and the authors at least should cite some of them. Also, the citations to other hybrid quantum-classical methods are missing.]
Response 2: The authors agree with this comment. In the process of finalizing the article, additional literary research was conducted and as a result, citations were added to the following articles:
9 Emmanuel Lorin, Xu Yang. Quasi-optimal domain decomposition method for neural network-based computation of the time-dependent Schrödinger equation. Computer Physics Communications, Volume 299, June 2024, 109129, https://doi.org/10.1016/j.cpc.2024.109129.
10 E.C. Gabrick, E. Sayari, A.S.M. de Castro, J. Trobia, A.M. Batista, E.K. Lenzi Fractional Schrödinger equation and time dependent potentials. Communications in Nonlinear Science and Numerical Simulation, Volume 123, August 2023, 107275, https://doi.org/10.1016/j.cnsns.2023.107275.
18 Jiangming Xie, Maojun Li. A fast BDF2 Galerkin finite element method for the one-dimensional time-dependent Schrödinger equation with artificial boundary conditions. Applied Numerical Mathematics Volume 187, May 2023, Pages 89-106, https://doi.org/10.1016/j.apnum.2023.02.006.
19 David Navia, Ángel S. Sanz. Exploring the nonclassical dynamics of the “classical” Schrödinger equation. Annals of Physics, Volume 463, April 2024, 169637, https://doi.org/10.1016/j.aop.2024.169637.
40 Akshay Ajagekar, Fengqi You Variational quantum circuit based demand response in buildings leveraging a hybrid quantum-classical strategy. Applied Energy, Volume 364, 15 June 2024, 123244, https://doi.org/10.1016/j.apenergy.2024.123244.
41 Sandeep Suresh Cranganore, Vincenzo De Maio, Ivona Brandic, Ewa Deelman. Paving the way to hybrid quantum–classical scientific workflows. Future Generation Computer Systems, Volume 158, September 2024, Pages 346-366, https://doi.org/10.1016/j.future.2024.04.030.
42 José Luis Hevia, Guido Peterssen, Mario Piattini. qSOA®: Dynamic integration for hybrid quantum/Classical software systems. Journal of Systems and Software, Volume 214, August 2024, 112061, https://doi.org/10.1016/j.jss.2024.112061.
43 Alok Shukla, Prakash Vedula. A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations. Applied Mathematics and Computation, Volume 442, 1 April 2023, 127708, https://doi.org/10.1016/j.amc.2022.127708.
44 François Gay-Balmaz, Cesare Tronci. Evolution of hybrid quantum–classical wavefunctions. Physica D: Nonlinear Phenomena, Volume 440, 15 November 2022, 133450, https://doi.org/10.1016/j.physd.2022.133450
[The text in the manuscript has been updated. Added links 9, 10, 18, 19, 40-44 – in the Introduction, p. 1]
Comment 3: [Thirdly, in the results part the authors show a few plots of the results of the alloy system. To be honest, I don’t know what the plots are at all as there are no explanations for how the physical quantities are calculated. This part is completely missing.]
Response 3: The authors agree with this comment.
In the article, the graphs were constructed according to the methodology described in [45] – (Zagrebin M.A. Crystal structure, phase diagrams, electronic and magnetic properties of three-, four- and five-component Geisler alloys: Dis.... Doctor of Physical and Mathematical Sciences. – Chelyabinsk, 2021. – 326 p.).
The text in the manuscript has been updated. Added explanations: [Figure 7 shows graphs of the dependence of magnetostrictive deformations on the modulus of elasticity (Figure 7, a) and temperature (Figure 7, b)when the alloy is found in magnetic fields of different intensities 5, 14, 25 and 30 T.] – on page 7 of the manuscript.
The text in the manuscript has been updated. Added explanations: [The temperature and elastic dependences of deformations at constant magnetic fields of 5, 14, 25 and 30 T, shown in Figure 7, show that the hysteresis width decreases with increasing value of the external field, and in a field with an induction value of more than 25 T, the hysteresis disappears.] – on pages 7-8 of the manuscript.
The text in the manuscript has been updated. Added explanations: [A comparison of the graphs in Figure 7 with the known results of modeling Ni-Mn-Ga alloys and experimental data of similar characteristics shown in Figure 8 shows deviations of no more than 5% when modeling the dependence of deformation on the modulus of elasticity and no more than 7% when constructing its dependence on temperature, at the boundary points of the hysteresis loop or in the inflection points of the graphs, in its absence.] – on page 8 of the manuscript.
