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A dynamical algebra of protocol-induced transformations on Dicke states. 协议诱导的Dicke状态转换的动态代数。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0415
Pierre-Antoine Bernard, Luc Vinet
{"title":"A dynamical algebra of protocol-induced transformations on Dicke states.","authors":"Pierre-Antoine Bernard, Luc Vinet","doi":"10.1098/rsta.2024.0415","DOIUrl":"https://doi.org/10.1098/rsta.2024.0415","url":null,"abstract":"<p><p>Quantum [Formula: see text]-qubit states that are totally symmetric under the permutation of qubits are essential ingredients of important algorithms and applications in quantum information. Consequently, there is significant interest in developing methods to prepare and manipulate Dicke states, which form a basis for the subspace of fully symmetric states. Two simple protocols for transforming Dicke states are considered. An algebraic characterization of the operations that these protocols induce is obtained in terms of the Weyl algebra [Formula: see text] and [Formula: see text]. Fixed points under the application of the combination of both protocols are explicitly determined. Connections with the binary Hamming scheme, the Hadamard transform and Krawtchouk polynomials are highlighted.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240415"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The bicomplex-real calculus and applications to bicomplex Hermite-Itô polynomials. 双复实微积分及其在双复Hermite-Itô多项式中的应用。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0416
Daniel Alpay, Kamal Diki, Mihaela Vajiac
{"title":"The bicomplex-real calculus and applications to bicomplex Hermite-Itô polynomials.","authors":"Daniel Alpay, Kamal Diki, Mihaela Vajiac","doi":"10.1098/rsta.2024.0416","DOIUrl":"https://doi.org/10.1098/rsta.2024.0416","url":null,"abstract":"<p><p>In this paper, we extend the notions of complex C-R-calculus and complex Hermite polynomials to the bicomplex setting and compare the bicomplex polyanalytic function theory with the classical complex case. Specifically, we introduce two kinds of bicomplex Hermite polynomials and present some of their basic properties, such as the Rodrigues formula and generating functions. We also define three bicomplex Landau operators and calculate their action on the bicomplex Hermite polynomials of the first kind.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240416"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simple quantum coins enable pretty good state transfer on every hypercube. 简单的量子币可以在每个超立方体上实现很好的状态转移。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0418
Hanmeng Zhan
{"title":"Simple quantum coins enable pretty good state transfer on every hypercube.","authors":"Hanmeng Zhan","doi":"10.1098/rsta.2024.0418","DOIUrl":"https://doi.org/10.1098/rsta.2024.0418","url":null,"abstract":"<p><p>We consider pretty good state transfer in coined quantum walks between antipodal vertices on the hypercube [Formula: see text]. When [Formula: see text] is a prime, this was proven to occur in the arc-reversal walk with Grover coins. We extend this result by constructing weighted Grover coins that enable pretty good state transfer on every [Formula: see text]. Our coins are real and require modification of the weight on only one arc per vertex. We also generalize our approach and establish a sufficient condition for pretty good state transfer to occur on other graphs.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240418"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Variational quantum and neural quantum states algorithms for the linear complementarity problem. 线性互补问题的变分量子和神经量子态算法。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0423
Saibal De, Oliver Knitter, Rohan Kodati, Paramsothy Jayakumar, James Stokes, Shravan Veerapaneni
{"title":"Variational quantum and neural quantum states algorithms for the linear complementarity problem.","authors":"Saibal De, Oliver Knitter, Rohan Kodati, Paramsothy Jayakumar, James Stokes, Shravan Veerapaneni","doi":"10.1098/rsta.2024.0423","DOIUrl":"10.1098/rsta.2024.0423","url":null,"abstract":"<p><p>Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems-and whether quantum-inspired classical algorithms can match their performance-remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240423"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12508771/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Distance measures for quantum states and channels: properties and applications. 量子态和通道的距离测量：性质和应用。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0425
Vita Borovyk, Badri N Vellambi
{"title":"Distance measures for quantum states and channels: properties and applications.","authors":"Vita Borovyk, Badri N Vellambi","doi":"10.1098/rsta.2024.0425","DOIUrl":"https://doi.org/10.1098/rsta.2024.0425","url":null,"abstract":"<p><p>Discriminating between quantum states and channels is an important task in the field of quantum computation and quantum information theory. Metrics and statistical distances form the tools for various approaches proposed for this task. We analyse existing results to compare properties, main purpose, computability and advantages and disadvantages of each approach.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240425"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
What is a Gaussian channel, and when is it physically implementable using a multiport interferometer? 什么是高斯信道，什么时候可以使用多端口干涉仪进行物理实现？
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0422
Repana Devendra, Tiju Cherian John, Sumesh Kappil
{"title":"What is a Gaussian channel, and when is it physically implementable using a multiport interferometer?","authors":"Repana Devendra, Tiju Cherian John, Sumesh Kappil","doi":"10.1098/rsta.2024.0422","DOIUrl":"https://doi.org/10.1098/rsta.2024.0422","url":null,"abstract":"<p><p>Quantum Gaussian channels are fundamental models for communication and information processing in continuous-variable quantum systems. This work addresses both foundational aspects and physical implementation pathways for these channels. Firstly, we provide a rigorous, unified framework by formally proving the equivalence of three principal definitions of quantum Gaussian channels prevalent in the literature. Secondly, we investigate the physical realization of these channels using linear optics, a key platform in photonics. The central research contributions are (i) a new characterization of Gaussian channels in terms of their ampliations, (ii) a precise characterization of the specific pairs of matrices [Formula: see text] that correspond to Gaussian channels physically implementable via linear optical multiport interferometers, (iii) answering the questions posed by Parthasarathy (Parthasarathy KR. 2015 Symplectic dilations, Gaussian states and Gaussian channels. <i>Indian J. Pure Appl. Math.</i> <b>46</b>, 419-439. (doi:10.1007/s13226-015-0144-5)) and (iv) a discussion on some common misunderstandings in the literature. This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240422"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Grover's quantum walk on segmented complete graphs. 格罗弗在分段完全图上的量子行走。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0419
Gamal Mograby, Benjamin Maloy, Anastasiia Minenkova
{"title":"Grover's quantum walk on segmented complete graphs.","authors":"Gamal Mograby, Benjamin Maloy, Anastasiia Minenkova","doi":"10.1098/rsta.2024.0419","DOIUrl":"https://doi.org/10.1098/rsta.2024.0419","url":null,"abstract":"<p><p>We study Grover's quantum walk on a new class of graphs, termed segmented complete graphs, which combine high symmetry with detailed spectral properties. Using these graphs, we implement Grover's search algorithm and investigate its performance, focussing on the relationship between graph volume, optimal search time and success probabilities. Our results generalize classical findings for directed weighted graphs and provide new insights into enhancing quantum search algorithms on complex graph structures.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240419"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Partial Chebyshev polynomials and fan graphs. 部分切比雪夫多项式和扇形图。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0417
Wojciech Młotkowski, Nobuaki Obata
{"title":"Partial Chebyshev polynomials and fan graphs.","authors":"Wojciech Młotkowski, Nobuaki Obata","doi":"10.1098/rsta.2024.0417","DOIUrl":"https://doi.org/10.1098/rsta.2024.0417","url":null,"abstract":"<p><p>Motivated by the product formula of the Chebyshev polynomials of the second kind [Formula: see text], we newly introduce the partial Chebyshev polynomials [Formula: see text] and [Formula: see text] and derive their basic properties, relations to the classical Chebyshev polynomials and new factorization formulas for [Formula: see text]. To calculate the quadratic embedding constant (QEC) of a fan graph [Formula: see text], we derive a new polynomial [Formula: see text], which is factorized by the partial Chebyshev polynomial [Formula: see text]. We prove that [Formula: see text] is given in terms of the minimal zero of [Formula: see text] and obtain the explicit value of [Formula: see text] for an even [Formula: see text] and its reasonable estimate for an odd [Formula: see text].This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240417"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Orthogonal polynomials and perfect state transfer. 正交多项式与完全状态转移。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0414
Rachel Bailey
{"title":"Orthogonal polynomials and perfect state transfer.","authors":"Rachel Bailey","doi":"10.1098/rsta.2024.0414","DOIUrl":"https://doi.org/10.1098/rsta.2024.0414","url":null,"abstract":"<p><p>The aim of this review is to discuss some applications of orthogonal polynomials in quantum information processing. The hope is to keep the paper self-contained so that someone wanting a brief introduction to the theory of orthogonal polynomials and continuous time quantum walks on graphs may find it in one place. In particular, we focus on the associated Jacobi operators and discuss how these can be used to detect perfect state transfer (PST). We also discuss how orthogonal polynomials have been used to give results which are analogous to those given by Karlin and McGregor when studying classical birth and death processes. Finally, we show how these ideas have been extended to quantum walks with more than nearest-neighbour interactions using exceptional orthogonal polynomials (XOPs). We also provide a (non-exhaustive) list of related open questions.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240414"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
State transfer in chiral quantum walks. 手性量子行走中的状态转移。
IF 3.7 3区 综合性期刊
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2025-10-09 DOI: 10.1098/rsta.2024.0420
Antonio Acuaviva, Ada Chan, Summer Eldridge, Chris Godsil, Matthew How-Chun-Lun, Christino Tamon, Emily Wright, Xiaohong Zhang
{"title":"State transfer in chiral quantum walks.","authors":"Antonio Acuaviva, Ada Chan, Summer Eldridge, Chris Godsil, Matthew How-Chun-Lun, Christino Tamon, Emily Wright, Xiaohong Zhang","doi":"10.1098/rsta.2024.0420","DOIUrl":"https://doi.org/10.1098/rsta.2024.0420","url":null,"abstract":"<p><p>The chiral quantum walk is an emerging tool for state transfer as it helps circumvent the barrier of no-go theorems in quantum transport. Yet, it remains largely unexplored. We prove a conjecture that universal monogamy violations for perfect quantum transfer in large graphs require couplings beyond the simple imaginary [Formula: see text]. This motivates our constructions of new monogamy violations on sparse graph products. Then, we show a novel violation of periodicity and the first known examples of one-way perfect quantum transfer via transcendental couplings.This article is part of the theme issue 'Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms'.</p>","PeriodicalId":19879,"journal":{"name":"Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences","volume":"383 2306","pages":"20240420"},"PeriodicalIF":3.7,"publicationDate":"2025-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145252123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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