Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms [0.03%]
数值分析、谱图理论、正交多项式及量子算法
Anastasiia Minenkova,Gamal Mograby,Hanmeng Zhan
Anastasiia Minenkova
Recent progress in quantum computing shows the need to incorporate many branches of mathematics (graph theory, matrix theory, optimization, theory of orthogonal polynomials and more) into physics, computer science and chemistry. At the 2024...
A dynamical algebra of protocol-induced transformations on Dicke states [0.03%]
由协议诱导的Dicke态变换的动力学代数
Pierre-Antoine Bernard,Luc Vinet
Pierre-Antoine Bernard
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 de...
The bicomplex-real calculus and applications to bicomplex Hermite-Itô polynomials [0.03%]
双复数实函数计算及其在双复赫尔墨特-伊藤多项式中的应用
Daniel Alpay,Kamal Diki,Mihaela Vajiac
Daniel Alpay
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 kin...
Wojciech Młotkowski,Nobuaki Obata
Wojciech Młotkowski
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, relati...
Simple quantum coins enable pretty good state transfer on every hypercube [0.03%]
简单的量子硬币使每一种超立方体上的非常良好的状态传输成为可能
Hanmeng Zhan
Hanmeng Zhan
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 ext...
Gamal Mograby,Benjamin Maloy,Anastasiia Minenkova
Gamal Mograby
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 perform...
Antonio Acuaviva,Ada Chan,Summer Eldridge et al.
Antonio Acuaviva et al.
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 perfe...
What is a Gaussian channel, and when is it physically implementable using a multiport interferometer? [0.03%]
高斯通道是什么，何时可以用多端口干涉仪实现？
Repana Devendra,Tiju Cherian John,Sumesh Kappil
Repana Devendra
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. Fir...
Variational quantum and neural quantum states algorithms for the linear complementarity problem [0.03%]
线性补问题的变分量子和神经量子状态算法
Saibal De,Oliver Knitter,Rohan Kodati et al.
Saibal De et al.
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) ...
Rachel Bailey
Rachel Bailey
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 polyno...