We analyze the dynamics of multiparticle discrete-time quantum walk on the two-dimensional lattice, with an interaction inspired on a classical model for gas collision, called HPP model. In this classical model, the direction of motion changes only when the particles collide head-on, preserving momentum and energy. In our quantum model, the dynamics is driven by the usual quantum-walk evolution operator if the particles are on different nodes, and is driven by the HPP rules if the particles are in the same node, linearly extended for superpositions. Using this new form of evolution operator, we numerically analyze three physical quantities for the two-walker case: The probability distribution of the position of one walker, the standard deviation of the position of one walker, and the entanglement between the walkers as a function of the number of steps. The numerical analysis implies that the entanglement between the walkers as a function of the number of steps initially increases and quickly tends to a constant value, which depends on the initial condition. We compare the results obtained using the HPP interaction with the equivalent ones using the phase interaction, which is based on an evolution operator that inverts the sign of the coin operator if the walkers are in the same position.
Investigating graph isomorphism in cospectral graphs via multiparticle quantum walk in fermionic basis and entanglement entropy
研究了一类共谱网络的图同构问题。当两个图通过顶点的重新标号而相互关联时，它们是同构的。本文利用多粒子量子游走方法研究了两个可伸缩（n + 2）正则图G4（n; n + 2）和G5（n; n + 2）的GI.对任意正整数n，这两个图是一对非同构的连通上谱正则图。为了研究这两个图的GI，我们在反对称费米子基上重写了图的邻接矩阵，并证明了这两个图的邻接矩阵是不同的。因此，多粒子量子行走能够区分非同构图对.我们还构造了两个新的图T4（n; n + 2）和T5（n; n + 2），并重复了G4和G5的相同过程，利用多粒子量子行走来研究GI问题.然后我们利用纠缠熵研究了GI。为此，我们计算了网络两部分之间的纠缠熵。在我们的模型中，节点被认为是相同的量子谐振子。解析计算了G4（n; n+2）和G5（n; n+2）两个特殊部分之间的纠缠熵。结果表明，纠缠熵也可以区分不同构的共谱图对。
Nonstabilizerness generation in a multiparticle quantum walk
University of Oradea（奥拉德大学）；Budapest University of Technology and Economics（布达佩斯技术与经济大学）；National Institute for R&D of Isotopic and Molecular Technologies（同位素和分子技术研究与开发国家研究所）；Nokia Bell Laboratories（诺基亚贝尔实验室）
Low-entropy arrays of microwave-shielded molecules prepared by interaction blockade
Institute for Molecules and Materials, Radboud University（鲁道夫大学分子与材料研究所）；Department of Physics, Columbia University（哥伦比亚大学物理系）；James Franck Institute and Department of Physics, The University of Chicago（芝加哥大学詹姆斯·弗兰克研究所和物理系）
