Aperiodic Quantum Random Walks

通用量子硬币对二元非周期量子行走中扩散与纠缠的影响

Influence of generic quantum coins on the spreading and entanglement in binary aperiodic quantum walks

该研究通过数值模拟探究通用量子硬币对三类序列二元非周期量子行走的影响，发现硬币选择显著影响行走行为，动态斐波那契行走存在局域化，特定硬币参数可调控扩散与纠缠程度，推进了对非均匀量子行走中硬币作用的理解。

Average scattering entropy for periodic, aperiodic and random distribution of vertices in simple quantum graphs

This work deals with the average scattering entropy of quantum graphs. We explore this concept in several distinct scenarios that involve periodic, aperiodic and random distribution of vertices of distinct degrees. In particular, we compare distinct situations to see how they behave as we change the arrangements of vertices and the topology and geometry of the proposed structures. The results show that the average scattering entropy may depend on the number of vertices, and on the topological and geometrical disposition of vertices and edges of the quantum graph. In this sense, it can be seen …

超扩散量子行走背后的噪声关联

Noise correlations behind superdiffusive quantum walks

本研究探讨短程关联噪声对离散时间量子行走的影响，发现空间噪声关联可将指数局域化转为超扩散传播，时间关联噪声亦诱导超扩散，替代扩散机制，并揭示量子门敏感性差异及潜在机制。

一维格上持久随机游走与量子游走之间插值游走具有反正弦律的正态方差混合

Normal variance mixture with arcsine law of an interpolating walk between persistent random walk and quantum walk

提出一维格上单参数插值量子游走与持久随机游走的模型，证明其极限分布服从反正弦律的正态方差混合。

Mapping a finite and an infinite Hadamard quantum walk onto a unique case of a random walk process

A new model that maps a quantum random walk described by a Hadamard operator to a particular case of a random walk is presented. The model is represented by a Markov chain with a stochastic matrix, i.e., all the transition rates are positive, although the Hadamard operator contains negative entries. Using a proper transformation that is applied to the random walk distribution after n steps, the probability distributions in space of the two quantum states |1>, |0> are revealed. These show that a quantum walk can be entirely mapped to a particular case of a higher dimension of a random walk mode…

Temporal Fluctuations of Continuous-Time Quantum Random Walks on Circles

This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and continuous- and discrete-time classical random walks.

Investigation of the time evolution of entanglement and trace distance in an atom-cavity system described with random walk and non-random walk states

An atom-cavity system consists of an atom or group of atoms inside a cavity. When an atom in cavity is stimulated by a laser pump, it is affected by the atom-field interaction shows the quasi-random walk behavior. This can change the entanglement and trace distance of system. In this work, the change entanglement and trace distance of system in two different cases namely the random walk and non-random walk is considered. The descriptive system is a two-level atom in the electrodynamics cavity based on the Jaynes-Cummings model, which is stimulated by two longitudinal and transverse laser pumps…

Restoring coherence via aperiodic drives in a many-body quantum system

We study the unitary dynamics of randomly or quasi-periodically driven tilted Bose-Hubbard (tBH) model in one dimension deep inside its Mott phase starting from a $\mathbb{Z}_2$ symmetry-broken state. The randomness is implemented via a telegraph noise protocol in the drive period while the quasi-periodic drive is chosen to correspond to a Thue-Morse sequence. The periodically driven tBH model (with a square pulse protocol characterized by a time period $T$) is known to exhibit transitions from dynamical regimes with long-time coherent oscillations to those with rapid thermalization. Here we s…

光子量子行走中无本征态的安德森局域化

Anderson localization without eigenstates in photonic quantum walks

本研究针对含时驱动下安德森局域化易被破坏的问题，证明对硬币算符施加静态无序的离散时间光子量子行走中可观测无本征态局域化现象，且可推广至非厄米动力学。

由两个单位元序列驱动的Su-Schrieffer-Heeger模型：周期性、拟周期性、非周期性和随机协议

Su-Schrieffer-Heeger model driven by sequences of two unitaries: periodic, quasiperiodic, aperiodic, and random protocols

本文研究了通过交替应用两个单位元操作符U₁和U₂的不同组合驱动Su-Schrieffer-Heeger模型的影响，探讨了周期性、拟周期性、非周期性和随机协议对系统拓扑性质和Loschmidt回声的影响。

Quantum percolation in quasicrystals using continuous-time quantum walk

We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the octagonally symmetric Ammann-Beenker tiling. The dynamics of the quantum particle is modelled using continuous-time quantum walk (CTQW) formalism. We present a comparison of the behaviour of the CTQW on the two aperiodic quasicrystal lattices and the square lattice when all the vertices are connected and when disorder is introduced in the form of disconnections betwee…

带陷阱的光子随机行走

Photonic random walks with traps

本文研究一维晶格中带陷阱的光子随机行走，发现经典随机行走中光子必然被陷阱摧毁，而量子随机行走中光子可永久存活，并利用可控退相干的合成网格晶格实现量子与经典随机行走之间的切换。

What is random about a quantum random walk?

We use simple deterministic dynamical systems as coins in studying quantum walks. These dynamical systems can be chosen to display, in the classical limit, a range of behaviors from the integrable to chaotic, or deterministically random. As an example of an integrable coin we study the Fourier walk that generalizes the Hadamard walk and show that the walker slows down with coin dimensionality, which controls the effective Planck constant. Introducing multi-Harper maps as deterministic models of random walks we study the effect of coin chaos on the quantum walk. We also demonstrate that breakin…

在集成光子晶格中定制量子行走

Tailoring quantum walks in integrated photonic lattices

本文通过实验比较线性和非线性光子波导阵列，揭示量子行走中非经典性的产生，并展示非周期性阵列设计生成最大纠缠态的潜力。

Limit theorems and absorption problems for one-dimensional correlated random walks

There has recently been considerable interest in quantum walks in connection with quantum computing. The walk can be considered as a quantum version of the so-called correlated random walk. We clarify a strong structural similarity between both walks and study limit theorems and absorption problems for correlated random walks by our PQRS method, which was used in our analysis of quantum walks.