Quantum Walks

Addie Jordon, Austin Hawkins-Seagram, Ulrike Stege

Quantum walks (QWs) are the quantum analogue to classical random walks. We explore various implementations of QWs and create visualizations for each, with the goal of increasing educational accessibility. A new QW, called sticky walk, is introduced, where the walker sticks to targets once found. Corresponding pseudocode and Qiskit implementations are provided. Sticky walk helps bridge the gap between non-searching QWs and Quantum Walk Search (which may be an unintuitive search algorithm for those new to QWs).

Norio Konno

Chusei Kiumi

In this paper, the 2-state decomposed-type quantum walk (DQW) on a line is introduced as an extension of the 2-state quantum walk (QW). The time evolution of the DQW is defined with two different matrices, one is assigned to a real component, and the other is assigned to an imaginary component of the quantum state. Unlike the ordinary 2-state QWs, localization and the spreading phenomenon can coincide in DQWs. Additionally, a DQW can always be converted to the corresponding 4-state QW with identical probability measures. In other words, a class of 4-state QWs can be realized by DQWs with 2 states. In this work, we reveal that there is a 2-state DQW corresponding to the 4-state Grover walk. Then, we derive the weak limit theorem of the class of DQWs corresponding to 4-state QWs which can be regarded as the generalized Grover walks.

Norie Konno

Salvador Elías Venegas-Andraca

Kei Saito

The discrete-time quantum walk (QW) is determined by a unitary matrix whose components are complex numbers. Konno (2015) extended the QW to the quaternionic quantum walk (QQW) whose components are quaternions and presented some properties of the QQW. Furthermore, Konno (2015) presented the question of whether or not the dynamics of a QQW is exactly the same as that of the corresponding QW. We give an answer to the problem by calculating the probability distribution and the weak limit density function of some classes of the QQW.