One Dimensional Quantum Walks with Two-step Memory

2019/04/13 by Qing Zhou, Zhou, Qing, Songfeng Lu +1
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.1904.06528

openalex publication_date 2019/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we investigate one dimensional quantum walks with two-step memory, which can be viewed as an extension of quantum walks with one-step memory. We develop a general formula for the amplitudes of the two-step-memory walk with Hadamard coin by using path integral approach, and numerically simulate its process. The simulation shows that the probability distribution of this new walk is different from that of the Hadamard quantum walk with one-step memory, while it presents some similarities with that of the normal Hadamard quantum walk without memory.

Related

• Limit theorems for quantum walks with memory
• Properties of long quantum walks in one and two dimensions
• Path integral approach to one-dimensional discrete-time quantum walk
• One-dimensional discrete-time quantum walks with general coin
• Mapping a finite and an infinite Hadamard quantum walk onto a unique case of a random walk process