Coined Quantum Walks

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Perustieteiden korkeakoulu | Bachelor's thesis
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Date

2025-09-05

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Major/Subject

Quantum Technology

Mcode

SCI3103

Degree programme

Aalto Bachelor’s Programme in Science and Technology

Language

en

Pages

34+9

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Abstract

Quantum computing is a developing field that applies the properties of quantum mechanics to develop solutions to complex problems that the most powerful classical computers cannot solve or cannot solve efficiently. Solving difficult tasks requires sophisticated and efficient algorithms that can utilize stochastic processes as the primary techniques. The typical models of these stochastic processes include discrete-time random walks and continuous ones. Quantum walks represent a quantum extension of discrete random walks, whose demonstrated utility in algorithm design has motivated signi cant interest in quantum computational research. Therefore, the purpose of this thesis is to explore the potential of discrete-time coined quantum walks using the Python package with high-performance computing (HPC) compared to classical walks by conducting a literature review. To supplement this research, some simulations are implemented to analyze the spreading behavior of coined quantum walks, compare them with classical walks, and demonstrate their application in search tasks, such as binary hypercube search algorithm. These simulations aim to clarify the extent to which quantum walks can be effectively modeled and applied in computational contexts. The results gained show that coined quantum walks exhibit faster spreading than classical random walks, which contributes to a deeper understanding of potential applications of quantum walks, such as quantum simulation, in the future.

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Supervisor

Raasakka, Matti

Thesis advisor

Raasakka, Matti

Keywords

coined walks, Markov chain, probability distribution, quantum system, search algorithms, shift operator

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https://urn.fi/URN:NBN:fi:aalto-202510218384

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[kand] Perustieteiden korkeakoulu / SCI