View Proposal

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Proposer

Kai Lin Ong

Title

Quantum walks and their applications

Goal

To demonstrate the application of quantum walks in a selected domain

Description

Random walks are stochastic processes defined on some mathematical state space, consisting of a sequence of steps described by independent identically distributed random variables. Numerous algorithms designed using classical random walks were developed where each has its areas of importance, contributing to the emergence of various applications in computing and technological fields. Quantum walks are quantum analogues of classical random walks. The core difference is that unlike classical random walks where randomness arises from the transition probability between different states, quantum walks exhibit randomness via quantum mechanical properties such as superposition and the measurement postulate. This resulted in them to have greater advantage over its classical counterpart, for instance, with exponentially faster hitting times. This project is devoted to studying quantum walks comprehensively and their applications in a selected field, supported by some simulations using Qiskit Python or other suitable programming. Some well-known applications are in developing search algorithms and quantum cryptography.

Resources

Shenvi, N., Kempe, J., Whaley, K. B. (2003). Quantum random-walk search algorithm. Physical Review A - Atomic, Molecular, and Optical Physics, 67(5), 523071-5230711. [052307]. https://arxiv.org/pdf/quant-ph/0210064.pdf Kempe, J. (2003). Quantum random walks: An introductory overview. Contemporary Physics, 44, 307 - 327. https://arxiv.org/pdf/quant-ph/0303081.pdf Qiskit textbook: Quantum-walk search algorithm https://qiskit.org/textbook/ch-algorithms/quantum-walk-search-algorithm.html

Background

Url

Difficulty Level

Challenging

Ethical Approval

None

Number Of Students

1

Supervisor

Kai Lin Ong

Keywords

quantum walks, search algorithms, quantum computing

Degrees

Bachelor of Science in Statistical Data Science