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Quantum Computing and Quantum Algorithms – An Undergraduate Approach

Mr. D. S. Rakeshgowda, Dr. S. K. Mydhili, S. Priyadharshini, A. Varalakshmi, T. Gowtham

Published Jan 12, 2026• 0 citations
Publisher
DOI
10.5281/zenodo.18473495

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This is the text for a one quarter or one semester undergraduate course on quantum computing that has been given at the University of California Santa Cruz. It is intended for students in the physical sciences who have already studied linear algebra (though a review of this topic is given in the course). No prior knowledge of quantum mechanics is required. The most important topics covered are Shor's algorithm and an introduction to quantum error correction. Most of the text is a build-up to these topics.
There is a growing need for scientists and engineers with Quantum Information Science and Technology (QIST) skills.To address this need for 'quantum aware' graduates we describe a two-course sequence in quantum computing suitable for undergraduate students studying electrical engineering, physics, and computer science.Our approach is unique in that it aims to take full advantage of the diverse backgrounds of second and third year undergraduate students from these three STEM disciplines.Students will work in interdisciplinary teams to (1) understand the physics and the computational theory relevant to quantum computing, (2) develop computer code that simulates a quantum computer, (3) understand the relevance and importance of existing quantum computing algorithms, and (4) appreciate the need for future research in quantum computing.Our approach is informed in part by our experience working with a pair of undergraduate students this past summer on the development of a Python-based quantum computer simulator.This experience showed that building a simulator was an effective way to teach the theory underlying quantum computing.Building a simulator also provides an excellent foundation upon which to explore student-accessible research projects in quantum computing, which is a high-impact educational practice.
The primordial model of quantum computation was introduced over thirty years ago and the first quantum algorithms have appeared for over twenty years. Yet the exact architectures for quantum computer seem foreign to an undergraduate student major in computer science or engineering, even though the mass media has helped popularize the terminologies in the past decade. Despite being a cutting-edge technology from both the theoretical and the experimental perspectives, quantum computation is indeed imminent and it would be helpful to give the undergraduate students at least a skeleton understanding of what a quantum computer stands for. Since instruction-set architectures originated from classical computing models are familiar, we propose analogously a set of quantum instructions, which can be composed to implement renowned quantum algorithms. Albeit the similarity one can draw between classical and quantum computer architectures, current quantum instructions are fundamentally incommensurable from their classical counterparts because they lack the innate capability to implement logical deductions and recursions. We discuss this trait in length and illustrate why it is held responsible that current quantum computers not be considered general computers.