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arXiv:2408.04859 · Physical Review Physics Education Research

Investigating and improving student understanding of the basics of quantum computing

Peter Hu, Yangqiuting Li, Chandralekha Singh

Published Aug 6, 2024• 23 citations
arXivHTMLPDF

Abstract

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N -bit classical and N -qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2 N for a quantum computer (e.g., 2 N qubits must be initialized and 2 N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2 N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024

DOI
10.1103/physrevphyseducres.20.020108

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[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Quantum information science and engineering (QISE) is a rapidly developing field that leverages the skills of experts from many disciplines to utilize the potential of quantum systems in a variety of applications. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of QISE, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a Quantum Interactive Learning Tutorial, on the basics and applications of quantum computing. These include an overview of key quantum mechanical concepts relevant to quantum computation (including ways a quantum computer is different from a classical computer), properties of single- and multiqubit systems, and the basics of single-qubit quantum gates. The tutorial uses guided inquiry-based teaching-learning sequences. Its development and validation involved conducting cognitive task analysis from both expert and student perspectives and using common student difficulties as a guide. For example, before engaging with the tutorial, after traditional lecture-based instruction, one reasoning primitive that was common in student responses is that a major difference between an N -bit classical and N -qubit quantum computer is that various things associated with a number N for a classical computer should be replaced with the number 2 N for a quantum computer (e.g., 2 N qubits must be initialized and 2 N bits of information are obtained as the output of the computation on the quantum computer). This type of reasoning primitive also led many students to incorrectly think that there are only N distinctly different states available when computation takes place on a classical computer. Research suggests that this type of reasoning primitive has its origins in students learning that quantum computers can provide exponential advantage for certain problems, e.g., Shor’s algorithm for factoring products of large prime numbers, and that the quantum state during the computation can be in a superposition of 2 N linearly independent states. The inquiry-based learning sequences in the tutorial provide scaffolding support to help students develop a functional understanding. The final version of the validated tutorial was implemented in two distinct courses offered by the physics department with slightly different student populations and broader course goals. Students’ understanding was evaluated after traditional lecture-based instruction on the requisite concepts and again after engaging with the tutorial. We analyze and discuss their improvement in performance on concepts covered in the tutorial. Published by the American Physical Society 2024
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Abstract Quantum information science is a rapidly growing interdisciplinary field that is attracting the attention of academics and industry experts alike. It requires talent from a wide variety of traditional fields, including physics, engineering, chemistry, and computer science, to name a few. To prepare students for such opportunities, it is important to give them a strong foundation in the basics of quantum information science, in which quantum computing plays a central role. In this study, we discuss the development, validation, and evaluation of a tutorial on the Bloch sphere, a useful visual tool for developing intuition about single quantum bits (qubits), which are the basic building block of any quantum computer. Students’ understanding was evaluated after they received traditional lecture-based instruction on the requisite topics, and again after engaging with the tutorial. We observe, analyze, and discuss their improvement in performance on concepts covered in the tutorial.
Quantum computing will likely change our world as we know it today. In bringing together fields such as quantum mechanics, mathematics, and computer science in their construction and application, quantum computers hold a promise of tremendous increase in processing power when compared to present day technology. For an educator, teaching this topic requires that consideration be given to the fact that quantum computing is not only based on hard-to-teach aspects of physics, math, and computing, but that quantum computing itself is still in the early stages of its development. What is certain is that concepts such as Shor’s and Grover’s algorithms have already been developed specifically for use with quantum computing. Both algorithms are the beneficiaries of quantum properties such as superposition and entanglement which are at the core of the new technology. This paper is presented in a bottom up structure starting with the explanation of the basic component, the qubit, before moving to superposition and entanglement and ending with a lucid explanation of both of the algorithms. Due to the complex nature of the topic, teaching this subject requires that certain measures be taken to teach all students at all levels and have them feel comfortable within themselves about the topic. The course is meant for anyone who wants to learn quantum computing. It is furthermore recommended that those attending have a blank slate so we start with new students. We would like to see a variety of students taking and passing the course, with that in mind, the explanations of the topics are done without employing an excessive amount of math common to other courses in quantum computing. The recommended approach for teaching is through the use of videos and a curriculum which is broken down so topics are made more general and the discussion of that effort is the main focus
Significant attention in the PER community has been paid to student cognition and reasoning processes in undergraduate quantum mechanics.Until recently, however, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses.We conducted exploratory interviews with 22 students in an upper-division quantum computing course at a large R1 university crosslisted in physics and computer science, as well as 6 graduate students in a similar graduate-level QIS course offered in physics.We classify and analyze students' responses to a pair of questions regarding the fundamental differences between classical and quantum computers.We specifically note two key themes of importance to educators: (1) when reasoning about computational power, students often struggled to distinguish between the relative effects of exponential and linear scaling, resulting in students frequently focusing on distinctions that are arguably better understood as analog-digital than classical-quantum, and (2) introducing the thought experiment of analog classical computers was a powerful tool for helping students develop a more expertlike perspective on the differences between classical and quantum computers.