Characterizing representational learning : a combined simulation and tutorial on perturbation theory

We thank the University of St. Andrews for funding the development of simulations.Analyzing, constructing and translating between graphical, pictorial and mathematical representations of physics ideas and reasoning flexibly through them ("representational competence'') is a key characteristic of expertise in physics but is a challenge for learners to develop. Interactive computer simulations and University of Washington style tutorials both have affordances to support representational learning. This article describes work to characterize students' spontaneous use of representations before and after working with a combined simulation and tutorial on first-order energy corrections in the context of quantum-mechanical time-independent perturbation theory. Data were collected from two institutions using pre-, mid- and post-tests to assess short- and long-term gains. A representational competence level framework was adapted to devise level descriptors for the assessment items. The results indicate an increase in the number of representations used by students and the consistency between them following the combined simulation tutorial. The distributions of representational competence levels suggest a shift from perceptual to semantic use of representations based on their underlying meaning. In terms of activity design, this study illustrates the need to support students in making sense of the representations shown in a simulation and in learning to choose the most appropriate representation for a given task. In terms of characterizing representational abilities, this study illustrates the usefulness of a framework focusing on perceptual, syntactic and semantic use of representations.Publisher PDFPeer reviewe

On Experimental Deterministic Quantum Computation with One Quantum Bit (DQC1)

Quantum information processors have the ability to drastically change our world. By manipulating bits of information ruled by the laws of quantum mechanics, computational devices can perform some computations that are classically intractable. Most quantum algorithms rely on pure qubits as inputs and require entanglement throughout the computation. In this thesis, we explore a model of computation that uses mixed qubits without entanglement known as DQC1 (deterministic quantum computation with one quantum bit), using the physical system of liquid-state Nuclear Magnetic Resonance (NMR). Throughout our research, we experimentally implement an algorithm that completely encapsulates the DQC1 model, and take a close look at the quantum nature of DQC1-states as given by the quantum discord and geometric quantum discord, which are measures of non-classicality that capture correlations weaker than those measured by entanglement. We experimentally detect and quantify these correlations in an NMR DQC1 quantum information processor

Student difficulties with quantum uncertainty in the context of discrete probability distributions

Funding: We thank the University of St Andrews for funding the development of simulations.Quantum uncertainty is a fundamental concept in quantum mechanics, but challenging for students to master. In this article, we describe student difficulties with visual and conceptual understanding of quantum uncertainty in the context of discrete probability distributions such as those for a spin 1/2 particle. We collected written responses from students at two institutions to a homework activity focusing on uncertainty of spin measurement outcomes, as well as written responses to a test question from one of the institutions. We also conducted interviews with six students to gain further insight into difficulties found. Common incorrect ideas found included a depiction of uncertainty as the error around each of the individual measurement outcomes, not depicting the uncertainty region from the expectation value outwards, and the idea that quantum uncertainty of an observable can never be zero. These ideas may indicate a confusion between quantum uncertainty and errors due to instrumental imperfections of the measurement apparatus, a lack of conceptual understanding of quantum uncertainty as the standard deviation of the probability distribution with respect to its mean, and an incorrect interpretation of the uncertainty relation between two incompatible observables to deduce that quantum uncertainty can never be zero. The results of this study show the importance of supporting students in visual and conceptual understanding of quantum uncertainty.Publisher PD

The question of equity: Who has access to US quantum information education programs?

Driven in large part by the National Quantum Initiative Act of 2018, quantum information science (QIS) coursework and degree programs are rapidly spreading across US institutions. Yet prior work suggests that access to quantum workforce education is inequitably distributed, disproportionately benefiting students at large research-focused institutions whose student bodies are unrepresentative of US higher education as a whole. We use regression analysis to analyze the distribution of QIS coursework across 456 institutions of higher learning as of fall 2022, identifying statistically significant disparities across institutions in particular along the axes of institution classification, funding, and geographic distribution. We also conduct a brief analysis of the distribution of emerging dedicated QIS degree programs. We conclude with a discussion of implications for educators, policymakers, and quantum workforce development initiatives.Comment: To be submitted to Quantum Science and Technology, focus issue on Perspectives on Societal Aspects and Impacts of Quantum Technologie

Enhancing student visual understanding of the time evolution of quantum systems

Authors thank the University of St Andrews for funding the development of simulations.Time dependence is of fundamental importance for the description of quantum systems, but is particularly difficult for students to master. We describe the development and evaluation of a combined simulation-tutorial to support the development of visual understanding of time dependence in quantum mechanics. The associated interactive simulation shows the time dependence of an energy eigenstate and a superposition state, and how the time dependence of the probability density arises from that of the wave function. In order to assess transitions in student thinking, we developed a framework to characterize student responses in terms of real and complex mathematical reasoning and classical and quantum visual reasoning. The results of pre-, mid-, and post-tests indicate that the simulation-tutorial supports the development of visual understanding of time dependence, and that visual reasoning is correlated with improved student performance on a question relating to the time evolution of the wave function and the probability density. The results also indicate that the analogy of a classical standing wave for the infinite well energy eigenfunctions may be problematic in cueing incorrect ideas of time dependence.Publisher PDFPeer reviewe

Comparing introductory and beyond-introductory students' reasoning about uncertainty

Uncertainty is an important concept in physics laboratory instruction. However, little work has examined how students reason about uncertainty beyond the introductory (intro) level. In this work we aimed to compare intro and beyond-intro students' ideas about uncertainty. We administered a survey to students at 10 different universities with questions probing procedural reasoning about measurement, student-identified sources of uncertainty, and predictive reasoning about data distributions. We found that intro and beyond-intro students answered similarly on questions where intro students already exhibited expert-level reasoning, such as in comparing two data sets with the same mean but different spreads, identifying limitations in an experimental setup, and predicting how a data distribution would change if more data were collected. For other questions, beyond-intro students generally exhibited more expert-like reasoning than intro students, such as when determining whether two sets of data agree, identifying principles of measurement that contribute to spread, and predicting how a data distribution would change if better data were collected. Neither differences in student populations, lab courses taken, nor research experience were able to fully explain the variability between intro and beyond-intro student responses. These results call for further research to better understand how students' ideas about uncertainty develop beyond the intro level.Comment: 19 pages, 12 figure

Context affects student thinking about sources of uncertainty in classical and quantum mechanics

Measurement uncertainty is an important topic in the undergraduate laboratory curriculum. Previous research on student thinking about experimental measurement uncertainty has focused primarily on introductory-level students' procedural reasoning about data collection and interpretation. In this paper, we extended this prior work to study upper-level students' thinking about sources of measurement uncertainty across experimental contexts, with a particular focus on classical and quantum mechanics contexts. We developed a survey to probe students' thinking in the generic question ``What comes to mind when you think about measurement uncertainty in [classical/quantum] mechanics?'' as well as in a range of specific experimental scenarios. We found that students primarily focused on limitations of the experimental setup in classical mechanics and principles of the underlying physics theory in quantum mechanics. Our results suggest that students need careful scaffolding to identify principles in appropriate classical experimental contexts and limitations in appropriate quantum experimental contexts. We recommend that future research probe how instruction in both classical and quantum contexts can help students better understand the range of sources of uncertainty present in classical and quantum experiments.Comment: 15 pages, 8 figure

New perspectives on student reasoning about measurement uncertainty: More or better data

Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical uncertainty in upper-division courses. This study is part of a larger project evaluating student thinking about uncertainty across these contexts. In this research, we investigate advanced physics student thinking about uncertainty by asking them conceptual questions about how a hypothetical distribution of measurements would change if `more' or `better' data were collected in four different experimental scenarios. The scenarios include both classical and quantum experiments, as well as experiments that theoretically result in an expected single value or an expected distribution. This investigation is motivated by our goal of finding insights into students' potential point- and set-like thinking about uncertainty and of shining light on the limitations of those binary paradigms.Comment: 15 pages, 5 figures, accepted to Physical Review Physics Education Researc

Investigating student interpretations of the differences between classical and quantum computers: Are quantum computers just analog classical computers?

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.Comment: Submitted to Proceedings of the 2022 Physics Education Research Conference, Grand Rapids, MI, US 7/13-7/14/2