Research-based assessments (RBAs) have proven to be valuable tools in PER, supporting both instructional reform and foundational research. In the rapidly-growing field of Quantum Information Science (QIS), the lack of suitable RBAs limits the field's ability to make evidence-based decisions about curricula and program development. In this paper, we introduce the Quantum Computing Conceptual Survey (QCCS), an instrument developed to help address this gap by measuring student conceptual understanding in the foundations of quantum computing. Using pilot data from over 50 courses and 700 students, we present evidence supporting the validity of the QCCS for use in introductory QIS courses, drawing on analyses from both classical test theory and the Rasch model. We detail the potential uses for the QCCS, intending for it to serve as both a practical tool for instructors and a means of facilitating measurement-driven QIS education research.

The Controlled-Not (CNOT) gate is essential to algorithms in quantum computing for its ability to entangle qubits. As such, it is important to understand how students learning quantum computing reason around the function and use of this critical quantum gate. To investigate this, we conducted think-aloud interviews in which students solved problems involving the CNOT gate to understand students' `CNOT toolbox' – the strategies and cognitive resources students use when reasoning about the effect of the CNOT gate. We identify three cognitive resources related to the CNOT gate: (1) the procedural resource of applying CNOT to specific states, (2) a qualitative description of CNOT's effect on the target qubit given the control qubit, and (3) the idea that the control qubit is not changed when CNOT is applied to computational basis states. We find that students' use of the first resource is foundational to their understanding of the second and third, that the second and third resources can sometimes lead students to incorrect conclusions, and that students can use each of these resources separately or in tandem. We also explore how students use these resources in conjunction with Dirac notation, superposition states, and entanglement to reason both productively and unproductively about quantum computing problems.

A major challenge for quantum workforce development is the need to both understand and reliably assess student learning of quantum information science (QIS) fundamentals. Yet student thinking is notoriously difficult to probe, even for seasoned education researchers. This article presents the story of Item 15 on the Quantum Computing Conceptual Survey (QCCS). This assessment item underwent more revision and discussion within the team than the remaining 19 assessment questions combined. This paper provides a behind-the-scenes look at the development of this assessment question: a story that both reveals interesting findings about student reasoning in quantum computing and illustrates why quantum education researchers insist on triangulating diverse quantitative and qualitative data sources when developing and refining assessment items, with implications for any researcher looking to understand and measure student conceptual reasoning in quantum computing, as well as for QIS curriculum and workforce development more broadly.

PER has consistently demonstrated the effectiveness of small-group tutorials in helping students develop conceptual understanding and fluency, but instructor uptake is limited by resource constraints. To test the effectiveness of out-of-class tutorials using computer-generated feedback as an instructor-friendly alternative, we conducted think-aloud interviews with students in a quantum computing course who were randomly assigned to either a traditional validated small-group, pencil-and-paper tutorial on tensor products, or a solo computerized adaptation thereof. We found that while the computer-generated feedback was broadly considered useful by students, student engagement patterns were markedly different in the solo setting, with students demonstrating reluctance to use the interface's built-in help features and tending to internalize failure in unproductive ways counter to our intention of a formative learning environment. We discuss implications for curriculum design and directions for future research that may help to answer the longstanding question in PER of why tutorials work so well.

Despite rapid growth of quantum information science (QIS) workforce development initiatives, perceived lack of agreement among faculty on core content has made prior research-based curriculum and assessment development initiatives difficult to scale. To identify areas of consensus on content coverage, we report findings from a survey of N=63 instructors teaching introductory QIS courses at US institutions of higher learning. We identify a subset of content items common across a large fraction (≥ 80%) of introductory QIS courses that are potentially amenable to research-based curriculum development, with an emphasis on foundational skills in mathematics, physics, and engineering. As a further guide for curriculum development, we also examine differences in content coverage by level (undergraduate/graduate) and discipline. Finally, we briefly discuss the implications of our findings for the development of a research-based QIS assessment at the postsecondary level.

Broadly speaking, many physicists value intuition in their work, and many instructors hope their students develop intuition (while possibly being wary of their initial, unrefined intuitions). These considerations are especially relevant in quantum mechanics, a subject many see as counterintuitive because it is removed from classical everyday experience. Do students consider quantum mechanics intuitive, how does this affect their approach to the subject, and what does “intuitive” mean to them? We investigate these questions through a mixed-methods approach within the context of one upper-division quantum mechanics class at an R1 university. We find that most students in this population expect to have little intuition for quantum mechanics, so many consider it more unintuitive than counterintuitive. We also find that students use the word intuitive to refer to a number of distinct ideas. Overall, students have a diverse set of perspectives on intuition and its role in studying quantum mechanics. This study lays groundwork for additional research into students’ views on intuition in physics and informs how we can address intuition as educators. Quantum instructors should be aware of their students’ perspectives on intuition, and can integrate the different ways students perceive intuition into their lessons.

Popular media is an unspoken yet ever-present element of the physics landscape and a tool we can utilize in our teaching. It is also well-understood that students enter the physics classroom with a host of conceptions learned from the world at large. It stands to reason, then, to suspect that media coverage may be a major contributing factor to students' views on physical phenomena and the nature of science - one whose influence will only grow amid the 21st century digital age. Yet the role of the media in shaping physics teaching and learning has remained largely unexplored in the physics education research (PER) literature so far. Here, we explore the phenomenon of media hype from a theoretical and practical perspective: how media rhetoric of current topics in science and technology evolves, and how it affects students and instructors. We argue that media hype of cutting-edge science can be a double-edged sword for educators, with the same amped-up rhetoric that motivates students to enter the classroom tending to result in inflated preconceptions of what the science and technology can actually do. We draw on examples related to teaching quantum computing as a case study, though the findings we present should generalize to other topics garnering significant media attention - from exoplanets to graphene to batteries for electric vehicles. We conclude with a set of practical recommendations for physics teachers at all levels who wish to be more cognizant of the role exposure to popular media has on students and to tailor our teaching accordingly.

We have developed a complete collection of freely available instructional materials to assist faculty in creating a student-centered quantum mechanics (QM) class that engages students while supporting them in developing both sense-making and calculational skills. Our materials are grounded in research on students' understanding of quantum mechanics and are intended to be adaptable to a variety of instructional settings and faculty styles or preferences. They were designed for a spins-first instructional paradigm and include a set of learning goals, concept (“clicker”) questions, pre-lecture surveys, and homework and exam questions, along with example lecture notes from three instructors at three different institutions. In this work, we describe what active learning can look like in the upper-division as well as describe each of the instructional tools and provide a few representative examples. We also discuss how these materials are used at each of our institutions, illustrating how they may be adapted for use at different institutions.

We conducted a multiyear project across three institutions to develop an instructional tutorial that supports student understanding of change of basis in quantum mechanics. Building from our previous work, we identified learning goals to guide activity development. The tutorial makes an analogy between spin-1/2 states and a Cartesian coordinate system. This paper details the iterative development process including reports of observations from classroom implementations and the resulting modifications to the activity. Further, we report preliminary findings on the success of the activity in improving students’ ability to correctly change basis and their articulation that change of basis is a choice of representation, not a change to the physical system.

A common task when problem solving in quantum mechanics, including in a spins-first curriculum, involves changing the basis of a given state. Our research in undergraduate quantum mechanics courses at three institutions explores student thinking about basis, basis expansion coefficients, and change of basis in the context of spin-1/2 systems. Our investigation is based on conceptual and computational written questions as well as student reasoning interviews. We identify student ideas about whether and how changing basis affects the state, examine how students perceive notation as indicative of choice of basis, explore students' interpretations of the structure and meaning of a basis expansion, and identify the range of methods students employ when changing basis. For instance, we find a recurring idea that changing basis alters the physical system, and observe that some students chose to relabel the ket representing a quantum state vector after changing basis. Together, these results paint a broad, qualitative picture of a variety of ways that students grapple with basis and change of basis, with potential implications for instruction.

As the field of Quantum Information Science (QIS) continues to advance, there is an increased need for a quantum-smart workforce to address the needs of the growing quantum industry.As institutions begin to expand their course offerings, there is a unique opportunity for discipline-based education researchers to have an impact on the curricular and pedagogical choices being made in these courses.As a first step, it is necessary for education researchers to have a representative picture of what QIS education currently looks like.We reviewed recent course catalogues from a large sample of institutions in the United States looking for courses focused on QIS content.Our conservative analysis reveals that roughly a quarter of the institutions we reviewed offer QIS courses.While encouraging for such an emerging field, we found disparities in the types of institutions offering these courses as the vast majority were Doctoral-granting institutions.Additionally, we found that some classifications of minority serving institutions were much less likely to offer a QIS course (for example Historically Black Colleges and Universities or Predominantly Black Institutions), while Asian American and Native American Pacific Islander serving institutions were more likely than the national average to offer a QIS course.These disparities may lead to further racial, socioeconomic, and geographic disparity in the future quantum workforce.We also found that there was no single department that offered a majority of the QIS courses, indicating that the best efforts to improve QIS education will need to consider the multi-disciplinary nature of the field of quantum information science.

Significant focus in the PER community has been paid to student reasoning in undergraduate quantum mechanics. However, these same topics have remained largely unexplored in the context of emerging interdisciplinary quantum information science (QIS) courses. We conducted 15 exploratory think-aloud interviews with students in an upper-division quantum computing course at a large R1 university cross-listed in the physics and computer science departments. Focusing on responses to one particular problem, we identify two notably consistent problem-solving strategies across students in the context of a particular interview prompt, which we term Naive Measurement Probabilities (NMP) and Virtual Quantum Computer (VQC), respectively. Operating from a resources framework, we interpret these strategies as choices of coherent (and potentially mutually-generative) sets of resources to employ and available actions to perform.

Interdisciplinary introduction to quantum information science (QIS) courses are proliferating at universities across the US, but the experiences of instructors in these courses have remained largely unexplored in the discipline-based education research (DBER) communities. Here, we address this gap by reporting on the findings of a survey of instructors teaching introduction to QIS courses at institutions across the US, primarily at the undergraduate or hybrid undergraduate/graduate level, as well as follow-up focus interviews with six individual instructors. Key themes from this analysis include challenges and opportunities associated with the diversity of instructor and student backgrounds, student difficulties with the mathematical formalism (especially though not exclusively with linear algebra), and the need for better textbooks and curricular materials. We also find that while course topics are ostensibly similar, each course is crafted by its instructor to tell a different story about QIS and to uniquely balance goals such as accessibility and academic rigor, such that no canonical introduction to QIS course emerges from our dataset. We discuss the implications of this finding with regard to the benefits and risks associated with standardization of curricula as QIS coursework matures.

In this paper, we analyze video recordings of students working on tutorials in Zoom breakout rooms in an upper-division quantum mechanics course. We investigate group behaviors in this virtual environment, including the effects of instructor presence. To this end, we modify the Color Frames coding scheme introduced by Scherr to suit the virtual nature of the interactions. By broadening the frames and allowing for multiple overlapping frames, we are able to describe some group behaviors not otherwise captured. For example, in some instances, students take on an authoritative role in the group, and in other instances, groups engage in overtly casual behavior while nonetheless having on-topic discussions. We observe significant variation in how much time each group spends in each frame, but find that all groups spend some time in all frames. Instructors can be present without dominating or eliminating discussion between students, and their presence need not significantly impact the time students spent in an "informal/friendly" frame. However, instructor presence significantly reduces time spent working individually. Our findings will support additional research into the dynamics of student discussions during tutorials and aid ongoing development of online tutorials that can, e.g., be assigned for use outside of class.

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.

Changing basis is a common task when solving quantum mechanical problems. As part of a research project investigating student understanding of basis and change of basis in quantum mechanics, we developed a tutorial to support students in learning about basis in the context of spin-1/2 systems. We have since created an interactive online version of the basis tutorial as part of a freely available suite of online quantum tutorials called ACE Physics (acephysics.net). The ACE Physics tutorials include dynamic guidance elements and, unlike other tutorials, are intended for use outside the classroom without instructor facilitation. After extensive study in an instructor-supported environment, we assigned the ACE Physics basis tutorial as homework in two semesters of upper-division quantum mechanics, and we report on the effectiveness of the activity based on pre-/post-testing and comparison of student exam performance with a similar semester that did not include the activity. We find that the tutorial produces sufficient learning gains to justify continued assignment as a homework problem in our classes.

Concept inventories arc commonly used tools in physics education research (PER) for evaluating teaching methods. Student responses to concept inventories have been studied using classical test theoretical methods such as factor analysis and network methods such as module analysis. The results of these studies have been used to evaluate the instruments and to find aggregate patterns that may be used to infer how students' think about the concepts on the inventory. In this work, we apply modified model analysis using partial correlations, a network based method using partial correlations, to evaluate the Quantum Mechanics Concept Assessment (QMCA). The QMCA is designed to measure student understanding of upper-division quantum mechanics in both the spatial wave function and the spins contexts. This represents the first time a network-based analysis has been applied to an upper-division concept inventory. The modules we found are related to the structure of the instrument. There were two broad classes of modules: those that connected responses (either both correct or both incorrect) to isomorphic pairs questions written to probe the same concept in the spatial wave function and the spin contexts. The second class of modules were explain pairs, where the first question asked about a concept and the second question asked students to explain their choice, again either both correct or both incorrect. This structure resembles the structure of the Force Concept Inventory where there are a common correct and a common incorrect pair for many concepts, compared to the Force and Motion Conceptual Evaluation, which has larger and more varied communities reflecting a smaller number of topics.

As part of ongoing research on student thinking about quantum mechanical concepts and formalism, we explored how students defined and made sense of expectation values. Previous research has focused on student difficulties when defining the expectation value for a generic operator and found that students conflate other quantum mechanical ideas with expectation values. In this study, we analyzed survey data collected from two universities over a number of years and interviews carried out at two points during the semester. With a focus on underlying student thinking, we used a concept image perspective to categorize students’ concept definitions of the expectation values in the context of measuring spin in a spin-1/2 system and in the contexts of measuring energy and position for a particle in an infinite square well potential. Analysis of interview data showed that students invoke many different ideas when explaining their reasoning. The two most common definitions for the expectation value were weighted average and most probable value. In interviews, students’ definitions were influenced by whether the problem context involves continuous or discrete observables.

The number and use of research-based assessments (RBAs) has grown significantly over the last several decades. Data from RBAs can be compared against national datasets to provide instructors with empirical evidence on the efficacy of their teaching practices. Many physics instructors, however, opt not to use RBAs due to barriers such as having to use class time to administer them. In this article we examine how these barriers can be mitigated through online administrations of RBAs, particularly through the use of free online RBA platforms that automate administering, scoring, and analyzing RBAs (e.g., the Learning About STEM Student Outcomes [LASSO], Colorado Learning Attitudes About Science Survey for Experimental Physics [E-CLASS], Physics Lab Inventory of Critical thinking [PLIC], and PhysPort DataExplorer platforms). We also explore the research into common concerns of administering RBAs online and conclude with a practical how-to guide for instructors.

We investigate student comfort with the material in an upper-division spins-first quantum mechanics course. Pre-lecture surveys probing students' comfort were administered weekly, in which students assigned themselves a "discomfort level" on a scale of 0--10 and provided a written explanation for their choice. The weekly class-wide average discomfort level was effectively constant over the semester, suggesting that the class found no single unit especially jarring nor especially easy. Student written responses were coded according to their reported source of discomfort---math, math-physics connection, physics, and notation. The relative prevalence of these categories varied significantly over the semester, indicating that students find that different units present different challenges, and also that some of these challenges fade in importance as the semester progresses. Semi-structured interviews with students in a similar quantum mechanics course at a different institution provided additional context and insight into these results.