  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.
