Hands-on quantum: teaching core quantum concepts to first-year undergraduates and high-school students

Traditional approaches to undergraduate-level quantum mechanics require extensive mathematical preparation, preventing most students from enrolling in a quantum mechanics course until the third year of a physics major. Here we describe an approach to teaching quantum mechanics that requires no more background than what is introduced in introductory non-calculus-based introductory mechanics, and therefore can be used with first-year undergraduate students and even high school students. Dirac notation is taught using an extension of the notation that students use to manipulate unit vectors, and Hilbert space is restricted to two dimensions (i.e., qubits). To make ideas more concrete, we introduce the Bloch Cube (https://blochcubes.org), a hands-on educational tool which simplifies the Bloch sphere by restricting the set of allowed quantum states. The Bloch Cube provides students with "hands-on" experiences that illustrate key quantum concepts without equations. This approach enables students to learn rigorous quantum mechanics at a much earlier stage in their academic career, which can help students prepare for careers in quantum science and engineering and advance the Second Quantum Revolution.