Homeschooling Quantum Mechanics

Brian N. Siegelwax
3 min readApr 10, 2020

While preparing our children for their respective next schoolyears, an unexpected opportunity arose to teach a little quantum mechanics. On one suggested homeschooling curriculum, I saw a simple electrical circuit. And if you know a little about transistors and classical computing circuits, you can easily transition to qubits and quantum computing circuits.

Start with a simple classical circuit that includes a switch and a lightbulb. When the switch is "off," the circuit is open -- there is a break in the path -- current does not flow, and the lightbulb does not shine. When the switch is "on," the circuit is closed -- the path is unbroken as if the switch is not even there -- current flows through, and the lightbulb shines.

An oversimplified transistor description is the same as the switch in this circuit. For a certain voltage range, a transistor acts like an open switch; current does not flow, and we represent that "off" state as a zero. For another voltage range, the transistor acts like a closed switch; current flows, and we represent that "on" state as a one.

We now have a classical computing bit, with which we can begin a comparison to a quantum computing bit, or qubit. Instead of an off/on lightswitch, we now have a unit sphere (Bloch sphere). A unit sphere is a sphere with a radius of 1, which makes certain calculations easier. While retaining the classical zero and one states, we introduce the concept of a superposition, pointing to the surface of the sphere for pure states and the space inside the sphere for mixed states. I even went so far as to mention Planck length as a reason why there are not really an infinite number of points on the sphere and inside the sphere, but it’s infinite for practical intents and purposes.