Homeschooling Quantum Mechanics

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.

A comparison can also be made regarding energy. While certain voltages result in a transistor being either "off" or "on," the lowest energy state of a qubit -- aka its ground state -- is represented as a zero and its highest energy state is represented as a one. It’s not a perfect analogy since transistor voltages are not necessarily at extreme highs or lows, but it’s one way to make sure you have the only child in an elementary school classroom who has a general idea what a Hamiltonian is.

To be completely honest, I had to use a simulator and a Hadamard gate to eliminate the look of confusion. I had essentially drawn the same thing with pencil and paper, but seeing it with a simulator definitely seemed to make a difference.

Next lesson: quantum entanglement.

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