Bridge to quantum computing

The last lesson left the transistor pinned against a wall of heat, a switch that is either on or off, a clean 1 or 0. That switch is the whole classical picture: definite, one thing at a time. This lesson takes you to the exact edge where that picture cracks. Fire the smallest thing you can, one particle, at two narrow slits, and it does something a pebble never could. What it does is the seed of an entirely different kind of machine.

Play: fire them one at a time

Press Fire one a few times, then Rapid fire to pile up hundreds. Each particle lands as a single dot in a single place, exactly like a pebble would. Watch what the dots build.

With no detector, the dots do not fall into two stripes. They stack into a set of many alternating bright and dark bands, an interference pattern. That pattern is what you get when a wave passes through both slits at once and the two overlapping ripples reinforce in some places and cancel in others, which you saw for water and sound in waves. But here there was never more than one particle in the box. A single electron, arriving as one dot, still landed as if it had gone through both slits and interfered with itself.

Superposition: both paths until you look

There is no way to keep the pattern and also say which slit each electron took. The honest description, stated as the conceptual core of quantum mechanics, is that between the source and the screen the electron is not at one slit or the other but in a superposition of both paths at once. The two possibilities are not our ignorance about a hidden truth; they genuinely coexist and interfere, and the striped screen is the physical proof.^[1]

Now turn the which-slit detector on and fire again. The instant you force each particle to reveal which slit it used, the interference bands vanish and you get exactly the two plain stripes you first predicted. Measuring which path the particle took collapses the superposition into one definite path, and once the particle is committed to a single slit, there is nothing to interfere with. This is measurement collapse: looking changes the result. Superposition only survives while nothing records the outcome.

From this to a qubit

A classical bit is the transistor from the last lesson: it is definitely 0 or definitely 1, like an electron forced through one known slit. A qubit is the electron before you looked: a two-state system that can sit in a superposition of 0 and 1 together, and only becomes one of them when you measure it.

You can feel why that might matter for scale. Describing the superposition of $n$ qubits takes $2^n$ numbers, one amplitude for every possible combination of bits, because all those combinations coexist. Thirty qubits already means over a billion amplitudes evolving together. For a few special problems, notably factoring huge numbers and simulating molecules and materials, quantum interference can reach the answer with far fewer steps than any known classical method, which is why Feynman first proposed building computers out of quantum parts to simulate quantum physics.^[2] Each amplitude is a number you can think of with the vectors you already know, and a measurement turns those amplitudes into the probabilities of each outcome.

# 3 classical bits are always exactly one of 8 states:
classical = "101"                 # one definite string, 3 bits

# 3 qubits carry an amplitude for every one of the 2**3 = 8 combinations at once:
import math
amplitudes = [1/math.sqrt(8)] * 8  # a superposition over 000..111
# measuring returns ONE string, with probability = amplitude squared:
# prob("101") = amplitudes[5] ** 2

# n qubits -> 2**n amplitudes evolving together. n = 300 already exceeds
# the number of atoms in the observable universe.
for n in [10, 50, 300]:
    print(n, "qubits ->", 2**n, "amplitudes")

Check yourself