A bit is a switch

In 1948 Claude Shannon put the word bit, which John Tukey had suggested, into print for the smallest choice a machine can record, a single yes or a no, written by engineers as 1 or 0. A classical computer, whether it is the beige machine in a 1984 bedroom or the phone in a pocket, stores letters and numbers as a long row of those switches, and each switch is in one position whenever you look.

Shannon was counting messages, not atoms. The switch is still the right picture for a classical bit, and it is the picture a qubit keeps refusing to sit inside.

A qubit, short for quantum bit, is that same kind of choice stored in something very small, such as two energy levels of an atom or the spin of an electron. Before anyone measures it, the qubit carries two amplitudes, which are numbers attached to the outcomes 0 and 1. On this shelf they are mostly positive or negative, and in general they can be complex. The chance of reading 0 is the squared size of the amplitude for 0. The chance of reading 1 is the squared size of the amplitude for 1, so the two chances add to one.

Keith told a visitor that the qubit was a switch stuck halfway between on and off, and Malcolm made him write the amplitudes on graph paper before he said it again. The paper had a number beside 0 and a number beside 1. Nothing on it was a lever hovering in the middle, which is the picture the halfway story usually leaves behind.

Superposition is the name for a qubit whose amplitudes for 0 and 1 are both nonzero. It describes those two numbers, and it is over once a measurement has returned one ordinary bit. Take a qubit whose amplitudes are both about 0.707. Square either number and you get a half, so each fresh copy reads 0 or 1 with equal chance, and a run of a thousand shots, which is what engineers call the repeated measurements, comes back with roughly five hundred of each.

The sign in front of an amplitude does not, on its own, change those chances. Two amplitudes of plus 0.707 give the same fifty-fifty readings as one plus and one minus. The sign starts to earn its keep when a later gate, the name for an operation that rewrites the amplitudes, sends the numbers along two routes that meet again. Numbers with the same sign add, and numbers with opposite signs subtract, cancelling fully when they are the same size. That meeting is called interference, and it is the arithmetic a quantum computer is built to arrange.

Keith still prefers the poster on which the machine peeks at every answer together. Malcolm’s graph paper has a column for amplitudes, a column for their squares, and a line for the sign. The notes on this shelf stay on that paper, and the bench at the bottom of this one asks you to build the equal superposition with matching signs.