Noise scrambles the sign

A qubit keeps a tidy pair of amplitudes only while it stays isolated from everything else that can move. Heat and stray electromagnetic fields couple the qubit to its surroundings, and the qubit becomes entangled with its surroundings, so it no longer has a pair of amplitudes of its own. Keith says the quantumness has leaked out. Malcolm’s version is that the detail has moved into the surroundings, where the experiment is not writing it down.

Dephasing is the part of decoherence that fades the relative phase, the sign or the angle between the amplitude for 0 and the amplitude for 1, as that coupling goes on. The chances of the two readings can linger after the phase has gone. Interference, the adding and the cancelling that the sign makes possible, needs the phase intact. Once the phase is scrambled, a circuit that was designed to cancel a wrong answer instead produces a smear of the wanted pattern, and the cancellation comes out partial, or fails once the phase is gone.

What remains, if you look only at the qubit, is often a mixed description. Mixed means the qubit alone has no single pair of amplitudes left, and its readings behave like ordinary chances over several such pairs. No single sign is left to cancel against, and a measurement still returns bits. Those bits no longer gather around the answer the circuit was drawn to favour, because the arithmetic of the signs has already been stirred.

A coherence time is a number read off one chip or one trap. It is not a constant of nature printed in the back of a book.

Coherence time is roughly how long a given device holds the phase before most of it has faded. A circuit has to finish well inside that time. Superconducting qubits, small circuits cooled close to absolute zero, and trapped-ion qubits, charged atoms held in electric fields, have published times that cover short circuits and run out on long ones. Quantum error correction is the programme that answers that limit. It spreads one logical qubit, the qubit you wish you had, across many physical qubits, so a scrambled phase or a flipped bit can be noticed and repaired without reading the logical state itself.

The overhead is the reason hardware groups expect to spend many physical qubits protecting each one they can trust with a long calculation. A bedroom diagram with one wire is still the right place to learn what the phase is doing. It is a poor picture of how many wires a protected answer will cost, and the courses next door take up that count.