Decoherence & Noise

Unless decoherence can be successfully combated, Preskill writes, the computer is sure to fail — and, he adds, even perfect isolation from the environment would not save us, because quantum gates are unitary transformations chosen from a continuum of possible values, and no physical control system can implement any continuous parameter with perfect accuracy.

In density-matrix language, decoherence is a pure state drifting into a mixed one: phase information, or even the qubit's basic 0/1 identity, leaks into the surrounding environment in a way that cannot practically be tracked or undone.

Two standard timescales quantify how fast this happens in the lab. T1, the relaxation time, measures how long a qubit prepared in |1⟩ takes to decay back toward |0⟩ — an energy-loss process. T2, the dephasing time, measures how long a superposition retains its relative phase before it randomizes, and satisfies T2 ≤ 2·T1 always.

Noise doesn't only cause slow decay between operations — it also causes gate errors, since any effective strategy to prevent errors must protect against small unitary errors in a circuit as well as against decoherence, in Preskill's phrasing. Every real gate implements only an imperfect approximation of its intended unitary, off by some small, unavoidable amount.

Run enough such gates in sequence, as any useful algorithm requires, and these small errors compound relentlessly, eventually overwhelming the computation entirely — unless something actively intervenes.

That intervention is the subject of the rest of this track. Quantum error correction does not eliminate physical noise; it suppresses noise's effect on the logical information being computed, provided the physical error rate stays below a critical threshold.