Decoherence
A qubit does not get the wrong answer when it decoheres. It stops having an answer — and the arrow retracts into the sphere.
Decoherence visualization
The arrow is shorter than the radius whenever the state is mixed. The translucent ball is everything the qubit no longer knows about itself. Drag to rotate, scroll to zoom.
Real hardware always satisfies T2 ≤ 2·T1: dephasing cannot be slower than the dephasing that energy loss alone already causes. The sliders let you break that bound so you can see what each channel does in isolation, but a device with T2 > 2·T1 does not exist.
Decoherence is not noise added to a signal
It is tempting to picture decoherence as a wrong bit sneaking in — the qubit was 0 and the environment flipped it to 1. That is not what happens. The qubit does not acquire a wrong value; it stops having a definite value at all.
Watch the arrow. It does not swing to a different point on the surface, it retracts toward the centre. A vector at the surface is a definite quantum state with a definite phase. A vector at the centre is a coin flip: 50/50 in every basis, with no phase information left to interfere with anything.
T1 and T2
T1 is energy relaxation. The qubit dumps its excitation into the environment and settles toward |0⟩, which is why the arrow drifts up toward the north pole no matter where it started. The z component follows 1 + (z₀ − 1)·e^(−t/T1).
T2 is dephasing. The phase gets scrambled by whatever the environment is doing, so the horizontal component shrinks: x and y both decay as e^(−t/T2), collapsing the state onto the vertical axis. Set T2 to 0.1 and T1 to 2 and watch the arrow fall flat onto the polar axis long before it gets anywhere near the pole. That collapse is the loss of interference — the thing that makes a quantum computer quantum.
Why quantum computers are hard
Every gate takes time, and T2 is running against you the whole time. The number of gates you can apply before the state is mush is roughly T2 divided by the gate time. On today's superconducting hardware that is a few thousand — enough for interesting demos, nowhere near enough for Shor's algorithm on a real key.
That single ratio is why error correction exists. Adding more qubits does not extend T2; it just gives you more things that are all decohering at once. You need many physical qubits encoding one logical qubit, with errors detected and corrected faster than they accumulate — which is why useful machines are counted in millions of physical qubits rather than hundreds.