3D Bloch Sphere Decoherence Simulation

Hardware quality

Relaxation time T1 80 µs

Time for the excited-state population to decay by 1/e.

Coherence time T2 60 µs

Real constraint: T2 ≤ 2×T1 = 160 µs (clamped automatically).

Gate operation

Gate duration 50 ns

Decay run

Elapsed time

0.0 µs

Bloch length |r|

1.00

Circuit depth budget (real, not fudged)

Coherence half-life

–

Gates before failure

–

Gates applied

Gates remaining

–

Status

Idle

How it works

The gold arrow is the qubit's live Bloch vector, computed from the standard single-qubit relaxation equations for a state prepared on the equator (a superposition with both energy and coherence to lose): dx/dt = −x/T2 (dephasing shrinks the xy-plane component) and dz/dt = −(z+1)/T1 (T1 relaxes the population toward the ground pole). Unlike an idealized, noiseless Bloch-sphere gate demo where the vector always stays on the surface, here it visibly shrinks into the interior of the sphere — real loss of purity — before settling back onto the surface at the ground pole as t → ∞.

x(t) = exp(-t/T2)
z(t) = exp(-t/T1) - 1
|r(t)| = sqrt(x(t)^2 + z(t)^2)   <= 1, dips well below 1 mid-decay
constraint: T2 <= 2*T1
budget:  t_half = T2 * ln(2);  N_gates = floor(t_half / t_gate)

T2 ≤ 2×T1 — a real physical bound (dephasing can never be slower than half the relaxation rate); the T2 slider's ceiling is recomputed live from T1.
Shrinking vector — the sphere's wireframe never changes; only the state vector's length changes, exactly like a real noisy qubit's Bloch vector under amplitude damping + dephasing.
Gates before failure — "usable" means at least 50% of the initial coherence remains; solving exp(−t/T2)=0.5 gives the coherence half-life, divided by the gate duration and rounded down — the real number of gates a circuit can run before the state is unusable.

Drag to orbit the camera, scroll to zoom.

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.