QEC ExplorerNoise Explorer
Part of QEC Explorer · Module 3 · Noise & Threshold
0 · Basics 1 · Detect errors 2 · Decoder race 3 · Noise explorer 4 · qLDPC Notebooks
Interactive · Monte Carlo · Runs in your browser

When does protection break?

Every decoder works fine when errors are rare. Crank the physical error rate up and eventually even a perfect code drowns. This module runs a real Monte Carlo experiment, sample thousands of random errors, decode each one with a real decoder, and measure how often a logical error slips through. Then sweep the error rate across code distances to look for the threshold: the crossover where making the code bigger finally starts helping.

Experiment

Code distance
Sweep mode runs all three distances (d=3, 5, 7) automatically.
Physical error rate p = 0.050
log-scaled · 0.001 → 0.5
Noise model
Z:X bias ratio ×30
Z errors at p × ratio
Decoder
Lookup decoder is only available at d=3.
Trials per data point
Above ~1000 trials, sweep mode (3 distances × ~9 points) can take many seconds at d=7.
Logical error rate
,
Trials run
0
Failures
0

Convergence, cumulative logical error rate

Press Run experiment. The curve shows the running logical error rate; watch it settle as more trials accumulate (Monte Carlo noise shrinks like 1/√trials).

Threshold sweep, logical vs physical error rate

d = 3
d = 5
d = 7
break-even (y = x)
Press Run experiment in sweep mode. This runs the Monte Carlo loop at ~9 error rates for each of d = 3, 5, 7 and plots three curves on log-log axes.
What you're looking for

The threshold, and why d = 3..7 makes it muddy

The ideal: below a critical error rate, the curves should fan out so that bigger distance = lower logical error rate (d=7 under d=5 under d=3), and above it the order flips. That crossover is the threshold. The reality at this scale: distances 3 to 7 with a few hundred trials are small and noisy. Real threshold plots use distances up to about 25 and millions of shots. So you'll often see the curves cross in a band rather than fan out cleanly, and at very low p the estimates are mostly Monte Carlo noise. The high-p order-flip is the most reliable signal here. This module shows you the actual numbers, muddiness and all, rather than a cleaned-up cartoon.