Frontier physics
Quantum error correction and decoherence
Study the three-qubit repetition code: syndrome measurement locates a bit-flip error without disturbing the encoded state, and verify the decode-failure rate drops below when the error probability e is small. Vary the noise level to see decoherence and the code's break-even point.
Equipment
- Three encoded qubits with a virtual syndrome table
- Noise slider (bit-error probability e)
- Parameter and physical-parameter sliders of the model
- Readout of $p_{fail}=3e^2-2e^3$ and decoding fidelity
Procedure
See errors detected by the syndrome
Keep the noise low: on the canvas a random bit-flip occasionally flips one of three qubits, and the syndrome (disagreement among qubit pairs) reveals the error's location without reading the encoded value — so the quantum superposition is preserved.
Measure the decode-failure rate
Raise the noise e and read the result: the code corrects one error, but two simultaneous errors defeat the majority vote, giving . At e = 1% we get — about 30 times better than a bare qubit.
Find the code's break-even point
Keep raising e into the tens of percent: the fidelity curve shows that above e > 1/2 the code corrupts more than it corrects. Estimate the crossing from the plot (e = 1/2) and discuss why practical decoders need physical error rates below ~10% on larger surface codes.