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WHAT GOES WRONG
Errors are inevitable
Bit flips
0 and 1 swap.
Phase flips
|+⟩ becomes |−⟩: an error classical bits don't have.
Others
Small over-rotations, leakage to |2⟩, readout mistakes.
Quantum errors are richer than classical ones.
REDUNDANCY
The repetition code
Encode
|0⟩ → |000⟩, without copying an unknown state.
Check
Parity checks spot a flip without reading the data.
Vote
Fails only if most qubits flip: 3p2 − 2p3.
Spreading information out makes it robust.
DECODING
Find the error from the clues
Syndrome
The pattern of parity checks that disagree.
Decoder
Works out the most likely error from the syndrome.
Real time
Has to keep up with the qubits, in microseconds.
Error correction is a constant cycle of checking and fixing.
THE THRESHOLD
When bigger codes win
Surface code
A 2D grid of data and check qubits.
Threshold
About 1% error per operation.
2024
Google showed logical errors falling as its code grew.
Below threshold, more qubits mean fewer errors. That's the path to scale.
THE COST
Physical vs logical qubits
Overhead
Hundreds to thousands of physical qubits per logical qubit.
Better qubits
Shrink the overhead dramatically.
The goal
Millions of physical qubits for useful machines.
Every improvement in fabrication cuts the size of the machine we need.
UNIT 13 STUDY COMPLETE
🛡️
Ready for the Fab Challenge?
You've decoded error syndromes and seen how the surface code turns noisy qubits into reliable ones.