Quantum Computing · Instrument 05 · Error Correction

Error Correction — protect a qubit you can't even look at

Measuring a qubit destroys its superposition — so how do you check it for errors? The trick: spread one logical qubit across three, then measure only the relationships between them. That reveals which one slipped without ever revealing the secret it holds. Step through the smallest code that does it.

The protected qubit

PHYSICAL REGISTER — 3 data qubits hold the logical state, 2 ancillas read the syndrome

Syndrome — the two parity checks

check A

check B

parity checks compare neighbours — they fire only if exactly one differs

Outcome

—

fidelity of the recovered qubit vs. the original

same error on a bare qubit → —

The duality & what's next

From this toy to a real machine

The 3-qubit code here is the teaching ancestor of the surface code — the same trick (measure stabilizer parities, never the logical state) laid out on a 2D lattice, where a parameter called the distance sets how many errors it can survive. That's what runs on today's hardware.

          PROOF OF WORK · 2024

          Google's Willow ran a distance-7 surface code on 101 qubits and crossed below threshold: each step up in distance cut the logical error rate by Λ ≈ 2.1×, and the logical qubit outlived its best physical qubit by 2.4×. More qubits made it better, not worse.

The open problem is no longer whether this works — it's stacking ~100→millions of physical qubits per logical one. See instrument 01's updated frontier panel.