ExperimentsExperiment 12 · Quantum information

Quantum Error Correction

Encode, inject an error, detect it, correct it.

1. Learn
2. Watch
3. Interact
4. Predict
5. Run
6. Observe
7. Record
8. Answer
9. Research

① What is the problem?

How can we protect quantum information from errors without looking at it?

② How does a classical computer approach it?

Repeat each bit three times and take a majority vote.

③ How does the quantum approach differ?

We can't copy or read the state, but we can entangle it across 3 qubits and measure only parities (the syndrome).

Original information ↓
Encoded information ↓
Noise ↓
Error detected ↓
Correction ↓
Recovered information

Inject bit-flip errors on:

Tip: select any gate to learn what it does.

step 1/6

Original logical qubit α|0⟩ + β|1⟩ on q0

data |000⟩ · p=0.750data |100⟩ · p=0.250

Errors injected

Syndrome (a, b)

—

Recovery fidelity

—

Outcome

…

Does encoding help? (Monte-Carlo, 400 simulated runs per point)

Why this works without looking

The ancillas measure only whether neighbouring qubits agree — never whether they are 0 or 1 — so α and β survive. This code handles single bit flips; real codes (e.g. the surface code) also handle phase flips.

④ What is happening mathematically?

α|0⟩+β|1⟩ → α|000⟩+β|111⟩. Syndrome (Z₀Z₁, Z₁Z₂) identifies which qubit flipped. Logical error rate 3p²−2p³ < p when p < ½.

⑤ What does the simulation show?

The full 5-qubit simulation: encoding, error, syndrome, correction, recovery fidelity, and a measured logical-error curve.

⑥ What did we learn?

Error correction trades more qubits for fewer logical errors — but only works if physical errors are rare enough.

⑦ What can you experiment with?

Inject two errors. Why does the code fail?

📓 Record: my lab notebook

Write your observations. Notes are saved only in this browser.