schemd
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Quantum Error Correction

Quantum

The 3-qubit bit-flip code: one logical qubit is spread across three physical qubits, a bit-flip error is injected on any line, and two ancilla qubits extract a syndrome that names the culprit — without ever measuring the data. A majority-vote correction restores the logical state and the fidelity returns to one.

6 components · 13 connections · stabilizer parity + syndrome decoder

recommended lab 8 of 11

Infer a single-qubit bit flip from syndrome parity without reading the logical state.

Builds on: Bell-State Entanglement Visualizer

predict · then test

What information do the two syndrome measurements reveal?

Commit before the explanation appears. This is a prediction, not a quiz score.

governing model
∣0⟩L=∣000⟩, ∣1⟩L=∣111⟩  ⋅  s=(q0⊕q1, q1⊕q2)|0\rangle_L = |000\rangle,\ |1\rangle_L = |111\rangle \;\cdot\; s = (q_0{\oplus}q_1,\ q_1{\oplus}q_2)
structural inventory
  • logical qubit →3\to 3 physical
  • injectable XX error
  • 22 ancilla syndrome bits
  • majority-vote decoder
boundaries
  • corrects any single bit-flip
  • syndrome ∈{00,01,10,11}\in\{00,01,10,11\}
  • logical fidelity 0/10/1
diagnosis challenge Fault identity withheld: infer it from the changed outputs first.
causal signal trace paused

Prepare ∣ψ⟩\lvert ψ\rangle One logical qubit enters the encoder.

step 1 / 6 Prepare |ψ⟩

control console

Inject a bit-flip on any physical qubit. The two parity checks name the culprit without ever reading α,β\alpha,\beta. Then correct and read the fidelity.

switchboard · fault injection

test bed · mode=full

Quantum Error Correction6 components and 13 connections.PSI|ψ⟩do0o1o2EncodeENCEncodei0i1i2o0o1o2ChannelERRChanneli0i1i2o0o1o2s0s1SyndromeSYNSyndromei0i1i2s0s1dCorrectCORCorrectMOUT|ψ⟩
Quantum Error Correction

instrumentation rack

q0q_{\htmlData{math-slot=value}{\mathtt{0}}} ·
q0q_{\htmlData{math-slot=value}{\mathtt{0}}} ·
q0q_{\htmlData{math-slot=value}{\mathtt{0}}} ·
syndrome
s0=0s_{\htmlData{math-slot=index}{\mathtt{0}}}=\htmlData{math-slot=value}{\mathtt{0}} s0=0s_{\htmlData{math-slot=index}{\mathtt{0}}}=\htmlData{math-slot=value}{\mathtt{0}}
no error detectedXq—\htmlData{math-slot=state}{\text{no error detected}}\quad X_{q_{\htmlData{math-slot=qubit}{\text{—}}}}
logical fidelity
Flogical=0F_{\mathrm{logical}}=\htmlData{math-slot=value}{\mathtt{0}}
diagnostic probe