3-Qubit Syndrome Tester: Manual Bit-Flip Injection

Encode Logical Qubit

Inject Errors (manual)

Toggle any physical qubit(s) by hand, then measure the syndrome — no randomness, so you control exactly how many qubits are wrong.

Run

Syndrome & Decode

s₁=0 s₂=0 → no error detected

Physical qubits

0 0 0

Decoded logical

|0⟩_L

Encode a state to begin

How it works

The 3-qubit bit-flip repetition code encodes one logical qubit into three physical qubits:

|0⟩_L = |000⟩
|1⟩_L = |111⟩

You flip physical qubits by hand instead of a random noise channel. Two stabilizer parity measurements read out the error location without ever measuring — and collapsing — the logical state itself:

s₁ = Z₁Z₂  (parity of qubits 1,2)
s₂ = Z₂Z₃  (parity of qubits 2,3)

Lookup table used for correction:

s₁ s₂ → correction
0  0  → none
1  0  → flip qubit 1
0  1  → flip qubit 3
1  1  → flip qubit 2

Flip exactly one qubit and the syndrome always points at it — correction always succeeds. Flip two qubits and the syndrome instead matches the pattern of a different single-qubit error: the decoder "corrects" the wrong qubit, flips the code into the other codeword, and reports the wrong logical bit. This is not a bug — it is the fundamental limit of a distance-3 code, the same limit that makes real quantum hardware use larger codes (surface codes) for lower error rates.