Stabilizer Formalism · Syndrome Measurement · Pauli Errors
Code Selection
Stabilizer Group
S|ψ⟩ = |ψ⟩ for all S ∈ 𝒮
Syndrome: s_i = eigenvalue of Sᵢ
d_min = min weight of undetectable error
Syndrome will appear here.
Theory
An [[n,k,d]] stabilizer code encodes k logical qubits in n physical qubits with distance d. Stabilizers are Pauli operators S with S|ψ⟩=|ψ⟩. Syndrome measurement identifies errors without collapsing the logical state. Shor (1995) showed quantum error correction is possible — overcoming the no-cloning theorem. The threshold theorem guarantees fault-tolerant computation if p < p_th ≈ 1%.