Quantum Error Correction: 3-Qubit Bit-Flip Code

This simulator implements the quantum repetition code exactly: a chosen logical qubit α|0⟩+β|1⟩ is encoded as α|000⟩+β|111⟩ across three physical qubits, each rendered as its own Bloch sphere. Injecting a random or manual bit-flip error on any qubit visibly shrinks and flips its individual Bloch vector — a direct demonstration that a single physical qubit's reduced state is mixed and carries none of the encoded phase — while the two parity-check "syndrome" bits identify the faulty qubit without ever measuring the protected state. Applying the syndrome-indicated correction restores the decoded logical qubit, shown on its own larger sphere alongside a ghost arrow marking the originally encoded state, and running repeated automatic trials builds up an empirical failure rate you can compare directly against the theoretical 3p²−2p³ formula for two-or-more simultaneous errors.