Perfect Quantum Error Correcting Code

TLDR

We present a quantum error correction code that protects a qubit against general one‑qubit errors. The code encodes a qubit into five physical qubits using a circuit that distributes the information, can be reversed to decode, and restores the original state via a simple unitary transformation.

Abstract

We present a quantum error correction code which protects a qubit of information against general one qubit errors. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We describe a circuit which takes the initial state with four extra qubits in the state $|0〉$ to the encoded state. It can also be converted into a decoder by running it backward. The original state of the encoded qubit can then be restored by a simple unitary transformation.