Perfect Quantum Error Correction Code

TL;DR

This paper introduces a five-qubit quantum error correction code that protects against general one-qubit errors, using a simple encoding and decoding circuit to detect and correct errors.

Contribution

It presents the minimal five-qubit code for quantum error correction and provides a straightforward circuit implementation for encoding and decoding.

Findings

Successfully encodes a qubit over five qubits

Detects and corrects all single-qubit errors

Provides a simple circuit for practical implementation

Abstract

We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing quantum information over five qubits, the minimal number required for this task. We give a simple circuit which takes the initial state with four extra qubits in the state |0> to the encoded state. The circuit can be converted into a decoding one by simply running it backward. Reading the extra four qubits at the decoder's output we learn which one of the sixteen alternatives (no error plus all fifteen possible 1-bit errors) was realized. The original state of the encoded qubit can then be restored by a simple unitary transformation.