Quantum Decoding with Venn Diagrams

TL;DR

This paper simplifies quantum error correction theory for engineers, illustrating it with examples like a five-qubit Hamming-like code and the Shor code, making complex concepts more accessible.

Contribution

It introduces a more understandable approach to quantum error correction using Venn diagrams, with practical examples like the five-qubit code and Shor code.

Findings

Simplified quantum error correction visualization

Illustrative example of a five-qubit code

Analysis of the Shor code

Abstract

The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to engineers. An illustrative example is presented of a naive perfect quantum code (Hamming-like code) with five-qubits for transmitting a single qubit of information. Also the (9,1)-Shor codes is addressed.