Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial

TL;DR

This tutorial explains how to design and simulate quantum circuits for stabilizer error correcting codes, focusing on five-qubit and Steane codes, with practical implementation on IBM Qiskit.

Contribution

It provides detailed quantum encoder and decoder circuit designs for stabilizer codes, including nearest neighbor compliant versions, and demonstrates their verification.

Findings

Successfully designed quantum circuits for five-qubit and Steane codes.

Verified circuits using IBM Qiskit simulations.

Provided nearest neighbor compliant circuit implementations.

Abstract

Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve quantum advantage. However, quantum bits are extremely noisy and prone to decoherence. Thus, keeping the qubits error free is extremely important toward reliable quantum computing. Quantum error correcting codes have been studied for several decades and methods have been proposed to import classical error correcting codes to the quantum domain. However, circuits for such encoders and decoders haven't been explored in depth. This paper serves as a tutorial on designing and simulating quantum encoder and decoder circuits for stabilizer codes. We present encoding and decoding circuits for five-qubit code and Steane code, along with verification of these circuits using IBM Qiskit. We also provide nearest neighbour compliant encoder and decoder circuits for the five-qubit code.