Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial

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.

References in corpus (3)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Correcting Quantum Errors with Entanglement
• A Survey on Quantum Channel Capacities

Cited by in corpus (5)

• Quantum SWAP gate realized with CZ and iSWAP gates in a superconducting architecture
• Systematic Design and Optimization of Quantum Circuits for Stabilizer Codes
• An Optimized Nearest Neighbor Compliant Quantum Circuit for 5-qubit Code
• CNOT Minimal Circuit Synthesis: A Reinforcement Learning Approach
• Encoder Circuit Optimization for Non-Binary Quantum Error Correction Codes in Prime Dimensions: An Algorithmic Framework