Software Implementation of Quantum Error-Correction

Abstract

The transmission of information is prone to errors that alter the information to an extent depending on the channel. To reduce errors, error-correcting protocols have been developed to increase the reliability of the communication and preserve the information. In quantum communication, quantum bits (qubits) are used to transmit information, and due to the nature of qubits, they offer tremendous advantages over their classical counterparts, the bits. However, their nature also makes them extremely fragile and susceptible to three types of errors: bit-flip, phase-flip, and bit and phase flip. The field of quantum error-correction (QEC) is concerned with the development of protocols to protect qubits and establish reliable communication in quantum channels. An important class of quantum error-correcting codes (QECCs) is the Calderbank-Shor-Steane (CSS) family of codes that use classical error-correcting codes to construct quantum codes. This project is concerned with the evaluation of the performance of CSS codes via conducting Monte Carlo simulations and calculating the probability of error per word for the code in relations to the probability of error in a quantum channel using a Python script. Simulations were conducted to evaluate the performance of the [[7, 1]] and the [[31, 11]] CSS codes. It was found that each code performs better than the other in a given region of values of channel error probability and perform equally at channel error probability about 5 × 10−3.