Comparative Performance Analysis of Quantum Error Correction Codes under Simulated Depolarizing Noise using Qiskit

Abstract: Fault-tolerant quantum computation requires quantum error correction (QEC), and while the performance of various QEC codes has been well characterized under idealized noise conditions, it has not been sufficiently characterized by simulation under realistic noise conditions. In this paper, the performance of three basic QEC codes (3-qubit Bit-Flip, 3-qubit Phase-Flip and Shor's 9-qubit [[9,1,3]]) under simulated depolarizing noise, by using Qiskit Aer, is analyzed systematically in three stages. Stage 1 is a validation of all three implementations under ideal circumstances. Stage 2 tests for 6 different error rates of 0% to 5%, and runs 2048 shots per error rate. Stage 3 brings the analysis from stage 2 to 0% to 10%, but with an uncorrected baseline for comparison. Results verify that Shor's > Bit-Flip > Phase-Flip is consistent over practically relevant error rates. At 1% noise, within current IBM Quantum hardware range, all three codes achieve a logical fidelity of over 98.7%. An error rate of 7–8% is used to identify a cross-over threshold above which the simpler Bit-Flip code can match Shor's code in fidelity with only one-third the number of qubits.

Keywords: Quantum Error Correction, Depolarizing Noise, Bit-Flip Code, Phase-Flip Code, Shor's Code, Logical Fidelity, Qiskit, NISQ, Fault-Tolerant Quantum Computing, Error Correction Threshold.