Qubit Error Correction in Quantum Computing Simulations: Do Larger Repetition Codes Reduce Logical Errors?

Quantum computers are powerful tools for certain computational problems, but their fragile quantum states are easily disrupted by environmental noise, causing errors that degrade computational accuracy. Quantum error correction (QEC) addresses this challenge by encoding one logical qubit across multiple physical qubits, so that individual errors can be identified and reversed through redundancy. We used Qiskit Aer, a free open-source quantum circuit simulator, to test the repetition code, one of the simplest QEC methods, under three types of noise: bit-flip, phase-flip, and depolarizing. We compared an unprotected single-qubit baseline (n = 1) to 3-qubit (n = 3) and 5-qubit (n = 5) repetition codes, sweeping the physical error rate p from 0 to 0.15 with 4,000 simulation shots per data point. We hypothesized that larger codes would achieve higher logical success probabilities at all tested noise levels, with n = 5 outperforming n = 3, which would outperform the unprotected baseline. Our results confirmed this scaling trend across all three noise types. At p = 0.10 under bit-flip noise, the baseline achieved 0.713 logical success, while n = 3 reached 0.791 and n = 5 reached 0.843. At low noise (p = 0.02), the n = 5 code approached 0.994 logical success. Simulation results closely matched exact theoretical predictions derived from the binomial failure probability formula, validating our experimental implementation. These findings confirm that even the simplest QEC methods provide meaningful error reduction and that larger codes offer greater protection, demonstrating a foundational principle of quantum error correction using only free simulation tools.