Gate Fidelity and State Preparation Requirements for Effective Quantum Error Correction

The development of quantum computers that demonstrate a viable computational advantage across a broad range of domains hinges on the successful implementation of quantum error correction techniques due to the immense challenge of isolating qubits from the extended thermal environment. Extensive analysis has evaluated the performance of various error correction schemes under different noise channels; however, the effects of gate control errors and imperfect state preparation have received less attention. In this work, we investigate how gate control errors and thermal state preparation influence the ability of quantum error correction schemes to suppress errors below those of a single unprotected qubit. Furthermore, we examine how the complexity of a quantum error correction algorithm affects the required gate fidelity, offering insights into the challenges facing the design of future quantum computers.