Quantum Error Correction During 50 Gates

Fault tolerant protocol assumes the application of error correction after every quantum gate. However, correcting errors is costly in terms of time and number of qubits. Here we demonstrate that quantum error correction can be applied significantly less often with only a minimal loss of fidelity. This is done by simulating the implementation of 50 encoded, single-qubit, quantum gates within the [[7,1,3]] quantum error correction code in a noisy, non-equiprobable Pauli error environment with error correction being applied at different intervals. We find that applying error correction after every gate is rarely optimal and even applying error correction only once after all 50 gates, though not generally optimal, sacrifices only a slight amount of fidelity with the benefit of 50-fold saving of resources. In addition, we find that in cases where bit-flip errors are dominant, it is best not to apply error correction at all.