Optimizing the Frequency of Quantum Error Correction.

A common assumption is that one applies a fault-tolerant quantum error correction (FTQEC) after every gate during quantum computing. However, it is known that this is not always optimal, since the FTQEC procedure itself can introduce errors. Here we vary the number of logical gates between FTQEC operations given that a failure of a postselection condition may cause the FTQEC to be skipped. We derive an expression for the logical error rate as a function of the error-correction frequency and find the optimal frequency for the application of the FTQEC. Furthermore, we show that this is relatively insensitive to the postselection failure probability for a large range of such probabilities. We provide an example of the application of the analytic expression to the ⟦7,1,3⟧ Steane code and data derived from a Monte Carlo simulation.