Coherent errors and quantum error correction
There are many ways that errors arise in quantum computers. If the error is due to a fast noise process, then it can often be described by an incoherent or stochastic error. For slow noise processes, the error is often a coherent error. When we consider a memory error, stochastic errors have the property that the probability of failing is linear with the memory time for small errors. For coherent errors, the error probability can increase quadratically with the memory time. Most quantum error correction codes have been designed for stochastic errors and there has been a concern that coherent errors may cause unwanted damage due to this quadratic increase in error. We have found that coherent errors at the physical level map to effectively stochastic errors at the logical level regardless of the code.