13.11 Error-correcting assumptions

Throughout this section we have been making certain key assumptions about how errors can occur. For example, we have always assumed that all errors are independent, and that only single-qubit errors can occur. Although this describes many simple scenarios, it is does not do a very good job of modelling what happens in practice. It might be the case that many-qubit errors can occur, and that once a specific error has occurred it makes other errors more or less likely. Before we can describe fully fault-tolerant computation, we need to be able to deal with these more complicated scenarios, and this forms the topic of a large chunk of Chapter 14.

However, there are other assumptions that we are making that we will not discuss in this text, because they fall out of the scope of “introductory” and instead become the topic of specialised research in error correction and fault tolerance. One such assumption is that we never have any errors affecting our ancilla qubits, so that we can trust our error-syndrome measurements; similarly we assume that when we actually come to apply the error correction, we can do so in an error-free environment. Another assumption is something more “implementation-focused”, namely that we are correctly operating the measurement devices, and that they are well-calibrated, otherwise we run into the problem of measurement errors. Often combined with this is the problem of state preparation276 — how do we know that we really are preparing the state that we call |0\rangle? Such worries, and many more besides, are important if we wish to develop a truly robust theory of error correction.

  1. The combination of state preparation and measurement errors is sometimes called SPAM. This can be dealt with in various ways, appealing to the fact that their effect does not get worse as circuit depth increases since these problems are located at the very beginning and very end of the circuit.↩︎