The use of decoder confidence to lower logical error rates and enable new QEC paradigms

Fault-tolerant quantum computers use decoders to monitor for errors and find a plausible correction. A decoder may also output 'soft information' in the form of a decoder confidence score (DCS) to gauge its success. One example is swim distance, computed from the shortest path between syndrome clusters. Such a score can be used in diverse ways to enhance the performance of quantum computers.

For shallow circuits, it is trivial to exploit a DCS simply by aborting an unpromising execution: for a distance-13 surface code under circuit-level noise, rejecting a mere 0.1% of possible DCS values improves the entire circuit's logical error probabiliy (LEP) by more than 5 orders of magnitude. For larger algorithms comprising up to billions of decoding windows one can use a (sufficiently accurate) DCS to assign each circuit's output a unique LEP, and use it as a basis for maximum likelihood estimation. This can reduce the effects of noise by an order of magnitude at no quantum cost.

Moving beyond these filtering and inference methods, a DCS can be used as a more radical enabler: it can make possible forms of logical representation and processing that would otherwise be infeasible due to the risk of correlated errors. I will illustrate this in the context of an approach to silicon spin quantum computing.