Fast estimation of sparse quantum noise

To achieve a scalable estimation of quantum noise we need to learn efficient and complete representations of that noise. We can do this by using descriptions that have clear and relevant physical assumptions baked in. Here I will present work on a scalable and complete protocol to learn a Pauli channel which only has s non-negligible Pauli error rates. So long as the number of error rates scales polynomially with the number of qubits, then this is an efficient protocol and requires only O(n s) experiments, linear in the number of qubits. The classical computational effort is also efficient in n. Learning these error rates is directly relevant to improving quantum error correction and we have already implemented this to efficiently learn all the errors on a 14-qubit quantum device.