Efficient learning of Pauli channels: learning tensor network models.

Noise is the central obstacle to building large-scale quantum computers. Of crucial importance is the ability to reliably and efficiently characterize quantum noise afflicting a large scale quantum device with high precision. Here we show that where we have a Pauli channel whose errors are have only k-local correlations we can learn the entire n-qubit Pauli channel to relative precision ε with only O(ε^-2 n² log(n)) measurements. This is efficient in the number of qubits and represents a major breakthrough in the characterization of multi-qubit devices. These results have proven recovery guarantees for quantum channels to relative precision, representing a qualitative shift in the ability to characterize quantum devices. These results are practical, relevant and immediately applicable to characterizing error rates in current intermediate scale and future large-scale quantum devices on hundreds to thousands of qubits.