The learnability of Pauli noise

Understanding quantum noise is a major challenge for scaling up quantum computing systems. Despite recent developments in quantum noise characterization methods, the fundamental question of what information about gate noise is self-consistently learnable has been unclear even for a single CNOT gate. In this work, we give a precise characterization about the learnability of Pauli noise associated with Clifford gates using graph theoretical tools, showing that the learnable information corresponds exactly to the cycle space of the pattern transfer graph of a given gate set. We show that a modified version of cycle benchmarking can extract all learnable information of Pauli noise. We experimentally demonstrate Pauli noise characterization of IBM’s CNOT gate, where we learn all 14 learnable degrees of freedom and bound the 2 unlearnable degrees of freedom using physical constraints. The implications of these results for quantum error mitigation will be discussed. We will also talk about the possibility to resolve the unlearnability by going beyond qubits and leveraging additional energy levels.