Fig. 2: Illustration of the regime in which exponential sample complexity arises to accomplish the (ε, δ, w)-Pauli channel learning task.
From: On the fundamental resource for exponential advantage in quantum channel learning
The regime is denoted as a function of the maximum weight w and the number of ancilla qubits k. In this figure, we focus on the case k and w scale proportionally with n. As stated in Theorem 2, the boundary of this regime is linear for w≤n/2, and becomes concave for w > n/2. According to Eq. (14), within our stabilizer-covering scheme, polynomial sample complexity is achievable only when k = n. This case is indicated by the black dashed line.
