Adaptivity is not helpful for Pauli channel learning

Abstract

We prove that adaptive strategies offer no advantage over non-adaptive ones for learning and testing Pauli channels using entangled inputs. This key observation allows us to characterize the query complexity for several fundamental tasks by translating optimal classical estimation algorithms into the quantum setting. First, we determine the tight query complexity for learning a Pauli channel under the general ${\ell }_p$ norm, providing results that improve upon or match the best-known bounds for the ${\ell }_1,{\ell }_2,$ and ${\ell }_{\infty }$ distances. Second, we resolve the complexity of testing whether a Pauli channel is a white noise source. Finally, we show that the optimal query complexities for estimating the Shannon entropy and support size of the channel's error distribution, and for estimating the diamond distance between two Pauli channels, are all $\Theta \left(\frac{4^n}{n{\epsilon }^2}\right)$.

We correct misprints in the previous versions

References in corpus (13)

• Noise tailoring for scalable quantum computation via randomized compiling
• Characterizing Quantum Gates via Randomized Benchmarking
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Efficient estimation of Pauli channels
• Quantum advantages for Pauli channel estimation
• The learnability of Pauli noise
• Pauli error estimation via Population Recovery
• Bell sampling from quantum circuits
• Tight bounds on Pauli channel learning without entanglement
• ${\ell }_p$ Testing and Learning of Discrete Distributions
• Lower Bounds on Learning Pauli Channels with Individual Measurements
• Efficient learning of the structure and parameters of local Pauli noise channels

Cited by in corpus (1)

• Efficient self-consistent learning of gate set Pauli noise