Single snapshot non-Markovianity of Pauli channels

TL;DR

This paper investigates the non-Markovian nature of Pauli channels in quantum computing, revealing that negative or complex rates are common and that allowing such rates improves noise modeling accuracy.

Contribution

It demonstrates that Pauli channels often exhibit non-Markovianity with negative or complex rates, challenging the assumption of Markovian generators in quantum noise models.

Findings

Negative rates are nearly always present in random Pauli channels.

Negative rates are common in physically motivated noise models, even if the underlying noise is Markovian.

Allowing negative rates improves the accuracy of noise predictions in experiments.

Abstract

Pauli channels are widely used to describe errors in quantum computers, particularly when noise is shaped via Pauli twirling. A common assumption is that such channels admit a Markovian generator, namely a Pauli-Lindblad model with non-negative rates, but the validity of this assumption has not been systematically examined. Here, using CP-indivisibility as our criterion for non-Markovianity, we study multi-qubit Pauli channels from a single snapshot of the dynamics. We find that while the generator always has the same structure as the standard Pauli-Lindblad model, the rates may be negative or complex. We show that random Pauli channels are almost always non-Markovian, with the probability of encountering a negative rate converging doubly exponentially to unity with the number of qubits. For physically motivated noise models shaped by Pauli twirling, including single-qubit over-rotations and two-qubit amplitude damping errors, we find that negative rates are generic, even when the underlying physical noise is Markovian. We generalize probabilistic error amplification and cancellation to non-Markovian generators, and quantify the sampling overhead introduced by negative and complex rates. Experiments on superconducting qubits confirm that allowing negative rates in the learned noise model yields more accurate predictions than restricting to non-negative rates.