Non-Markovianity induced by Pauli-twirling

TL;DR

This paper investigates how Pauli twirling can induce non-Markovian behavior in quantum noise channels, revealing that Markovian channels often become non-Markovian after twirling, which impacts noise modeling and error mitigation.

Contribution

It establishes a criterion linking negative Pauli-Lindblad parameters to non-Markovianity induced by Pauli twirling in quantum channels.

Findings

Pauli twirling can turn Markovian channels into non-Markovian ones.

Negative Pauli-Lindblad parameters are necessary for non-Markovianity after twirling.

Implications for accurate noise modeling and quantum error mitigation.

Abstract

Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the $\sqrt{X}$-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.