Efficiently learning non-Markovian noise in many-body quantum simulators

TL;DR

This paper presents a protocol for efficiently learning non-Markovian noise in large-scale quantum simulators, achieving logarithmic sample complexity under Gaussian noise assumptions, which is a significant step beyond existing Markovian models.

Contribution

It introduces a scalable method to learn non-Markovian noise in quantum simulators, extending efficient protocols from Markovian to non-Markovian noise models under Gaussian assumptions.

Findings

Sample complexity scales logarithmically with system size.

Protocol requires initial product state preparation and single-qubit Clifford gates.

Effective for geometrically local lattice models with quantum and classical noise.

Abstract

As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed system models (described by a Hamiltonian) or open system models (described by a Lindbladian), have been developed, it remains less well understood whether similar protocols for non-Markovian models exist. In this paper, we consider geometrically local lattice models with both quantum and classical non-Markovian noise and show that, under a Gaussian assumption on the noise, we can learn the noise with sample complexity scaling logarithmically with the system size. Our protocol requires preparing the simulator qubits initially in a product state, introducing a layer of single-qubit Clifford gates and measuring product observables.