Efficient self-consistent learning of gate set Pauli noise

TL;DR

This paper introduces an efficient, self-consistent method for learning gate set Pauli noise in quantum systems, providing a comprehensive approach to characterize noise across entire gate sets with theoretical guarantees.

Contribution

It develops a novel algebraic graph theory-based framework for self-consistent, complete, and efficient learning of gate set Pauli noise, applicable to various physically motivated noise models.

Findings

All learnable noise information can be estimated with relative precision.

The method applies to local and quasi-local noise models.

Experimental demonstrations on parallel CZ gates validate the approach.

Abstract

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model that has been widely applied in quantum benchmarking, error mitigation, and error correction. Despite intensive study, most existing works focus on learning Pauli noise channels associated with some specific gates rather than treating the gate set as a whole. A learning algorithm that is self-consistent, complete, and efficient at the same time is yet to be established. In this work, we study the task of gate set Pauli noise learning, where a set of quantum gates, state preparation, and measurements all suffer from unknown Pauli noise channels with a customized noise ansatz. Using tools from algebraic graph theory, we analytically characterize the self-consistently learnable degrees of freedom for Pauli noise models with arbitrary linear ansatz, and design experiments to efficiently learn all the learnable information. Specifically, we show that all learnable information about the gate noise can be learned to relative precision, under mild assumptions on the noise ansatz. We then demonstrate the flexibility of our theory by applying it to concrete physically motivated ansatzs (such as spatially local or quasi-local noise) and experimentally relevant gate sets (such as parallel CZ gates). These results not only enhance the theoretical understanding of quantum noise learning, but also provide a feasible recipe for characterizing existing and near-future quantum information processing devices.