A taxonomy of small Markovian errors

TL;DR

This paper introduces a new, more intuitive way to model quantum gate errors by transforming process matrices into error generators, classifying elementary errors, and constructing simplified models with fewer parameters.

Contribution

It develops a basis of elementary error generators, classifies them, and demonstrates how to build reduced error models for quantum gates that are more interpretable and efficient.

Findings

A basis of simple, physically intuitive error generators is constructed.

Any gate's error can be represented as a mixture of elementary error generators.

A reduced model with 9N^2 parameters effectively describes most common errors on N-qubit processors.

Abstract

Errors in quantum logic gates are usually modeled by quantum process matrices (CPTP maps). But process matrices can be opaque, and unwieldy. We show how to transform a gate's process matrix into an error generator that represents the same information more usefully. We construct a basis of simple and physically intuitive elementary error generators, classify them, and show how to represent any gate's error generator as a mixture of elementary error generators with various rates. Finally, we show how to build a large variety of reduced models for gate errors by combining elementary error generators and/or entire subsectors of generator space. We conclude with a few examples of reduced models, including one with just $9N^2$ parameters that describes almost all commonly predicted errors on an N-qubit processor.