# Logical Randomized Benchmarking

## TL;DR

Logical randomized benchmarking is a new method that directly measures the performance of quantum error correction at the logical level, providing more accurate assessments than traditional physical error rate extrapolations.

## Contribution

It introduces a logical benchmarking procedure that reduces to physical randomized benchmarking, enabling direct and reliable evaluation of logical error correction performance.

## Key findings

- Reliable reporting of logical performance
- Estimation of correctable and uncorrectable error probabilities
- Reduces assumptions compared to traditional methods

## Abstract

Extrapolating physical error rates to logical error rates requires many assumptions and thus can radically under- or overestimate the performance of an error correction implementation. We introduce logical randomized benchmarking, a characterization procedure that directly assesses the performance of a quantum error correction implementation at the logical level, and is motivated by a reduction to the well-studied case of physical randomized benchmarking. We show that our method reliably reports logical performance and can estimate the average probability of correctable and uncorrectable errors for a given code and physical channel.