# Quantification and Characterization of Leakage Errors

## TL;DR

This paper introduces a comprehensive framework for quantifying and characterizing leakage errors in quantum systems, including new metrics and methods to evaluate their impact on quantum gate performance.

## Contribution

It presents new metrics for leakage and seepage, and adapts randomized benchmarking to robustly estimate these errors in quantum gates.

## Key findings

- New metrics for leakage and seepage rates.
- Modified randomized benchmarking protocol for leakage characterization.
- Framework applicable to superconducting qubits.

## Abstract

We present a general framework for the quantification and characterization of leakage errors that result when a quantum system is encoded in the subspace of a larger system. To do this we introduce new metrics for quantifying the coherent and incoherent properties of the resulting errors, and we illustrate this framework with several examples relevant to superconducting qubits. In particular, we propose two quantities: the leakage and seepage rates, which together with average gate fidelity allow for characterizing the average performance of quantum gates in the presence of leakage and show how the randomized benchmarking protocol can be modified to enable the robust estimation of all three quantities for a Clifford gate set.