# Randomised Benchmarking

## Contents

## Functionality DescriptionEdit

Randomized benchmarking refers to a collection of methods that aim to reliably estimating the magnitude of an average error of a quantum gate set in a robust fashion against state preparation and measurement error. It achieves this goal by applying sequences of feasible quantum gates of varying length, so that small errors are amplified with the sequence length leading

From a pragmatic point of view, RB protocols thereby define benchmarks that can be used to compare different digital quantum devices.In important instances (Standard Randomised Benchmarking), the benchmark can be related to the average gate fidelity, rendering RB protocols flexible certification tools. To this end, a group structure of the gate set is made use to achieve two goals: On the one hand, this is to control the theoretical prediction of error-free sequences.

RB is most prominently considered for Clifford gates and has been extended to other finite groups. Assumptions on having identical noise levels per gate have been lessened (Standard Randomised Benchmarking) and Randomised Benchmarking with confidence introduced. RB schemes have been generalized to other measures of quality, such as relative average gate fidelities (Interleaved Randomised Benchmarking), the unitarity Purity Benchmarking, measures for losses Robust characterization of loss rates, leakage Robust characterization of leakage errors, addressibility Characterization of addressability by randomized benchmarking or even tomographic schemes that combine data from multiple RB experiment.

## ProtocolsEdit

## PropertiesEdit

- The figure of merits in different protocols are: average error rate, average fidelity of a noise quantum circuit, unitarity, measures for losses, leakage, addressibility and cross-talk.

## Related PapersEdit

- E.Knill et al (2007) arXiv:0707.0963: gate and time-independent noise model
- E. Mageson et al (2011) arXiv:1009.3639: multi-parameter model
- Magesan et al. PRL (2012): Interleaved Randomized Benchmarking
- Harper et al (2016) arXiv:1608.02943v2: Interleaved Randomised Benchmarking to estimate fidelity of T gates
- Wallman, Granade, Harper, F., NJP 2015: Purity benchmarking

**contributed by Rhea Parekh*