# Complete randomized benchmarking protocol accounting for leakage errors

@article{Chasseur2015CompleteRB, title={Complete randomized benchmarking protocol accounting for leakage errors}, author={Tobias Chasseur and Frank K. Wilhelm}, journal={Physical Review A}, year={2015}, volume={92}, pages={042333} }

Randomized Benchmarking allows to efficiently and scalably characterize the average error of an unitary 2-design such as the Clifford group $\mathcal{C}$ on a physical candidate for quantum computation, as long as there are no non-computational leakage levels in the system. We investigate the effect of leakage errors on Randomized Benchmarking induced from an additional level per physical qubit and provide a modified protocol that allows to derive reliable estimates for the error per gate in…

## 26 Citations

Randomized benchmarking in measurement-based quantum computing

- Computer Science
- 2016

This work adapts the randomized benchmarking protocol for a single qubit to a linear cluster state computation, which provides partial, yet efficient characterization of the noise associated with the target gate set.

Scalable randomized benchmarking of quantum computers using mirror circuits

- Computer Science, Physics
- 2021

This work uses a simple and customizable class of circuits — randomized mirror circuits — to perform scalable, robust, and flexible randomized benchmarking of Clifford gates, and shows that this technique approximately estimates the infidelity of an average many-qubit logic layer.

Scalable randomized benchmarking of non-Clifford gates

- Computer Science
- 2015

In their theoretical study, the researchers demonstrate how randomized benchmarking approaches can be expanded to a much broader range of logical operations, thereby enabling error benchmarking for all common logical operations used in leading quantum computing protocols.

From randomized benchmarking experiments to gate-set circuit fidelity: how to interpret randomized benchmarking decay parameters

- Computer ScienceNew Journal of Physics
- 2018

It is proved that single-qubit RB decay parameter p coincides with the decay parameter of the gate-set circuit fidelity, a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gate, and conjecture that these results also hold for higher dimensions.

What Randomized Benchmarking Actually Measures.

- MathematicsPhysical review letters
- 2017

New theories of theRB decay are presented that are accurate for all small errors describable by process matrices, and it is shown that the RB decay curve is a simple exponential for all such errors.

Efficient unitarity randomized benchmarking of few-qubit Clifford gates

- Computer SciencePhysical Review A
- 2019

This work provides a bound on the required number of data points for Clifford URB as a function of confidence and experimental parameters and shows that the unitarity of single-qubit Clifford gates can be rigorously estimated using few hundred data points under the assumption of gate-independent noise.

Quantification and characterization of leakage errors

- Computer Science
- 2018

Two quantities are proposed: 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.

Direct Randomized Benchmarking for Multiqubit Devices.

- Computer SciencePhysical review letters
- 2019

This Letter proposes a direct RB protocol that uses random circuits over the native gates in a device, which are seeded by an initial layer of Clifford-like randomization, and it can be extended to processors with more qubits and it reports a more directly informative and flexible error rate than the one reported by Clifford RB.

Randomized benchmarking with gate-dependent noise

- Physics, Computer Science
- 2017

It is proved that the exact impact of gate-dependent noise can be described by a single perturbation term that decays exponentially with the sequence length, and it is shown that the operational meaning of the decay parameter for gate- dependent noise is essentially unchanged.

Randomized Benchmarking as Convolution: Fourier Analysis of Gate Dependent Errors

- Mathematics, Computer ScienceQuantum
- 2021

It is shown that the Randomized Benchmarking protocol is a convolution amenable to Fourier space analysis, and an alternative proof of Wallman's and Proctor's bounds on the effect of gate-dependent noise on randomized benchmarking is provided.

## References

SHOWING 1-10 OF 18 REFERENCES

Quantum computation and quantum information

- PhysicsMathematical Structures in Computer Science
- 2007

This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal…

MATH

- Biology
- 1992

It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.

Matrix Analysis and Applied Linear Algebra

- Mathematics
- 2000

The author presents Perron-Frobenius theory of nonnegative matrices Index, a theory of matrices that combines linear equations, vector spaces, and matrix algebra with insights into eigenvalues and Eigenvectors.

Phys

- Rev. A 77, 012307
- 2008

Phys

- Rev. A 89, 062321
- 2014

Phys

- Rev. Lett. 106, 180504
- 2011

Phys

- Rev. Lett. 114, 100503
- 2015

Characterization of Leakage Errors via Randomized Benchmarking

- 2014