Given access to a quantum device,

• how can one figure out how well it works?
• what are its most significant errors?
• how can one correct these errors an develop error-robust?
• what are meaningful benchmarks?

There is a large zoo of protocols aimed at these questions. Here, we outline a few approaches.

Gate set tomography is a characterization approach that simultaneously and self-consistently extracts a tomographic description of the implementation of an entire set of quantum gates, as well as the initial state and measurement, from experimental data.

See https://arxiv.org/abs/2112.05176 for details.

For the related task of quantum process tomography, see e.g.
https://arxiv.org/abs/1803.00572
https://arxiv.org/abs/1701.03135

In its many variants, randomized benchmarking (RB) is a broadly used technique for assessing the quality of gate implementations on quantum computers.

See https://arxiv.org/abs/2212.06181 for details.

The complexity of quantum devices renders the certification of their correct functioning a challenge. However, often efficient certification is nevertheless possible.

See https://arxiv.org/abs/2010.05925 for a mathematical introduction to the topic.

See https://arxiv.org/abs/1812.01023 for limitations on the certification of quantum supremacy experiments.