Regensburg 2022 – scientific programme
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QI: Fachverband Quanteninformation
QI 3: Certification and Benchmarking of Quantum Systems
QI 3.1: Invited Talk
Monday, September 5, 2022, 15:00–15:30, H8
Generalized randomized benchmarking with short random quantum circuits — Markus Heinrich1, •Martin Kliesch1, and Ingo Roth2 — 1Heinrich Heine University Düsseldorf, Germany — 2Technology Innovation Institute, Abu Dhabi, United Arab Emirates
The characterization of the quality of quantum gate implementations is among the most important certification tasks in the quantum sciences. State preparation and measurement errors render this task a challenge, in particular for large qubit numbers. Randomized benchmarking (RB) is among the most popular approaches to address this challenge. Rigorous theoretical guarantees for RB methods rely on sequences of unitary operations each of which is drawn uniformly from a group, often the Clifford group. Due to compiling, such RB strategies effectively require the implementation of quantum circuits with an unfavourable scaling of the circuit depth with the number of qubits. In practice, this scaling results in a restriction to a few qubits.
This talk starts with an introduction to RB, a generalized version thereof and a review of the idea of drawing the unitaries from a generating gate set of the group rather than from its uniform distribution in order to reduce the required circuit depths. Then we show analytically how this changes the exponential decay behaviour observed in RB. In particular, shorter circuits can result in decays that are a combination of the usual RB decay plus a decay corresponding to mixing properties (spectral gap of the moment operator) of the gate set. In this way, we shine new light on the important question of how quantum gates can be certified using short circuits.