## Jonas Helsen

*QuTech- TUDelft*

Jonas Helsen is a PhD student in the group of Prof. Stephanie Wehner at QuTech TU Delft (Netherlands). He is interested in verifying and validating quantum computers, quantum error correction and computational complexity.

Randomized benchmarking is an essential and widely used technique for reliably estimating average fidelities and other parameters of sets of quantum operations. Standard randomized benchmarking using the Clifford group yields data that can be fitted to a single exponential decay, allowing the average fidelity of the gateset to be extracted reliably.

However, protocols that go beyond standard randomized benchmarking, such as benchmarking gatesets with T-gates, simultaneous benchmarking or standard randomized benchmarking in the presence of leakage errors yield data that must be fitted to a linear combination of multiple exponential decays making it experimentally much harder to extract the average fidelity.

We propose a new version of the randomized benchmarking protocol that solves this problem. We adapt the randomized benchmarking procedure by adding an extra weighted averaging step that leverages the theory of group representations to isolate single exponential decays. By repeating the experiment multiple times we can then reliable extract all decay constants and hence the average fidelity.

We illustrate the effectiveness of this new protocol by two examples. Firstly we analyze the protocol for benchmarking T-gates (as proposed by Cross et al. NPJ-QI 2 (2016)). This protocol has two decay channels and we show how to use the character benchmarking technique to reliably estimate both associated decay parameters. Secondly we design a new interleaved benchmarking experiment that extracts the average fidelity of a 2-qubit Clifford gate using only single-qubit Clifford gates as reference. This is advantageous relative to standard interleaved benchmarking as usually single-qubit gates have higher fidelities than two-qubit gates, allowing a better estimate of the fidelity of the interleaved gate.

Finally we argue that character randomized benchmarking remains efficient even when finite sampling constraints are taken into account. This is non-trivial as the extra averaging step ranges over a set of exponential size (in the number of qubits). However, by carefully considering the quantities being estimated in character randomized benchmarking we argue that only a small subset of this set must be sampled for reliable estimation.

We expect character randomized benchmarking to become a valuable addition to the toolkit of device characterization techniques for quantum computing.