Efficient measurement of quantum gate error by interleaved randomized benchmarking

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 e...

We implement a complete randomized benchmarking protocol on a system of two superconducting qubits. The protocol consists of randomizing over gates in the Clifford group, which experimentally are generated via an improved two-qubit cross-resonance gate implementation and single-qubit unitaries. From this we extract an optimal average error per Clifford of 0.0936. We also perform an interleaved experiment, alternating our optimal two-qubit gate with random two-qubit Clifford g...

Quantum computers have the potential to outperform classical computers in a range of computational tasks, such as prime factorisation and unstructured searching. However, real-world quantum computers are subject to noise. Quantifying noise is of vital importance, since it is often the dominant factor preventing the successful realisation of advanced quantum computations. Here we propose and demonstrate an interleaved randomised benchmarking protocol for measurement-based quan...

Randomized benchmarking is a technique for estimating the average fidelity of a set of quantum gates. For general gatesets, however, it is difficult to draw robust conclusions from the resulting data. Here we propose a new method based on representation theory that has little experimental overhead and applies to a broad class of benchmarking problems. As an example, we apply our method to a gateset that includes the $T$-gate, and analyze a new interleaved benchmarking protoco...

With improved gate calibrations reducing unitary errors, we achieve a benchmarked single-qubit gate fidelity of 99.95% with superconducting qubits in a circuit quantum electrodynamics system. We present a method for distinguishing between unitary and non-unitary errors in quantum gates by interleaving repetitions of a target gate within a randomized benchmarking sequence. The benchmarking fidelity decays quadratically with the number of interleaved gates for unitary errors bu...

We present a protocol for Interleaved Randomized Benchmarking of arbitrary quantum gates using Monte Carlo sampling of quantum states. It is generally applicable, including non-Clifford gates while preserving key advantages of Randomized Benchmarking such as error amplification as well as independence from state preparation and measurement errors. This property is crucial for implementations in many contemporary systems. Although the protocol scales exponentially in the numbe...

Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be the set of Clifford operators, the randomized benchmarking algorithm is particularly easy to perform and its results have an important interpretation with respect to quantum computation. The aim of the benchmark is to provide a simple, use...

Randomized benchmarking is a promising tool for characterizing the noise in experimental implementations of quantum systems. In this paper, we prove that the estimates produced by randomized benchmarking (both standard and interleaved) for arbitrary Markovian noise sources are remarkably precise by showing that the variance due to sampling random gate sequences is small. We discuss how to choose experimental parameters, in particular the number and lengths of random sequences...

Randomized benchmarking (RB) is an efficient and robust method to characterize gate errors in quantum circuits. Averaging over random sequences of gates leads to estimates of gate errors in terms of the average fidelity. These estimates are isolated from the state preparation and measurement errors that plague other methods like channel tomography and direct fidelity estimation. A decisive factor in the feasibility of randomized benchmarking is the number of sampled sequences...

We describe and expand upon the scalable randomized benchmarking protocol proposed in Phys. Rev. Lett. 106, 180504 (2011) which provides a method for benchmarking quantum gates and estimating the gate-dependence of the noise. The protocol allows the noise to have weak time and gate-dependence, and we provide a sufficient condition for the applicability of the protocol in terms of the average variation of the noise. We discuss how state preparation and measurement errors are t...