Measurement-based interleaved randomised benchmarking using IBM processors

Abstract

Quantum computers have the potential to outperform classical computers at certain computational tasks, such as prime factorisation and unstructured searching. However, experimental realisations of quantum computers are subject to noise. Quantifying the noise is of fundamental importance, since noise is often the dominant factor preventing the successful realisation of advanced quantum computations. Here we propose an interleaved randomised benchmarking protocol for measurement-based quantum computers, in which any single-qubit measurement-based 2-design can be used to estimate the fidelity of any single-qubit measurement-based gate. We test our protocol by using a weak approximate measurement-based 2-design to estimate the fidelity of the Hadamard gate and the T gate (a universal single-qubit set) on IBM superconducting quantum computers. To this end, single-qubit measurements were performed on entangled linear cluster states of up to 31 qubits. Our estimated gate fidelities show good agreement with gate fidelities calculated from process tomography results. Furthermore, by artificially increasing noise in the measurement-based gates, we were able to show that our protocol is able to detect large noise variations in different measurement-based implementations of a gate.