  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 quantum computers that can be used to estimate the fidelity
of any single-qubit measurement-based gate. We tested the protocol on IBM
superconducting quantum processors by estimating the fidelity of the Hadamard
and T gates - a universal single-qubit gate set. Measurements were performed on
entangled cluster states of up to 31 qubits. Our estimated gate fidelities show
good agreement with those calculated from quantum process tomography. By
artificially increasing noise, we were able to show that our protocol detects
large noise variations in different implementations of a gate.
