The quantum computers currently available suffer levels of noise that cannot be neglected, therefore it is essential to develop methods to check the correctness of their outputs. To tackle this problem we provide and experimentally demonstrate an “accreditation protocol,” namely a protocol to upper-bound the variation distance between the probability distribution of the outputs of a noisy quantum computer and its noiseless counterpart. The quantum circuits in our experiment range from depth 4 circuits on 10 qubits to depth 21 circuits on 4 qubits and are implemented on programmable superconducting hardware. Our protocol requires implementing the desired quantum circuit along with a set of random Clifford circuits and subsequently post-processing the outputs of these Clifford circuits. Importantly, all the post-processing can be done efficiently and our protocol is fully scalable for the long term. Moreover, by testing entire circuits rather than gates, our protocol can detect noise that may be missed by benchmarking individual gates. We thus demonstrate a scalable and reliable method to ascertain the correctness of the outputs of noisy quantum computers.