In recent years there has been an increasing interest in quantum computing from non-pundits, companies and researchers from fields other than quantum computing.

This is undoubtedly due to the deployment of quantum computing resources to research institutions and companies, which fostered the search for new applications of quantum computing.

Currently available quantum processing units (QPUs) are typically small and are plagued by noise. Two main solutions are being investigated to improve them: on the one hand there is an ongoing technological effort in scaling up these devices controlling the noise and, at the same time, develop error correction codes which will make the QPUs robust to errors; on the other hand there are efforts in making the current small and noisy devices useful. Quantum error mitigation is a class of techniques aiming at reducing the errors in running codes on quantum computers. 

Within this framework we introduce an efficient and accurate readout measurement scheme for single and multi-qubit states. Our method uses Bayesian inference to build an assignment probability distribution for each qubit state based on a reference characterization of the detector response functions. This allows us to account for system imperfections and thermal noise within the assignment of the computational basis. We benchmark our protocol on a quantum device with five superconducting qubits, testing initial state preparation for single and two-qubit states and an application of the Bernstein-Vazirani algorithm executed on five qubits. Our method shows a substantial reduction of the readout error and promises advantages for near-term and future quantum devices.