Single-shot number-resolved detection of microwave photons with error mitigation

Single-photon detectors are ubiquitous and integral components of photonic quantum cryptography, communication, and computation. Many applications, such as Gaussian boson sampling, require not only detecting the presence of photons, but distinguishing the number present with a single shot. Here, we present a single-shot, high-fidelity photon number-resolving detector of up to 15 microwave photons in a cavity-qubit circuit QED platform. This detector functions by measuring a series of generalized parity operators which make up the bits in the binary decomposition of the photon number. Photon loss and ancilla readout errors can flip one or more bits, causing nontrivial errors in the outcome, but these errors have a traceable form which can be captured in a simple hidden Markov model. Relying on the independence of each bit measurement, we mitigate biases in the measurement result, showing good agreement with the predictions of the model. The mitigation improves the average total variation distance error of Fock states from 13.5% to 1.3%.