Realistic photon-number resolution in Gaussian boson sampling

Gaussian boson sampling (GBS) is a model of nonuniversal quantum computation that claims to demonstrate quantum supremacy with current technologies. This model entails sampling photocounting events from a multimode Gaussian state at the outputs of a linear interferometer. In this scheme, collision events—those with more than one photon for each mode—are infrequent. However, they are still used for validation purposes. Therefore, the limitation of realistic detectors to perfectly resolve adjacent photon numbers becomes pivotal. We derive a photocounting probability distribution in GBS schemes which is applicable for use with general detectors and photocounting techniques. This probability distribution is expressed in terms of functionals of the field-quadrature covariance matrix, e.g., Hafnian and Torontonian in the well-known special cases of photon-number-resolving and on-off detectors, respectively. Based on our results, we consider a GBS validation technique involving detectors with realistic photon-number resolution. Published by the American Physical Society 2024