SPAD-based quantum random number generator with a Nth-order rank algorithm on FPGA

We present a compact, all-solid-state, low-cost quantum random number generator (QRNG) based on a single-photon avalanche diode (SPAD) and a field programmable gate array (FPGA). A new algorithm for random bit generation is described, ranking the inter-arrival times of a group of $M$ photons detected by the SPAD device, and processed directly on the FPGA. The proposed approach improves the efficiency of generated random bits per detected photon, spanning from 0.5 bits/photon in case of 0 order rank, up to 0.875 bits/photon for second order rank. By extending the algorithm to higher orders, the proposed system approaches the maximum theoretical value of 1.0 bit/photon. The rate of generation of random numbers is limited by the SPAD minimum deadtime, achieving an experimentally proven bit rate of 7.3 Mbps. The standard randomness statistical tests are passed for a wide range of photon fluxes and for all the implemented rank orders with no additional post-processing on the generated sequence.