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We present a photonic approach for fast quantum random number generation based on optically sampled amplified spontaneous emission (ASE). This approach utilizes a terahertz optical asymmetric demultiplexer to sample the ASE and then digitize the sampled optical pulses into random bits using a multi-bit parallel comparator. A proof-of-concept experiment demonstrates that 40 Gb/s random bits with verified randomness can be obtained using our method. The current generation rate is mainly limited by the bandwidth of the available ASE source.