  Cross entropy (XE) measure is a widely used benchmarking to demonstrate
quantum computational advantage from sampling problems, such as random circuit
sampling using superconducting qubits and boson sampling (BS). We present a
heuristic classical algorithm that attains a better XE than the current BS
experiments in a verifiable regime and is likely to attain a better XE score
than the near-future BS experiments in a reasonable running time. The key idea
behind the algorithm is that there exist distributions that correlate with the
ideal BS probability distribution and that can be efficiently computed. The
correlation and the computability of the distribution enable us to post-select
heavy outcomes of the ideal probability distribution without computing the
ideal probability, which essentially leads to a large XE. Our method scores a
better XE than the recent Gaussian BS experiments when implemented at
intermediate, verifiable system sizes. Much like current state-of-the-art
experiments, we cannot verify that our spoofer works for quantum advantage size
systems. However, we demonstrate that our approach works for much larger system
sizes in fermion sampling, where we can efficiently compute output
probabilities. Finally, we provide analytic evidence that the classical
algorithm is likely to spoof noisy BS efficiently.
