Spoofing Cross-Entropy Measure in Boson Sampling.

Area of Science:

• Quantum Information Science
• Computational Physics
• Classical Algorithms

Background:

• Cross-entropy (XE) is a key metric for demonstrating quantum computational advantage in sampling problems.
• Boson sampling (BS) experiments are a primary benchmark for quantum advantage.
• Current classical methods struggle to match the XE scores of quantum BS experiments.

Purpose of the Study:

• To develop a heuristic classical algorithm that surpasses current and near-future boson sampling (BS) experimental XE scores.
• To demonstrate a verifiable classical approach to simulating quantum sampling problems.
• To explore the potential of classical algorithms in spoofing quantum advantage claims.

Main Methods:

• Developed a heuristic classical algorithm based on efficiently computable distributions that correlate with the ideal BS probability distribution.
• Utilized the correlation and computability to postselect heavy outcomes without direct computation of the ideal probability.
• Implemented and tested the algorithm on intermediate-sized systems for Gaussian boson sampling and fermion sampling.

Main Results:

• The algorithm achieved a better XE score than current Gaussian BS experiments in verifiable regimes.
• The method demonstrated effectiveness for larger system sizes in fermion sampling, where probabilities are efficiently computable.
• Analytic evidence suggests the classical algorithm can efficiently spoof noisy BS.

Conclusions:

• The proposed classical algorithm offers a competitive approach to boson sampling (BS) benchmarks.
• This work challenges the interpretation of XE as a definitive measure of quantum advantage in current BS experiments.
• The findings necessitate further development of robust verification methods for quantum computational advantage.