QubitLogic
arXiv

Proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezed input modes

Gaussian boson sampling (GBS) is a sampling task proposed to demonstrate quantum advantage. We consider Gaussian boson sampling on $M$ optical modes, with $K$ equally squeezed input modes and $N$ observed photon counts.

We complete the proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezers $K$.

Why this matters

This research completes the proof of the hiding conjecture for Gaussian boson sampling, which is important for demonstrating quantum advantage. Understanding the classical hardness of such problems is crucial for the progression of quantum computing technologies.

What they actually achieved

The authors completed the proof of the hiding conjecture for Gaussian boson sampling with an arbitrary number of squeezed input modes. They showed that, for certain conditions, the symmetric product is close in total variation distance to a symmetric complex Gaussian matrix.

What they did not achieve

The density-based instance generating method previously used fails for Gaussian boson sampling with fewer squeezed modes relative to output modes. This indicates a limitation in applying this method universally across different scenarios in GBS.

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