  Optical losses are the main obstacle to demonstrating a quantum advantage via
boson sampling without leaving open the possibility of classical spoofing. We
propose a method for generating low-depth optical circuits suitable for boson
sampling with very high efficiencies. Our circuits require only a constant
number of optical components (namely three) to implement an optical
transformation suitable for demonstrating a quantum advantage. Consequently,
our proposal has a constant optical loss regardless of the number of optical
modes. We argue that sampling from our family of circuits is computationally
hard by providing numerical evidence that our family of circuits converges to
that of the original boson sampling proposal in the limit of large optical
systems. Our work opens a new route to demonstrate an optical quantum
advantage.
