Exploring shallow-depth boson sampling: Toward a scalable quantum advantage

Boson sampling is a sampling task proven to be hard to simulate efficiently using classical computers under plausible assumptions, which makes it an appealing candidate for quantum advantage. However, due to a large noise rate for near-term quantum devices, it is still unclear whether those noisy devices maintain the quantum advantage for much larger quantum systems. Since the noise rate typically grows with the circuit depth, an alternative is to find evidence of simulation hardness at the shallow-depth quantum circuit. To find the evidence, one way is to identify the minimum depth required for the average-case hardness of approximating output probabilities, which is considered a necessary condition for the state-of-the-art technique to prove the simulation hardness of boson sampling. In this work, we analyze the output probability distribution of shallow-depth boson sampling for Fock states and Gaussian states and examine the limitation of the average-case hardness argument at this shallow-depth regime for geometrically local architectures. We propose a shallow-depth linear optical circuit architecture that can overcome the problems associated with geometrically local architectures. Our numerical results suggest that this architecture demonstrates possibilities of average-case hardness properties in a shallow-depth regime through its resemblance to the global Haar-random boson sampling circuit. This result implies that the corresponding architecture has the potential to be utilized for scalable quantum advantage with its shallow-depth boson sampling.