Exact logarithmic-depth boson sampling with continuous gates

Establish whether exact boson sampling for interferometers specified by an exact finite description admits a logarithmic-depth implementation using polynomially many qubits and efficiently computable parameters for continuous gates.

Background

The proved result concerns approximate sampling and uses finite-precision Clifford+T gate synthesis. The discussion distinguishes this result from the exact-sampling setting in which the interferometer has an exact finite description and continuous-gate parameters may be used.

The authors explicitly state that it remains unresolved whether exact boson sampling can achieve the same logarithmic-depth and polynomial-width scaling while keeping the continuous-gate parameters efficiently computable.