Sublogarithmic-depth simulation of boson sampling

Determine whether arbitrary boson-sampling distributions can be simulated with inverse-polynomial total-variation error by polynomial-width qubit circuits of depth strictly less than logarithmic in the number of optical modes under the stated model of arbitrary qubit connectivity and a finite gate set.

Background

The main theorem gives an O(log(m/epsilon))-depth Clifford+T simulation using polynomially many qubits and arbitrary qubit connectivity. The construction therefore establishes logarithmic depth as an upper bound, but it does not show that logarithmic depth is necessary.

The paper explicitly identifies the possibility of reducing the depth below logarithmic as unresolved under the present circuit model.