Classical simulation of non-Gaussian bosonic circuits

Understand

We propose efficient classical algorithms which (strongly) simulate the action of bosonic linear optics circuits applied to superpositions of Gaussian states.

• Our approach relies on an augmented covariance matrix formalism to keep track of relative phases between individual terms in a linear combination.
• This yields an exact simulation algorithm whose runtime is polynomial in the number of modes and the size of the circuit, and quadratic in the number of terms in the superposition.
• We also present a faster approximate randomized algorithm whose runtime is linear in this number.