Classical simulation of linear optics subject to nonuniform losses

Abstract

We present a comprehensive study of the impact of non-uniform, i.e. path-dependent, photonic losses on the computational complexity of linear-optical processes. Our main result states that, if each beam splitter in a network induces some loss probability, non-uniform network designs cannot circumvent the efficient classical simulations based on losses.To achieve our result we obtain new intermediate results that can be of independent interest. First we show that, for any network of lossy beam-splitters, it is possible to extract a layer of non-uniform losses that depends on the network geometry. We prove that, for every input mode of the network it is possible to commute si layers of losses to the input, where si is the length of the shortest path connecting the ith input to any output. We then extend a recent classical simulation algorithm due to Clifford and Clifford to allow for arbitrary n-photon input Fock states (i.e. to include collision states). Consequently, we identify two types of input states where boson sampling becomes classically simulable: (A) when n input photons occupy a constant number of input modes; (B) when all but O(log n) photons are concentrated on a single input mode, while an additional O(log n) modes contain one photon each.

Classically simulating near-term partially-distinguishable and lossy boson sampling

“…Classical simulation methods can be generalised to this model by identifying a layer of uniform losses from the circuit, followed a non-uniform lossy circuit which can be simulated classically through the use of additional modes for lost photons [36,37]. These results showed that boson sampling under non-uniform loss can be classically simulated as long as the smallest number of components a photon encounters is logarithmic in n. More recently, methods were also developed to give a polynomial-time algorithm in the case where some photons experience little or no loss, by extracting losses into a layer of non-uniform loss and simulating via a generalisation of the Clifford and Clifford algorithm [43].…”