Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling

TL;DR

This paper demonstrates that sampling from photon-added or -subtracted squeezed states with parity measurements is computationally equivalent to boson sampling, expanding the class of quantum states with similar classical hardness.

Contribution

It establishes an exact equivalence between boson sampling and sampling from photon-added or -subtracted squeezed states, regardless of squeezing levels.

Findings

Sampling from these states is as hard as boson sampling.

The equivalence holds for arbitrary squeezing parameters.

Provides new quantum states in the same complexity class as boson sampling.

Abstract

Boson sampling is a simple model for non-universal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single photon states is fed through a Haar-random linear optics network and sampled at the output using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of new quantum states of light in the same complexity class as boson sampling.