Boson sampling is a well-defined scheme for demonstrating quantum supremacy with photons in the near term. However, relying only on multiphoton interference in nonadaptive linear-optical networks, the scheme is difficult to simulate classically. Here we study boson sampling using matrix product states, a powerful method from quantum many-body physics. This method stores the instantaneous quantum state during the evolution of photons in the optical quantum circuit, which allows us to reveal the dynamical features of single photons in boson sampling devices, such as entanglement entropy growth. We show the flexibility of this method by also applying it to dissipative optical quantum circuits, as well as circuits with fermionic particles. Our paper shows that matrix product states provide a powerful platform to simulate optical quantum circuits, which is readily extended to study quantum dynamics in multiparticle quantum walks beyond boson sampling.

• Received 20 December 2018

DOI:https://doi.org/10.1103/PhysRevA.100.032305