2014/02/28 by Kaushik P. Seshadreesan, Jonathan P. Olson, Keith R. Motes +2
Computer Science · Physics and Astronomy · #Boson #Cluster state #Coherent states #Coherent states in mathematical physics #Fock space #Fock state #Neural Networks and Reservoir Computing #Photon #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum computer #Quantum mechanics #Quantum optics #Quantum state #Squeezed coherent state #quant-ph
paper · pdf · doi:10.1103/physreva.91.022334
published as Phys. Rev. A 91, 022334 (2015) · 7 pages, 3 figures; published version
arxiv created 2015/02/27 · openalex publication_date 2015/02/27 · arxiv updated 2016/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.