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Abstract
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 photonnumber distribution of a linearoptical interferometric network, which is fed with singlephoton Fockstate 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 linearoptical 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 photonadded coherent states. It is easy to show that the sampling problem associated with displaced singlephoton Fock states and a displaced photonnumber 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 singlephotonadded coherent states and the same displaced photonnumber detection scheme demonstrates a computationalcomplexity 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.
Original language  English 

Article number  022334 
Pages (fromto)  02233410223346 
Number of pages  6 
Journal  Physical Review A  Atomic, Molecular, and Optical Physics 
Volume  91 
Issue number  2 
DOIs  
Publication status  Published  27 Feb 2015 
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ARC Centre of Excellence for Quantum Engineered Systems (EQuS) (RAAP)
Volz, T. & Doherty, A. C.
5/04/17 → …
Project: Research