TY - JOUR
T1 - Dynamical phase transitions in sampling complexity
JF - Phys. Rev. Lett.
Y1 - 2018
A1 - Abhinav Deshpande
A1 - Bill Fefferman
A1 - Minh C. Tran
A1 - Michael Foss-Feig
A1 - Alexey V. Gorshkov
AB - We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proc. 43rd Annu. ACM Symp. Theory Comput. STOC '11]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in the light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular and optical systems.

VL - 121
U4 - 12 pages, 4 figures. v3: published version
UR - https://arxiv.org/abs/1703.05332
CP - 030501
U5 - https://doi.org/10.1103/PhysRevLett.121.030501
ER -