Open AccessTrotterized adiabatic quantum simulation and its application to a simple all-optical system
Author(s) -
Yifan Sun,
JunYi Zhang,
Mark Byrd,
Lian-Ao Wu
Publication year - 2020
Publication title -
new journal of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.584
H-Index - 190
ISSN - 1367-2630
DOI - 10.1088/1367-2630/ab7a31
Subject(s) - physics , adiabatic process , hamiltonian (control theory) , adiabatic quantum computation , quantum , statistical physics , boson , quantum simulator , bilinear interpolation , quantum mechanics , quantum system , open quantum system , quantum computer , computer science , mathematical optimization , mathematics , computer vision
As first proposed for the adiabatic quantum information processing by Wu et al (2002 Phys. Rev. Lett. 89 057904), the Trotterization technique is a very useful tool for universal quantum computing, and in particular, the adiabatic quantum simulation of quantum systems. Given a boson Hamiltonian involving arbitrary bilinear interactions, we propose a static version of this technique to perform an optical simulation that would enable the identification of the ground state of the Hamiltonian. By this method, the dynamical process of the adiabatic evolution is mapped to a static linear optical array which is robust to the errors caused by dynamical fluctuations. We examine the cost of the physical implementation of the Trotterization, i.e. the number of discrete steps required for a given accuracy. Two conclusions are drawn. One is that the number of required steps grows much more slowly than the system size if the number of non-zero matrix elements of Hamiltonian is not too large. The second is that small fluctuations of the parameters of optical elements do not affect the first conclusion. This implies that the method is robust against the certain type of errors as we considered. Last but not least, we present an example of implementation of the simulation on a photonic chip as well as an optimized scheme. By such examples, we show a reduction of the costs compared to its classical counterpart and the potential for further improvement, which promotes a more general application.