title: Duality quantum algorithm efficiently simulates open quantum systems.
abstract: Because of inevitable coupling with the environment, nearly all practical quantum systems are open system, where the evolution is not necessarily unitary. In this paper, we propose a duality quantum algorithm for simulating Hamiltonian evolution of an open quantum system. In contrast to unitary evolution in a usual quantum computer, the evolution operator in a duality quantum computer is a linear combination of unitary operators. In this duality quantum algorithm, the time evolution of the open quantum system is realized by using Kraus operators which is naturally implemented in duality quantum computer. This duality quantum algorithm has two distinct advantages compared to existing quantum simulation algorithms with unitary evolution operations. Firstly, the query complexity of the algorithm is O(d(3)) in contrast to O(d(4)) in existing unitary simulation algorithm, where d is the dimension of the open quantum system. Secondly, By using a truncated Taylor series of the evolution operators, this duality quantum algorithm provides an exponential improvement in precision compared with previous unitary simulation algorithm.
authors.affiliation: State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P. R. China.
authors.forename: Shi-Jie
authors.initials: SJ
authors.lastname: Wei
authors.affiliation: State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P. R. China.|Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China.|Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.
authors.forename: Dong
authors.initials: D
authors.lastname: Ruan
authors.affiliation: State Key Laboratory of Low-dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, P. R. China.|Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, P. R. China.|Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.
authors.forename: Gui-Lu
authors.initials: GL
authors.lastname: Long