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(d3) in contrast to O(d4) 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.
Highlights
Quantum computer works quantum mechanically[1,2], and can efficiently factorize large numbers[3] and search in an unsorted database[4,5]
The physic picture is : a quantum system passing through a d-slits with its wave function being divided into d sub-waves, the dividing operation denoted as the quantum wave divider (QWD) operation
We have briefly described the dynamics of an open quantum system and the quantum operations can be elegantly represented in operator-sum representation
Summary
Realization of Kraus operators in duality quantum computer. A duality quantum computer is a moving quantum computer passing through a d-slit which exploits the wave-particle duality of quantum systems[17]. Different unitary operations are performed simultaneously on the sub-waves at different slits. Compared to ordinary quantum computers in which only unitary operators are allowed, One can perform different gate operations on the sub-wave functions at different slits in the duality quantum computer[17]. We only measure the final wave functions on 0-slit to realize a duality quantum gate, which is called single output duality quantum computing. Through QWD operation and QWC operation, every path on each-slit realized a duality quantum gate It means that d duality quantum gates are performed in one process. Different operations are performed on the different sub-waves, and three outputs of duality quantum computing are collected from three-slits on the right wall[18].
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