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(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.

When Entanglement Meets Classical Communications: Quantum Teleportation for the Quantum Internet

“…When an open quantum system S of interest -a qubit in our case -interacts with the environment E, they together form the closed quantum system SE [17], [18], [23], [79]. This closed system SE evolves according to a unitary transformation U SE formulated as:…”

Quantum processing by remote quantum control

“…By using the linearcombination technique, the dependence on precision can be exponentially improved [42] compared to the Harrow-Hassidim-Lloyd algorithm [43] for the quantum linear systems problem. It can also reduce the query complexity and improve precision for simulations of open quantum systems [26] based on linear combinations of Kraus operators [44]. These applications generally require linear combinations of a great number of unitary operations.…”

“…Although the number of linearcombining terms is restricted, the size of each term can be large and reconfigurable, providing sufficient computing power and flexibility for various applications. It is worth noting that the proposed LCC can also be interpreted by using the notion of duality quantum computation [24][25][26], which was originally proposed to exploit the wave-particle duality and then developed to work within the framework of conventional quantum computing.…”

Quantum Enhanced Inference in Markov Logic Networks

“…We would like to thank the anonymous referee 1 for suggesting to us refs 45, and 53,54,55,56 and the anonymous referee 2 for suggesting to us refs 7–11. P.W.…”