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Lecture notes in physics. M, Monographs

Evolution of an Open System

Alexander Semenovich Holevo

Published Jan 1, 2001• 0 citations
Publisher
DOI
10.1007/3-540-44998-1_4

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Practical quantum systems are open systems due to interactions with their environment. Understanding the evolution of open systems dynamics is important for quantum noise processes , designing quantum error correcting codes, and performing simulations of open quantum systems. Here we proposed an efficient quantum algorithm for simulating the evolution of an open quantum system on a duality quantum computer. 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 algorithm, the time evolution of open quantum system is realized by using Kraus operators which is naturally realized in duality quantum computing. Compared to the Lloyd's quantum algorithm [Science.273, 1073(1996)] , the dependence on the dimension of the open quantum system in our algorithm is decreased. Moreover, our algorithm uses a truncated Taylor series of the evolution operators, exponentially improving the performance on the precision compared with existing quantum simulation algorithms with unitary evolution operations.

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Evolution of an open system as a continuous measurement of this system by its environment

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The restricted-path-integral (RPI) description of a continuous quantum measurement is rederived starting from the description of an open system by the Feynman-Vernon influence functional. For this end the total evolution operator of the compound system consisting of the open system and its environment is decomposed into the sum of partial evolution operators. Accordingly, the influence functional of the open system is decomposed into the integral of partial influence functionals (PIF). If the partial evolution operators or PIF are chosen in such a way that they decohere (do not interfere with each other), then the formalism of RPI effectively arises. The evolution of the open system may then be interpreted as a continuous measurement of this system by its environment. This is possible if the environment is macroscopic or mesoscopic.

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Open Systems

R. S. Ingarden, Andrzej Kossakowski, M. Ohya

Springer eBooks•Jan 1, 1997•0 citations
Practical quantum systems are open systems due to interactions with their environment. Understanding the evolution of open systems dynamics is important for quantum noise processes , designing quantum error correcting codes, and performing simulations of open quantum systems. Here we proposed an efficient quantum algorithm for simulating the evolution of an open quantum system on a duality quantum computer. 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 algorithm, the time evolution of open quantum system is realized by using Kraus operators which is naturally realized in duality quantum computing. Compared to the Lloyd's quantum algorithm [Science.273, 1073(1996)] , the dependence on the dimension of the open quantum system in our algorithm is decreased. Moreover, our algorithm uses a truncated Taylor series of the evolution operators, exponentially improving the performance on the precision compared with existing quantum simulation algorithms with unitary evolution operations.
The restricted-path-integral (RPI) description of a continuous quantum measurement is rederived starting from the description of an open system by the Feynman-Vernon influence functional. For this end the total evolution operator of the compound system consisting of the open system and its environment is decomposed into the sum of partial evolution operators. Accordingly, the influence functional of the open system is decomposed into the integral of partial influence functionals (PIF). If the partial evolution operators or PIF are chosen in such a way that they decohere (do not interfere with each other), then the formalism of RPI effectively arises. The evolution of the open system may then be interpreted as a continuous measurement of this system by its environment. This is possible if the environment is macroscopic or mesoscopic.