The dynamics of a closed quantum system, under a unitary time evolution $U$ , is obviously linear. But, the reduced dynamics of an open quantum system $S$ , interacting with an environment $E$ , is not linear, in general. Dominy et al. [Quantum Inf. Process. 15, 465 (2016)] considered the case that the set $\mathcal{S}={{\ensuremath{\rho}}_{SE}}$ of possible initial states of the system-environment is convex, and also possesses another property, which they called $U$ -consistency. They have shown that, under such circumstances, the reduced dynamics of the system $S$ is linear. Whether the Dominy-Shabani-Lidar framework is the most general one is the subject of this paper. We assume that the reduced dynamics is linear and show that this leads us to their framework. In other words, the reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework.The dynamics of a closed quantum system, under a unitary time evolution $U$, is obviously linear. But, the reduced dynamics of an open quantum system $S$, interacting with an environment $E$, is not linear, in general. Dominy et al. [Quantum Inf. Process. 15, 465 (2016)] considered the case that the set $\mathcal{S}={{\ensuremath{\rho}}_{SE}}$ of possible initial states of the system-environment is convex, and also possesses another property, which they called $U$-consistency. They have shown that, under such circumstances, the reduced dynamics of the system $S$ is linear. Whether the Dominy-Shabani-Lidar framework is the most general one is the subject of this paper. We assume that the reduced dynamics is linear and show that this leads us to their framework. In other words, the reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework.

arXiv:2003.00460Physical Review AAug 11, 20208 citations

Linear Quantum Dynamics

IMPERIAL COLLEGE PRESS eBooksSep 1, 19950 citations

Non-Linear Multiscale Dynamics (NMD) Simulation using Quantum Simulation

Jincheng Zhang

Non-Linear Multiscale Dynamics (NMD) is a powerful computational technique used to study the behavior of complex biological systems by iteratively refining the model from coarse-grained to detailed simulations. This paper explores the application of quantum simulation to enhance the accuracy and efficiency of NMD simulations, particularly by leveraging quantum phenomena to improve the representation of the system's dynamics. We present a novel approach to quantum simulation within the NMD framework, focusing on optimizing the representation of key physical parameters and reducing computational costs. Our work demonstrates significant improvements in simulation fidelity and speed compared to traditional methods, offering a promising pathway toward more sophisticated NMD models. The core claim is that utilizing quantum simulation techniques significantly enhances the precision and efficiency of NMD simulations, thereby providing a deeper understanding of biological systems.Non-Linear Multiscale Dynamics (NMD) is a powerful computational technique used to study the behavior of complex biological systems by iteratively refining the model from coarse-grained to detailed simulations. This paper explores the application of quantum simulation to enhance the accuracy and efficiency of NMD simulations, particularly by leveraging quantum phenomena to improve the representation of the system's dynamics. We present a novel approach to quantum simulation within the NMD framework, focusing on optimizing the representation of key physical parameters and reducing computational costs. Our work demonstrates significant improvements in simulation fidelity and speed compared to traditional methods, offering a promising pathway toward more sophisticated NMD models. The core claim is that utilizing quantum simulation techniques significantly enhances the precision and efficiency of NMD simulations, thereby providing a deeper understanding of biological systems.

Aug 31, 20260 citations

Generalized Quantum Dynamics

János A. Bergou, Mark S. Hillery, Mark E. Saffman

Graduate texts in physicsJan 1, 20211 citation

Finite Quantum Dynamics

David Finkelstein, Mohsen Shiri-Garakani

arXiv:quant-ph/0602122International Journal of Theoretical PhysicsJan 21, 20113 citations

Semantic Analysis of a Linear Temporal Extension of Quantum Logic and Its Dynamic Aspect

Tsubasa Takagi

Although various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints have not been studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear temporal extension of quantum logic with a quantum implication, and extend it to Dynamic Linear Temporal Quantum Logic (DLTQL). This logic has temporal operators to express transitions by unitary operators (quantum gates) and dynamic ones to express those by projections (projective measurement). We then prove some logical properties of the relationship between these two transitions expressed by LTQL and DLTQL. A drawback in applying LTQL to the verification of quantum protocols is that these logics cannot express the future operator in linear temporal logic. We propose a way to mitigate this drawback by using a translation from (D)LTQL to Linear Temporal Modal Logic (LTML) and a simulation. This translation reduces the satisfiability problem of (D)LTQL formulas to that of LTML with the classical semantics over quantum states.Although various dynamic or temporal logics have been proposed to verify quantum protocols and systems, these two viewpoints have not been studied comprehensively enough. We propose Linear Temporal Quantum Logic (LTQL), a linear temporal extension of quantum logic with a quantum implication, and extend it to Dynamic Linear Temporal Quantum Logic (DLTQL). This logic has temporal operators to express transitions by unitary operators (quantum gates) and dynamic ones to express those by projections (projective measurement). We then prove some logical properties of the relationship between these two transitions expressed by LTQL and DLTQL. A drawback in applying LTQL to the verification of quantum protocols is that these logics cannot express the future operator in linear temporal logic. We propose a way to mitigate this drawback by using a translation from (D)LTQL to Linear Temporal Modal Logic (LTML) and a simulation. This translation reduces the satisfiability problem of (D)LTQL formulas to that of LTML with the classical semantics over quantum states.

ACM Transactions on Computational LogicDec 16, 20221 citation

The dynamics of a closed quantum system, under a unitary time evolution

U

, is obviously linear. But, the reduced dynamics of an open quantum system

S

, interacting with an environment

E

, is not linear, in general. Dominy et al. [Quantum Inf. Process. 15, 465 (2016)] considered the case that the set $\mathcal{S}={{\ensuremath{\rho}}_{SE}}$ of possible initial states of the system-environment is convex, and also possesses another property, which they called

U

-consistency. They have shown that, under such circumstances, the reduced dynamics of the system

S

is linear. Whether the Dominy-Shabani-Lidar framework is the most general one is the subject of this paper. We assume that the reduced dynamics is linear and show that this leads us to their framework. In other words, the reduced dynamics of the system is linear if and only if it can be formulated within the Dominy-Shabani-Lidar framework.