Quantum Complexity Theory represents a paradigm shift in our understanding of complex quantum systems, moving beyond static models to embrace dynamic, hybrid dynamical systems. This paper proposes a novel framework for analyzing quantum complexity by integrating quantum dynamics with hybrid dynamical systems, aiming to unveil hidden patterns and provide deeper insights into the behavior of these systems. The core mechanism involves a closed-loop simulation that continuously updates the system's state, driving a dynamic evolution guided by quantum principles. This approach offers a more complete and nuanced understanding of complexity compared to traditional approaches.Quantum Complexity Theory represents a paradigm shift in our understanding of complex quantum systems, moving beyond static models to embrace dynamic, hybrid dynamical systems. This paper proposes a novel framework for analyzing quantum complexity by integrating quantum dynamics with hybrid dynamical systems, aiming to unveil hidden patterns and provide deeper insights into the behavior of these systems. The core mechanism involves a closed-loop simulation that continuously updates the system's state, driving a dynamic evolution guided by quantum principles. This approach offers a more complete and nuanced understanding of complexity compared to traditional approaches.

Sep 3, 20260 citations

Dynamics of Complex Quantum Systems

V. M. Akulin

Theoretical and mathematical physicsDec 30, 201316 citations

Note on transmitted complexity for the modified compound states

Noboru Watanabe

In Ref. 27, Ohya proposed the information dynamics synthesizing several ways of studying complex systems. In information dynamics, there are two types of complexities, one is a complexity of state representing system itself and another is a transmitted complexity between two systems. Entropies in classical and quantum systems are examples of these complexities of information dynamics. Transmitted complexity is an important tool to analyze the efficiency of information transmission in communication processes. In order to treat a flow of dynamical process, dynamical entropies were introduced in not only classical but also quantum systems. Based on the transition expectation introduced by Accardi to study quantum Markov process, the KOW entropy for completely positive (CP) maps was defined in Ref. 17. The generalized AOW and the AF entropies was constructed by the KOW entropy. The compound states are important tool to define the transmitted entropy 43,44. The transmitted complexity associated with the separable compound states is defined by using the generalized AOW entropy in Refs. 36 and 45. In this paper, we define a transmitted complexity (quantum dynamical mutual entropy) by means of the modified compound states and we prove the fundamental inequalities of the transmitted complexity for the independent quantum dynamical systems.In Ref. 27, Ohya proposed the information dynamics synthesizing several ways of studying complex systems. In information dynamics, there are two types of complexities, one is a complexity of state representing system itself and another is a transmitted complexity between two systems. Entropies in classical and quantum systems are examples of these complexities of information dynamics. Transmitted complexity is an important tool to analyze the efficiency of information transmission in communication processes. In order to treat a flow of dynamical process, dynamical entropies were introduced in not only classical but also quantum systems. Based on the transition expectation introduced by Accardi to study quantum Markov process, the KOW entropy for completely positive (CP) maps was defined in Ref. 17. The generalized AOW and the AF entropies was constructed by the KOW entropy. The compound states are important tool to define the transmitted entropy 43,44. The transmitted complexity associated with the separable compound states is defined by using the generalized AOW entropy in Refs. 36 and 45. In this paper, we define a transmitted complexity (quantum dynamical mutual entropy) by means of the modified compound states and we prove the fundamental inequalities of the transmitted complexity for the independent quantum dynamical systems.

International Journal of Modern Physics AJul 9, 20221 citation

Dynamical complexity in the quantum to classical transition

Bibek Pokharel, Peter Duggins, Moses Misplon +5 more

We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equivβ$ and coupling to the environment, $Γ$ . We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $β$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant $\hbar_{eff}\equivβ$ and coupling to the environment, $Γ$. We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as $β$ decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.

arXiv:1604.02743Apr 10, 20164 citations

Quantum dynamics

Benjamin W. Schumacher, Michael D. Westmoreland

Cambridge University Press eBooksMar 25, 20100 citations

We study the dynamical complexity of an open quantum driven double-well oscillator, mapping its dependence on effective Planck's constant

\hbar_{eff}\equivβ

and coupling to the environment,

Γ

. We study this using stochastic Schrodinger equations, semiclassical equations, and the classical limit equation. We show that (i) the dynamical complexity initially increases with effective Hilbert space size (as

β

decreases) such that the most quantum systems are the least dynamically complex. (ii) If the classical limit is chaotic, that is the most dynamically complex (iii) if the classical limit is regular, there is always a quantum system more dynamically complex than the classical system. There are several parameter regimes where the quantum system is chaotic even though the classical limit is not. While some of the quantum chaotic attractors are of the same family as the classical limiting attractors, we also find a quantum attractor with no classical counterpart. These phenomena occur in experimentally accessible regimes.