Information Dynamics: In Classical And Quantum ...
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Quantum information dynamics is an emerging field that ties several topics together, including non-equilibrium and driven quantum systems, many-body localization and thermalization, quantum chaos and black holes, tensor network holography. Traditionally, one may think that physics is about the dynamics of matter and spacetime. Extending our scope to the dynamics of quantum information is a new trend, which in turn deepen our understanding of the dynamics of matter and spacetime.
A tool to quantify quantum information is the entanglement entropy, as well as various information measures that can be constructed out of it. A prominent difference between quantum and classical information lies in the phenomenon of quantum entanglement. Quantum entanglement is a non-local information storing scheme that can only be realized in quantum systems, where information is not stored in any particular entity that makes up the system but stored in the relationships among the the entities. Therefore any attempt to separate a subsystem out of an entangled quantum system would inevitably cut off its quantum entanglement with the rest of the system, which leads to an information loss, or equivalently an entropy growth. The amount of entropy associated with separating the subsystem is the entanglement entropy, which also quantifies the entanglement between the subsystem and its counterpart.
For a given quantum many-body state, each choice of the subsystem (which may be disconnected) is associated with an entanglement entropy. Many quantum information measures, such as mutual or tripartite information, can be constructed by adding and subtracting entanglement entropies over different subsystems. So one may attempt to give a full description of quantum information by the collection of entanglement entropies over all possible subsystems. However, the amount of data is enormous. For a system of \\(N\\) qubits, there are totally \\(2^N\\) different choices of subsystem and hence \\(2^N\\) potentially different entanglement entropies. How to arrange the exponentially large amount of data efficiently One idea is to encode the entanglement entropies in the energy function of a statistical mechanics model.
As the many-body state evolves with time, the entanglement features also evolves. Therefore we can formulate the dynamics of quantum information as the dynamics of the entanglement features that describes the entanglement Ising ensemble. Our group is working to develop and apply this idea to understand quantum information dynamics in quantum chaotic arXiv:1803.10425 or periodic driven systems. This Ising formulation of quantum many-body entanglement turns to to be closely related to tensor network holography, which allows us to explore the corresponding dynamics in holographic bulk as well.
Studying quantum chaos in strongly-correlated many-body systems is key to understanding quantum complexity and its implications for statistical physics, phases of matter, nonequilibrium dynamics, and information processing. As the general description of such phenomena represents a grand challenge for Quantum Information Science (QIS), it is useful to study toy models that elucidate essential features and phenomenology. To that end, the Kicked Top, introduced in 1987 by Fritz Haake and collaborators [1], was seminal in deepening our understanding of quantum chaos, and more recently its relationship to quantum simulations of quantum phase transitions. It describes a large spin-J that precesses around a fixed axis and is periodically kicked by quadratic twisting term. It is also a Trotter approximation to a traverse Ising model with all-to-all two-body pairwise interactions.
A team led by PhD student Manuel Muñoz-Arias, in collaboration with Pablo Poggi and Ivan Deutsch, has recently generalized this to so called p-spin models, a traverse Ising model with all-to-all p-body interactions; the Kicked Top is a special case with p=2. In a new publication in Physical Review E, Muñoz et al. presented the full characterization of the classical and quantum chaos of the family kicked p-spin models [2]. The rich nonlinear dynamics of this family shows surprising new features with potential implications for quantum simulation of quantum critical phenomena.
In this work, Muñoz et al. study both the quantum Floquet map and its classical (thermodynamic) limit. They show that regardless of the order of the interaction p, classically all models transition to global chaos in the same way. However, for weak kicking strengths, the models with p>2 display richer phenomena, with higher order bifurcations that introduce a type of complexity that is absent in the p=2 Kicked Top. These signatures of chaos persist into the quantum regime, as characterized in kinematic and dynamics properties. This new quantum complexity will have direct consequences when kicked p-spin models are used to describe gated-based quantum simulators and sensors.
Quantum Computing Group Research topics Projects on fluids Courses Lab facilities List of papers List of talks Group members Jeffrey Yepez Quantum Computing Group Research Dr. Yepez's research is in quantum information dynamics, particularly quantum computational models of quantum field theory and classical field theory. Here is an overview of his research topics. 59ce067264
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