Modeling computational complexity via Gauge/String duality

In this project, we will attempt to formulate the laws of physics as information theoretical processes, and analyze the consiquences of such a construction. Thus, we will investiage the laws of physics (including the geometric structure of spacetime itself), as an emmergent property which would emmerge as a consequence of an information theoretical process. We will develop the idea that the information present in a boundary theory is dual to the information present in the bulk. As entropy measures the loss of information during an information theoretical process, we will analyze aspects of holographic entanglement entropy of a boundary theory by performing calculations in the bulk. We will use this to analyze the black hole information paradox. We will also analyze the deformation of AdS bulk by first order sting corrections, and analyze how this could effect the entanglement entropy of such a system. It has been argued that complexity is a more important quantity from an informational theoretical point of view, as it measures the difficulty to process the information. As physical of laws can be represented as information theoretical processes, and complexity is an important information theoretical quantity, it is expected to be important for analyzing physical systems. We will analyze the applications of this idea of complexity to physical processes and investigate a formalism where we can express the physical processes in terms of complexity. We will also use holography to calculate the complexity of a boundary theory by performing bulk calculations. We will also analyze the holographic complexity and holographic entanglement entropy for time dependent geometries. It is known from the holography that the complexity of a conformal field theory can be calculated from the bulk, and it can be demonstrated that there is a bound on the maximum complexity of a boundary field theory. This bound is saturated by black holes, and thus black holes from the fastest quantum computers. It is known that analogous black holes like solutions can be formed in graphene and other condensed matter systems. We will use the idea of complexity in these systems, and attempt to develop a theoretical proposal for the fastest quantum computer.

In this project, we will attempt to formulate the laws of physics as information theoretical processes, and analyze the consiquences of such a construction. Thus, we will investiage the laws of physics (including the geometric structure of spacetime itself), as an emmergent property which would emmerge as a consequence of an information theoretical process. We will develop the idea that the information present in a boundary theory is dual to the information present in the bulk. As entropy measures the loss of information during an information theoretical process, we will analyze aspects of holographic entanglement entropy of a boundary theory by performing calculations in the bulk. We will use this to analyze the black hole information paradox. We will also analyze the deformation of AdS bulk by first order sting corrections, and analyze how this could effect the entanglement entropy of such a system. It has been argued that complexity is a more important quantity from an informational theoretical point of view, as it measures the difficulty to process the information. As physical of laws can be represented as information theoretical processes, and complexity is an important information theoretical quantity, it is expected to be important for analyzing physical systems. We will analyze the applications of this idea of complexity to physical processes and investigate a formalism where we can express the physical processes in terms of complexity. We will also use holography to calculate the complexity of a boundary theory by performing bulk calculations. We will also analyze the holographic complexity and holographic entanglement entropy for time dependent geometries. It is known from the holography that the complexity of a conformal field theory can be calculated from the bulk, and it can be demonstrated that there is a bound on the maximum complexity of a boundary field theory. This bound is saturated by black holes, and thus black holes from the fastest quantum computers. It is known that analogous black holes like solutions can be formed in graphene and other condensed matter systems. We will use the idea of complexity in these systems, and attempt to develop a theoretical proposal for the fastest quantum computer.

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