Related papers: The Complexity Geometry of a Single Qubit
Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are equipped with…
Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. In this review we study the…
Circuit complexity for two-dimensional topological quantum field theories (2D TQFT) was defined by Couch, Fan, and Shashi in [12]. In this paper, we study complexity for the 2D TQFT given by quantum cohomology of compact symplectic…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
Geometric quantization is an attempt at using the differential-geometric ingredients of classical phase spaces regarded as symplectic manifolds in order to define a corresponding quantum theory. Generally, the process of geometric…
Quantum entanglement was first recognized as a feature of quantum mechanics in the famous paper of Einstein, Podolsky and Rosen [18]. Recently it has been realized that quantum entanglement is a key ingredient in quantum computation,…
A generalised definition of the metric of quantum states is proposed by using the techniques of differential geometry. The metric of quantum state space derived earlier by Anandan, is reproduced and verified here by this generalised…
Recently Quantum Computation has generated a lot of interest due to the discovery of a quantum algorithm which can factor large numbers in polynomial time. The usefulness of a quantum com puter is limited by the effect of errors. Simulation…
Tensor networks impose a notion of geometry on the entanglement of a quantum system. In some cases, this geometry is found to reproduce key properties of holographic dualities, and subsequently much work has focused on using tensor networks…
Let $G$ be a finitely presented group. A new complexity called \textit{Karoubi-Weibel complexity} or \textit{covering type}, is defined for $G$. The construction is inspired by recent work of Karoubi and Weibel \cite{KW}, initially applied…
Motivated by the idea that consistent quantum field theories should admit a finite description, we investigate the complexity of effective field theories using the framework of effective o-minimality. Our focus is on quantifying the…
The Kolmogorov complexity of a physical state is the minimal physical resources required to reproduce that state. We define a second quantized quantum Turing machine and use it to define second quantized Kolmogorov complexity. There are two…
The computational efficiency of quantum mechanics can be defined in terms of the qubit circuit model, which is characterized by a few simple properties: each computational gate is a reversible transformation in a connected matrix group;…
Loop quantum gravity is a physical theory which aims at unifying general relativity and quantum mechanics. It takes general relativity very seriously and modifies it via a quantisation. General relativity describes gravity in terms of…
In this paper we give a definition for quantum Kolmogorov complexity. In the classical setting, the Kolmogorov complexity of a string is the length of the shortest program that can produce this string as its output. It is a measure of the…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
The quantum gravity has great difficulties with application of the probability notion. In given article this problem is analyzed according to algorithmic viewpoint. According to A.N. Kolmogorov, the probability notion can be connected with…
The conventional approach to understanding the characteristics of an unknown quantum state involves having numerous identical independent copies of the system in that state. However, we demonstrate that gleaning insights into specific…
The outcomes of quantum mechanical experiments are inherently random. It is therefore necessary to develop stringent methods for quantifying the degree of statistical uncertainty about the results of quantum experiments. For the…
The Fisher-Shannon statistical measure of complexity is analyzed for a continuous manifold of quantum observables. It is probed then than calculating it only in the configuration and momentum spaces will not give a complete description for…