Related papers: Nature as quantum computer
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…
The current proposals for the realization of quantum computer such as NMR, quantum dots and trapped ions are based on the using of an atom or an ion as one qubit. In these proposals a quantum computer consists from several atoms and the…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
Most of physical experiments are usually described as repeated measurements of some random variables. The experimental data registered by on-line computers form time series of outcomes. The frequencies of different outcomes are compared…
The relationships between game theory and quantum mechanics let us propose certain quantization relationships through which we could describe and understand not only quantum but also classical, evolutionary and the biological systems that…
Quantum computing improves substantially on known classical algorithms for various important problems, but the nature of the relationship between quantum and classical computing is not yet fully understood. This relationship can be…
We consider the problem of quantum behavior in the finite background. Introduction of continuum or other infinities into physics leads only to technical complications without any need for them in description of empirical observations. The…
This paper gives a complete selfcontained proof of our result announced in hep-th/9909126 showing that renormalization in quantum field theory is a special instance of a general mathematical procedure of extraction of finite values based on…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
As a natural generalization of ordinary Lie algebras we introduce the concept of quantum Lie algebras ${\cal L}_q(g)$. We define these in terms of certain adjoint submodules of quantized enveloping algebras $U_q(g)$ endowed with a quantum…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
This article reviews the history of digital computation, and investigates just how far the concept of computation can be taken. In particular, I address the question of whether the universe itself is in fact a giant computer, and if so,…
When the symmetry of a physical theory describing a finite system is deformed by replacing its Lie group by the corresponding quantum group, the operators and state function will lie in a new algebra describing new degrees of freedom. If…
We propose models of quantum neural networks through Clifford algebras, which are capable of capturing geometric features of systems and to produce entanglement. Due to their representations in terms of Pauli matrices, the Clifford algebras…
We place the renormalization procedure in quantum field theory into the familiar mathematical context of quantization of Poisson algebras. The Poisson algebra in question is the algebra of classical field theory Hamiltonians constructed in…
If the systems of quantum theory are thought of as elementary information carriers in the first place, rather than elementary constituents of matter, and their connections are logical connections within a given algorithm, rather than…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
The main objective consists in endowing the elementary particles with an algebraic space-time structure in the perspective of unifying quantum field theory and general relativity: this is realized in the frame of the Langlands global…