Related papers: Complex Rational Numbers in Quantum Mechanics
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…
We propose a quantum algorithm which uses the number of qubits in an optimal way and efficiently simulates a physical model with rich and complex dynamics described by the quantum sawtooth map. The numerical study of the effect of static…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the…
Expressions for the entropy and equations for the quantum distribution functions in systems of non-interacting fermions and bosons with an arbitrary, including small, number of particles are obtained in the paper
The symbolic representation of a number should be considered as a data structure, and the choice of data structure depends on the arithmetic operations that are to be performed. Numbers are almost universally represented using position…
Based on a brief review on developments of number system, a new developed pattern is proposed. The quaternion is extended to a matrix form aI+bC+cB+dA, in which the unit matrix I and three special matrices C,B,A correspond to number 1 and…
Probabilistic graphical models such as Bayesian networks are widely used to model stochastic systems to perform various types of analysis such as probabilistic prediction, risk analysis, and system health monitoring, which can become…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
To make progress in science, we often build abstract representations of physical systems that meaningfully encode information about the systems. The representations learnt by most current machine learning techniques reflect statistical…
Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that…
In this work a rationalized algorithm for calculating the quotient of two complex numbers is presented which reduces the number of underlying real multiplications. The performing of a complex number division using the naive method takes 4…
We construct Baxter operators for the homogeneous closed $\mathrm{XXX}$ spin chain with the quantum space carrying infinite or finite dimensional $s\ell_2$ representations. All algebraic relations of Baxter operators and transfer matrices…
We show that quantum computation circuits with coherent states as the logical qubits can be constructed using very simple linear networks, conditional measurements and coherent superposition resource states.
Conventional quantum mechanics is described in terms of complex numbers. However, all physical quantities are real. This indicates, that the appearance of complex numbers in quantum mechanics may be the emergent phenomenon, i.e. complex…
Some problems of the quantum error-correcting codes theory can be reduced to the investigation of the higher-rank numerical ranges of the operators related to the error operators. We constructively verify a conjecture on the structure of…
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…
Calcium is a C library for real and complex numbers in a form suitable for exact algebraic and symbolic computation. Numbers are represented as elements of fields $\mathbb{Q}(a_1,\ldots,a_n)$ where the extensions numbers $a_k$ may be…
In this paper we determine the group of rational automorphisms of binary cubic and quartic forms with integer coefficients and non-zero discriminant in terms of certain quadratic covariants of cubic and quartic forms. This allows one to…
Logarithmic operators and logarithmic conformal field theories are reviewed. Prominent examples considered here include c=-2 and c=0 logarithmic conformal field theories. c=0 logarithmic conformal field theories are especially interesting…