Related papers: Cubic Matrix, Nambu Mechanics and Beyond
We study the $S$-matrix interpretation of quantum theory in light of Categotical Quantum Mechanics. The $S$-matrix interpretation of quantum theory is shown to be a functorial semantics relating the algebras of quantum theory to the…
We present a method for optimizing quantum circuits architecture. The method is based on the notion of "quantum comb", which describes a circuit board in which one can insert variable subcircuits. The method allows one to efficiently…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
Quantum computers are discussed in the general framework of computation, the laws of physics and the foundations of quantum mechanics.
The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applications to quantum computing. Standard interferomeric techniques are used to construct a physical device capable of universal quantum computation. Some…
Taking the view that computation is after all physical, we argue that physics, particularly quantum physics, could help extend the notion of computability. Here, we list the important and unique features of quantum mechanics and then…
We study the quantization of a model proposed by Newton to explain centripetal force namely, that of a particle moving on a regular polygon. The exact eigenvalues and eigenfunctions are obtained. The quantum mechanics of a particle moving…
We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
Validation of a presumably universal theory, such as quantum mechanics, requires a quantum mechanical description of systems that carry out theoretical calculations and experiments. The description of quantum computers is under active…
We discuss possible applications of the 1-D direct and inverse scattering problem to design of universal quantum gates for quantum computation. The potentials generating some universal gates are described.
We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the…
In these notes we explore a variety of models comprising a large number of constituents. An emphasis is placed on integrals over large Hermitian matrices, as well as quantum mechanical models whose degrees of freedom are organised in a…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
Using a quantumlike description for light propagation in nonhomogeneous optical fibers, quantum information processing can be implemented by optical means. Quantum-like bits (qulbits) are associated to light modes in the optical fiber and…
In one-dimensional case, it is shown that the basic principles of quantum mechanics are properties of the set of intermediate cardinality.