Related papers: Quantum mechanics for military officers
Accurate models for open quantum systems -- quantum states that have non-trivial interactions with their environment -- may aid in the advancement of a diverse array of fields, including quantum computation, informatics, and the prediction…
Stochastic realization of the wave function in quantum mechanics, with the inclusion of soliton representation of extended particles, is discussed. The concept of Stochastic Qubits is used for quantum computing modeling.
We present a quantum-like (QL) model in that contexts (complexes of e.g. mental, social, biological, economic or even political conditions) are represented by complex probability amplitudes. This approach gives the possibility to apply the…
In this article, I show that a recent family of quantum algorithms, based on the quantum amplitude amplification algorithm, can be used to describe a cognitive heuristic called availability bias. The amplitude amplification algorithm is…
These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.
This research applies concepts from algorithmic probability to Boolean and quantum combinatorial logic circuits. A tutorial-style introduction to states and various notions of the complexity of states are presented. Thereafter, the…
One can view quantum mechanics as a generalization of classical probability theory that provides for pairwise interference among alternatives. Adopting this perspective, we ``quantize'' the classical random walk by finding, subject to a…
A local and distributive algorithm is proposed to find an optimal trial wave-function minimizing the Hamiltonian expectation in a quantum system. To this end, the quantum state of the system is connected to the Gibbs state of a classical…
A unified framework for different formulations of quantum theoery is introduced specifying what is meant by a quantum mechanical theory in general.
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual…
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
We show that quantum algorithms can be used to re-prove a classical theorem in approximation theory, Jackson's Theorem, which gives a nearly-optimal quantitative version of Weierstrass's Theorem on uniform approximation of continuous…
While we have intuitive notions of structure and complexity, the formalization of this intuition is non-trivial. The statistical complexity is a popular candidate. It is based on the idea that the complexity of a process can be quantified…
Partial symplectic conditional and joint probability representations of quantum mechanics are considered. The correspondence rules for most interesting physical operators are found and the expressions of the dual symbols of operators are…
A hypothetical formulation of quantum mechanics is presented so as to reconcile it with macro-realism. On the analogy drawn from thermodynamics, an objective description of wave packet reduction is postulated, in which a characteristic…
The method is introduced for fast data processing by reducing the probability amplitudes of undesirable elements. The algorithm has a mathematical description and circuit implementation on a quantum processor. The idea is to make a quick…
Quantum mechanics permits certain kinds of non-local effects. This paper demonstrates how these can be used for distributed computation with minimal communication between various processors. The problem considered is that of estimating the…
Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt…
We present a formulation of quantum mechanics based on orthogonal polynomials. The wavefunction is expanded over a complete set of square integrable basis in configuration space where the expansion coefficients are orthogonal polynomials in…