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The quest for improved sampling methods to solve statistical mechanics problems of physical and chemical interest proceeds with renewed efforts since the invention of the Metropolis algorithm, in 1953. In particular, the understanding of…
Quantum mechanics contains some strange unphysical concepts. Among these are complex numbers, Hilbert spaces with their unitary and self-adjoint operators, states represented by complex vectors, superpositions of states, collapse of wave…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
This paper develops a deterministic model of quantum mechanics as an accumulation-and-threshold process. The model arises from an analogy with signal processing in wireless communications. Complex wavefunctions are interpreted as expressing…
Quantum computing is a promising new area of computing with quantum algorithms offering a potential speedup over classical algorithms if fault tolerant quantum computers can be built. One of the first applications of the classical computer…
Stochastic models for quantum state reduction give rise to statistical laws that are in many respects in agreement with those of standard quantum measurement theory. Here we construct a counterexample involving a Hamiltonian with degenerate…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
Quantum simulation is a foundational application for quantum computers, projected to offer insights into complex quantum systems beyond the reach of classical computation. However, with the exception of Trotter-based methods, which suffer…
A method of quantization of classical soliton cellular automata (QSCA) is put forward that provides a description of their time evolution operator by means of quantum circuits that involve quantum gates from which the associated Hamiltonian…
In conventional quantum mechanics the quantum particle is a special object, whose properties are described by special concepts and quantum principles. The quantization is a special procedure, which is accompanied by introduction of special…
We give a pedagogical introduction to Linearized Soliton Perturbation Theory (LSPT), a new and efficient tool for calculations involving quantum solitons. It is a Hamiltonian approach with a focus on explicitly constructing the soliton…
The development of emerging technologies in quantum optics demands accurate models that faithfully capture genuine quantum effects. Mature semiclassical approaches reach their limits when confronted with quantized electromagnetic fields,…
Pseudo-random operators consist of sets of operators that exhibit many of the important statistical features of uniformly distributed random operators. Such pseudo-random sets of operators are most useful whey they may be parameterized and…
Stochastic quantisation normally involves the introduction of a fictitious extra time parameter, which is taken to infinity so that the system evolves to an equilibrium state.In the case of a locally supersymmetric theory, an interesting…
We will try to explore, primarily from the complexity-theoretic point of view, limitations of error-correction and fault-tolerant quantum computation. We consider stochastic models of quantum computation on $n$ qubits subject to noise…
We give a review of the tomographic probability representation of quantum mechanics. We present the formalism of quantum states and quantum observables using the formalism of standard probability distributions and classical-like random…
The quantum Liouville equation, which describes the phase space dynamics of a quantum system of fermions, is analyzed from statistical point of view as a particular example of the Kramers-Moyal expansion. Quantum mechanics is extended to…
Statistical functions such as the moment-generating function, characteristic function, cumulant-generating function, and second characteristic function are cornerstone tools in classical statistics and probability theory. They provide a…
We discuss how to simulate simple quantum logic operations with a large number of qubits. These simulations are needed for experimental testing of scalable solid-state quantum computers. Quantum logic for remote qubits is simulated in a…
We present the solid-state quantum circuits that have been developed in order to implement quantum bits suitable for a quantum processor. These qubits are either based on the quantum state of a single particle (semiconductor qubits), or on…