Related papers: Stochastic Representation of the Quantum Quartic O…
We present an implementation of a recently proposed procedure for defining time, based on the description of the evolving system and its clock as non-interacting, entangled systems, according to the Page and Wootters approach. We study how…
We review progress towards direct simulation of quantum dynamics in many-body systems, using recently developed stochastic gauge techniques. We consider master equations, canonical ensemble calculations and reversible quantum dynamics are…
We discuss a new analytical approach to real-time evolution in quantum many-body systems. Our approach extends the framework of continuous unitary transformations such that it amounts to a novel solution method for the Heisenberg equations…
This paper extends the energy-based version of the stochastic linearization method, known for classical nonlinear systems, to open quantum systems with canonically commuting dynamic variables governed by quantum stochastic differential…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
Classical stochastic processes can be generated by quantum simulators instead of the more standard classical ones, such as hidden Markov models. One reason for using quantum simulators is that they generally require less memory than their…
The field of classical stochastic processes forms a major branch of mathematics. They are, of course, also very well studied in biology, chemistry, ecology, geology, finance, physics, and many more fields of natural and social sciences.…
Simulating nonlinear classical dynamics on a quantum computer is an inherently challenging task due to the linear operator formulation of quantum mechanics. In this work, we provide a systematic approach to alleviate this difficulty by…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
Recently, variational quantum metrology was proposed for Hamiltonians with multiplicative parameters, wherein the estimation precision can be optimized via variational circuits. However, systems with generic Hamiltonians still lack these…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
We consider the problem of the driven harmonic oscillator in the probability representation of quantum mechanics, where the oscillator states are described by fair nonnegative probability distributions of position measured in rotated and…
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
How well can quantum computers simulate classical dynamical systems? There is increasing effort in developing quantum algorithms to efficiently simulate dynamics beyond Hamiltonian simulation, but so far exact resource estimates are not…
The accurate description and robust computational modeling of the nonequilibrium properties of quantum systems remain a challenge in condensed matter physics. In this work, we develop a linear-scale computational simulation technique for…
Quantum stochastic differential equations have been used to describe the dynamics of an atom interacting with the electromagnetic field via absorption/emission processes. Here, by using the full quantum stochastic Schroedinger equation…
The formalism of the particle dynamics in the space-time, where motion of free particles is primordially stochastic, is considered. The conventional dynamic formalism, obtained for the space-time, where the motion of free particles is…
We define a map which relates four dimensional classical stochastic matrices to qubit quantum channels. The map preserves the spectrum and the composition of processes. To do this we introduce the concept of Bloch tetrahedron which plays…
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.