Related papers: Quantum stochastic equation for the low density li…
Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters,…
The dynamics of many open quantum systems are described by stochastic master equations. In the discrete-time case, we recall the structure of the derived quantum filter governing the evolution of the density operator conditioned to the…
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…
Most of the mathematical approaches for quantum Langevin equation are based on the non-commutativity of the random force operators. Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
Efficient descriptions of open quantum systems can be obtained by performing an adiabatic elimination of the fast degrees of freedom and formulating effective operators for the slow degrees of freedom in reduced dimensions. Here, we perform…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral via the use of certain underlying stochastic differential…
Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard, belief propagation (BP) combined with…
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square…
By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the Parametric Representation with Environmental Coherent States) we derive an equation of motion for the reduced density operator of an…
In this paper a quantum mechanical phase space picture is constructed for coarse-grained free quantum fields in an inflationary Universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase…
We propose an operator constraint equation for the wavefunction of the Universe that admits genuine evolution. While the corresponding classical theory is equivalent to the canonical decomposition of General Relativity, the quantum theory…
We present here a brief overview of our work in developing a convolutionless quantum master equation approach suitable for mesoscopic sized systems. Our final equation can be used in the regimes where the golden rule approach is not…
We discuss a method to follow step-by-step time evolution of atomic and molecular systems based on QED (Quantum Electrodynamics). Our strategy includes expanding the electron field operator by localized wavepackets to define creation and…
The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…
We consider a minimal residual discretization of a simultaneous space-time variational formulation of parabolic evolution equations. Under the usual `LBB' stability condition on pairs of trial- and test spaces we show quasi-optimality of…
We present results concerning the nature of the cosmological big bounce(BB) transition within the loop geometry underlying loop quantum cosmology (LQC). Our canonical quantization method is an alternative to the standard LQC. An evolution…
We show that the effect of a Gaussian Bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary Bosonic modes initially at zero temperature and…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…