Related papers: Number-Phase Wigner Representation for Efficient S…
This is an abstract of authors PhD thesis which is devoted to studies of quantum field models with strong coupling. The {\em Schwinger-Dyson equations} (SDEs) in momentum representation are solved in Minkowski space. The original version of…
The efficient simulation of models defined in terms of stochastic differential equations (SDEs) depends critically on an efficient integration scheme. In this article, we investigate under which conditions the integration schemes for…
We introduce an efficient method to reconstruct the Wigner function of many-mode continuous variable systems. It is based on convex optimization with semidefinite programs, and also includes a version of the maximum entropy principle, in…
We demonstrate the unique capabilities of the Wigner function, particularly in its positive and negative parts, for exploring the phase diagram of the spin$-(\frac{1}{2\!}-\!\frac{1}{2})$ and spin$-(\frac{1}{2}\!-\!1)$ Ising-Heisenberg…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with…
In this paper, we investigate the stochastic evolution equations (SEEs) driven by $\log$-Whittle-Mat$\acute{{\mathrm{e}}}$rn (W-M) random diffusion coefficient field and $Q$-Wiener multiplicative force noise. First, the well-posedness of…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…
We propose a methodology to design Wigner representations in phase spaces with nontrivial topology having evolution equations with desired mathematical properties. As an illustration, two representations of molecular rotations are developed…
Given the prevalence of superconducting platforms for uses in quantum computing and quantum sensing, the simulation of quantum superconducting circuits has become increasingly important for identifying system characteristics and modeling…
Graph-based surrogate models provide fast alternatives to high-fidelity CFD solvers, but their opaque latent spaces and limited controllability restrict use in safety-critical settings. A key failure mode in oscillatory flows is phase…
In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of \hbar can be constructed for them without referring to the…
This article explains and illustrates the use of a set of coupled dynamical equations, second order in a fictitious time, which converges to solutions of stationary Schr\"{o}dinger equations with additional constraints. We include three…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…
We experimentally investigate the non-Gaussian features of the phase-randomized coherent states, a class of states exploited in communication channels and in decoy state-based quantum key distribution protocols. In particular, we…
Due to the complexity of the space of quantum many-body states the computation of expectation values by statistical sampling is, in general, a hard task. Neural network representations of such quantum states which can be physically…
We derive the steady state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. The adiabatic limit of strong…
The introduction of phase coherence in the detection of quantum noise of light yields a pure quantum measurement of spectral modes. We theoretically show that such coherent quantum measurement performed with the technique of resonator…
Advancements in quantum system lifetimes and control have enabled the creation of increasingly complex quantum states, such as those on multiple bosonic cavity modes. When characterizing these states, traditional tomography scales…
We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…