Related papers: Exponentiating virtual imaginary contributions in …
A differentially private selection algorithm outputs from a finite set the item that approximately maximizes a data-dependent quality function. The most widely adopted mechanisms tackling this task are the pioneering exponential mechanism…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and…
In this article, we compare the methods implementing the real-time evolution operator generated by a unitary diagonal matrix where its entries obey a known underlying real function. When the size of the unitary diagonal matrix is small, a…
Polarization beam splitter (PBS) is a crucial photonic element to separately extract transverse-electric (TE) and transverse-magnetic (TM) polarizations from the propagating light fields. Here, we propose a concise, continuously tunable and…
The fastest known classical algorithm deciding the $k$-colorability of $n$-vertex graph requires running time $\Omega(2^n)$ for $k\ge 5$. In this work, we present an exponential-space quantum algorithm computing the chromatic number with…
Rational-function simplification is key bottlenecks in integration-by-parts (IBP) reduction of Feynman integrals. We study denominator factorization patterns appearing in IBP coefficients and develop practical algorithms for extracting and…
Fixing the number of particles $N$, the quantum canonical ensemble imposes a constraint on the occupation numbers of single-particle states. The constraint particularly hampers the systematic calculation of the partition function and any…
An approximate exponential quantum projection filtering scheme is developed for a class of open quantum systems described by Hudson- Parthasarathy quantum stochastic differential equations, aiming to reduce the computational burden…
In conventional parton showers (including ones based on dipoles/antennae), a given $(\mathrm{Born}+m)$-parton configuration can typically be reached via ${\mathcal O}(m!)$ different "shower histories". In the context of…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the…
We review the path integral method wherein quantum systems are mapped with Feynman's path integrals onto a classical system of "ring-polymers" and then simulated with the Monte Carlo technique. Bose or Fermi statistics correspond to…
Phase space cuts are implemented by inserting Heaviside theta functions in the integrands of momentum-space Feynman integrals. By directly parametrizing theta functions and constructing integration-by-parts (IBP) identities in the…
In this article, we propose an algorithm for approximating the action of $\varphi-$functions of matrices against vectors, which is a key operation in exponential time integrators. In particular, we consider matrices with Kronecker sum…
We review the staircase algorithm to decompose the exponential of a generalized Pauli matrix and we propose two alternative recursive methods which offer more efficient quantum circuits. The first algorithm we propose, defined as the…
We propose a computationally efficient method to solve the dynamics of operators of bosonic quantum systems coupled to their environments. The method maps the operator under interest to a set of complex-valued functions, and its adjoint…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
We derive an alternative representation of the leading-order contribution to the polarization operator in strong-field quantum electrodynamics with a plane-wave electromagnetic background field, which is manifestly symmetric with respect to…
A modified Green operator is proposed as an improvement of Fourier-based numerical schemes commonly used for computing the electrical or thermal response of heterogeneous media. Contrary to other methods, the number of iterations necessary…