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Structure-preserving linearly implicit exponential integrators are constructed for Hamiltonian partial differential equations with linear constant damping. Linearly implicit integrators are derived by polarizing the polynomial terms of the…
In this article, a family of two- and three-stage explicit multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) Runge-Kutta methods are introduced for solving ordinary differential equations. These methods are…
We present an efficient method for evaluating random phase errors in phase shifters within photonic integrated circuits, avoiding the computational cost of traditional Monte Carlo simulations. By modeling spatially correlated manufacturing…
While Wigner functions forming phase space representation of quantum states is a well-known fact, their construction for noncommutative quantum mechanics (NCQM) remains relatively lesser known, in particular with respect to gauge…
Quantum computing can be realized with numerous different hardware platforms and computational protocols. A highly promising approach to foster scalability is to apply a photonic platform combined with a measurement-induced quantum…
Achieving stable hopping has been a hallmark challenge in the field of dynamic legged locomotion. Controlled hopping is notably difficult due to extended periods of underactuation combined with very short ground phases wherein ground…
In this work we present a new class of Runge-Kutta (RK) methods for solving systems of hyperbolic equations with a particular structure, generalization of a wave-equation. The new methods are {\it partially implicit} in the sense that a…
Variational quantum eigensolvers (VQEs) are successful algorithms for studying physical systems on quantum computers. Recently, they were extended to the measurement-based model of quantum computing, bringing resource graph states and their…
In this paper, we propose a new direction of research for the realization of the quantum controlled-not gate based on a technique called ``interaction-free measurement'', where qubits are two-level atoms (or ions) and information is…
Fractional-step methods are a popular and powerful divide-and-conquer approach for the numerical solution of differential equations. When the integrators of the fractional steps are Runge--Kutta methods, such methods can be written as…
We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the…
We present a method to construct high-fidelity quantum phase gates, which are insensitive to errors in various experimental parameters. The phase gates consist of a pair of two sequential broadband composite pulses, with a phase difference…
We develop an intrinsic enumerator framework for quantum error correction in unitary representations of symmetry groups. An intrinsic quantum code is a subspace of a representation $V$ of a group $G$, and errors are organized by the…
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been constructed for this group. Unfortunately, the…
We give an algorithm to compute stable commutator length in free products of cyclic groups which is polynomial time in the length of the input, the number of factors, and the orders of the finite factors. We also describe some experimental…
The effect of noise on a quantum system can be described by a set of operators obtained from the interaction Hamiltonian. Recently it has been shown that generalized quantum error correcting codes can be derived by studying the algebra of…
In this paper a set of previous general results for the development of B--series for a broad class of stochastic differential equations has been collected. The applicability of these results is demonstrated by the derivation of B--series…
We introduce a class of exponential Runge-Kutta integration methods for kinetic equations. The methods are based on a decomposition of the collision operator into an equilibrium and a non equilibrium part and are exact for relaxation…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is…