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We consider the problem of solving a distributed optimization problem using a distributed computing platform, where the communication in the network is limited: each node can only communicate with its neighbours and the channel has a…
We consider some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to large moduli, and of the question of twin…
In a previous paper a method was developed to subtract the interactions due to periodically replicated charges (or other long-range entities) in one spatial dimension. The method constitutes a generalized "electrostatic layer correction"…
Inexact alternating direction multiplier methods (ADMMs) are developed for solving general separable convex optimization problems with a linear constraint and with an objective that is the sum of smooth and nonsmooth terms. The approach…
We propose several constructions for the original multiplication algorithm of D.V. and G.V. Chudnovsky in order to improve its scalar complexity. We highlight the set of generic strategies who underlay the optimization of the scalar…
We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show…
We present a general method, based on a multiple-scale approach, for deriving the perturbative solutions of the scaling equations governing the expansion of superfluid ultracold quantum gases released from elongated harmonic traps. We…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
Scalable arrays of individual atoms provide an ideal starting point for quantum information and simulation experiments. However, their preparation is often limited by light-assisted collisions (LACs), which typically result in…
As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for…
Augmentation methods for mixed-integer (linear) programs are a class of primal solution approaches in which a current iterate is augmented to a better solution or proved optimal. It is well known that the performance of these methods, i.e.,…
For a number of quantum channels of interest, phase-flip errors occur far more frequently than bit-flip errors. When transmitting across these asymmetric channels, the decoding error rate can be reduced by tailoring the code used to the…
The strong coupling of atoms to optical cavities can improve optical lattice clocks as the cavity enables metrologically useful collective atomic entanglement and high-fidelity measurement. To this end, it is necessary to cool the ensemble…
In the field of atom optics, the basis of many experiments is a two level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the…
Immense interest in quantum computing has prompted development of electronic structure methods that are suitable for quantum hardware. However, the slow pace at which quantum hardware progresses, forces researchers to implement their ideas…
In this paper we consider from two different aspects the proximal alternating direction method of multipliers (ADMM) in Hilbert spaces. We first consider the application of the proximal ADMM to solve well-posed linearly constrained…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These…
Quantum computing has emerged as a transformative paradigm, capable of tackling complex computational problems that are infeasible for classical methods within a practical timeframe. At the core of this advancement lies the concept of…
In this work, we investigate the security of Elliptic Curve Cryptosystem (ECC) implementations against Side-Channel Analysis (SCA). ECC is well known for its efficiency and strong security, yet vulnerable to SCA which exploits physical…