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In this paper, we propose a numerical method for verifying the positiveness of solutions to semilinear elliptic equations. We provide a sufficient condition for a solution to an elliptic equation to be positive in the domain of the…
We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
We propose an algorithm using a modified variant of amplitude amplification to solve combinatorial optimization problems via the use of a subdivided phase oracle. Instead of dividing input states into two groups and shifting the phase…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
Recently, several authors have suggested the use of first order methods, such as fast dual ascent and the alternating direction method of multipliers, for embedded model predictive control. The main reason is that they can be implemented…
The cylindrical algebraic covering method was originally proposed to decide the satisfiability of a set of non-linear real arithmetic constraints. We reformulate and extend the cylindrical algebraic covering method to allow for checking the…
We present improved quantum circuits for elliptic curve scalar multiplication, the most costly component in Shor's algorithm to compute discrete logarithms in elliptic curve groups. We optimize low-level components such as reversible…
Optimal control problem with a goal to squeeze wave packet of a trapped quantum particle is considered and solved analytically using adiabatic approximation. The analytical solution that drives the particle into a highly localized final…
Spatial quantum enhancement effects are studied under a unified framework. It is shown that the multiphoton absorption rate of photons with a quantum-enhanced lithographic resolution is reduced, not enhanced, contrary to popular belief. The…
The alternating direction method of multipliers (ADMM) is one of the most widely used first-order optimisation methods in the literature owing to its simplicity, flexibility and efficiency. Over the years, numerous efforts are made to…
This article proposes modifications to standard low order finite element approximations of the Stokes system with the goal of improving both the approximation quality and the parallel algebraic solution process. Different from standard…
We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and…
A new over-improved stout-link smearing algorithm, designed to stabilise instanton-like objects, is presented. A method for quantifying the selection of the over-improvement parameter, $\epsilon$, is demonstrated. The new smearing algorithm…
Molecular dynamics simulations at a constant electric potential are an essential tool to study electrochemical processes, providing microscopic information on the structural, thermodynamic, and dynamical properties. Despite the numerous…
We propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our…
Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum…
Quantum amplitude amplification algorithm is an important and basic technique in quantum computing. In this paper, our goal is to study distributed quantum amplitude amplification algorithms, and the main contributions are: (1) A…
In this paper, we study the multiplicative behaviour of quantum channels, mathematically described by trace preserving, completely positive maps on matrix algebras. It turns out that the multiplicative domain of a unital quantum channel has…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…