Related papers: Quantization-based Optimization with Perspective o…
Two-dimensional generalization of the original peak finding algorithm suggested earlier is given. The ideology of the algorithm emerged from the well known quantum mechanical tunneling property which enables small bodies to penetrate…
Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…
Quadratic unconstrained binary optimization (QUBO) is the mathematical formalism for phrasing and solving a class of optimization problems that are combinatorial in nature. Due to their natural equivalence with the two dimensional Ising…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to…
Quantum theory provides a comprehensive framework for quantifying uncertainty, often applied in quantum finance to explore the stochastic nature of asset returns. This perspective likens returns to microscopic particle motion, governed by…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We present a classical algorithm to find approximate solutions to instances of quadratic unconstrained binary optimisation. The algorithm can be seen as an analogue of quantum annealing under the restriction of a product state space, where…
Probably one of the most striking examples of the close connections between global optimization processes and statistical physics is the simulated annealing method, inspired by the famous Monte Carlo algorithm devised by Metropolis et al.…
Quantum computers use quantum resources to carry out computational tasks and may outperform classical computers in solving certain computational problems. Special-purpose quantum computers such as quantum annealers employ quantum adiabatic…
Students in a quantum mechanics course are often introduced to the Schr\"odinger equation as the standard mathematical tool. However, rarely do students develop an understanding as to why the equation is the choice for modeling quantum…
We propose a novel clustering method that is based on physical intuition derived from quantum mechanics. Starting with given data points, we construct a scale-space probability function. Viewing the latter as the lowest eigenstate of a…
Optimisation plays a central role in a wide range of scientific and industrial applications, and quantum computing has been widely proposed as a means to achieve computational advantages in this domain. To date, research into the design of…
In this paper, we construct quantum circuits for the Black-Scholes equations, a cornerstone of financial modeling, based on a quantum algorithm that overcome the cure of high dimensionality. Our approach leverages the Schr\"odingerisation…
The Schr\"odingerization method converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schr\"odinger-type equations with unitary evolution. It does so via the so-called warped phase…
We review quantum tunneling provoked by external field driving, focusing on the role of geometric effects. The discussion begins with an overview of tunneling phenomena, including the Landau-Zener model and the Schwinger effect, both of…
This work proposes a hybrid framework combining classical computers with quantum annealers for structural optimisation. At each optimisation iteration of an iterative process, two minimisation problems are formulated one for the underlying…
Clustering is a powerful machine learning technique that groups "similar" data points based on their characteristics. Many clustering algorithms work by approximating the minimization of an objective function, namely the sum of…
The Schwinger model, which describes lattice quantum electrodynamics in $1+1$ space-time dimensions, provides a valuable framework to investigate fundamental aspects of quantum field theory, and a stepping stone towards non-Abelian gauge…