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We introduce a quantum algorithm for computing the Ollivier Ricci curvature, a discrete analogue of the Ricci curvature defined via optimal transport on graphs and general metric spaces. This curvature has seen applications ranging from…
A large spectrum of problems in classical physics and engineering, such as turbulence, is governed by nonlinear differential equations, which typically require high-performance computing to be solved. Over the past decade, however, the…
We propose a scheme for quantum computation in optical lattices. The qubits are encoded in the spacial wavefunction of the atoms such that spin decoherence does not influence the computation. Quantum operations are steered by shaking the…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
Perspective functions arise explicitly or implicitly in various forms in applied mathematics and in statistical data analysis. To date, no systematic strategy is available to solve the associated, typically nonsmooth, optimization problems.…
One of the fundamental conditions for one-way quantum computation (1WQC) is the ability to make sequential measurements on isolated qubits that comprise the highly entangled resource for 1WQC, the cluster state. This has been a significant…
This paper argues that the requirement of applicableness of quantum linearity to any physical level from molecules and atoms to the level of macroscopic extensional world, which leads to a main foundational problem in quantum theory…
Quantum machines are among the most promising technologies expected to provide significant improvements in the following years. However, bridging the gap between real-world applications and their implementation on quantum hardware is still…
Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion…
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…
We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods…
This article presents a new and efficient alternative to well established algorithms for molecular geometry optimization. The new approach exploits the approximate decoupling of molecular energetics in a curvilinear internal coordinate…
Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission and processing power. Encoding the image information in quantum-mechanical systems instead of classical…
A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper…
Scalable and efficient quantum computation with photonic qubits requires (i) deterministic sources of single-photons, (ii) giant nonlinearities capable of entangling pairs of photons, and (iii) reliable single-photon detectors. In addition,…
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces. We survey these developments, with emphasis on connections…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
We interpret quantum computing as a geometric evolution process by reformulating finite quantum systems via Connes' noncommutative geometry. In this formulation, quantum states are represented as noncommutative connections, while gauge…
In this work we study quantum algorithms for Hopcroft's problem which is a fundamental problem in computational geometry. Given $n$ points and $n$ lines in the plane, the task is to determine whether there is a point-line incidence. The…