Related papers: Quantum Algorithm for Estimating Ollivier-Ricci Cu…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…
Quantum contextuality is a limitation on deterministic hidden variable models, testable in measurement scenarios where outcomes differ under quantum or classical descriptions due to a common set of constraints. When considering measurements…
Effective equations are often useful to extract physical information from quantum theories without having to face all technical and conceptual difficulties. One can then describe aspects of the quantum system by equations of classical type,…
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time…
Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have…
Variational quantum algorithms dominate contemporary gate-based quantum enhanced optimisation, eigenvalue estimation and machine learning. Here we establish the quantum computational universality of variational quantum computation by…
Many computer vision applications need to recover structure from imperfect measurements of the real world. The task is often solved by robustly fitting a geometric model onto noisy and outlier-contaminated data. However, recent theoretical…
We review combinatorial quantum gravity, an approach which combines Einstein's idea of dynamical geometry with Wheeler's "it from bit" hypothesis in a model of dynamical graphs governed by the coarse Ollivier-Ricci curvature. This drives a…
Quantum computing may speed up numerical problems involving large matrices that are demanding for classical computers, and active research on this possibility is ongoing. In this work, we propose quantum algorithms for the exact simulation…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Classical algorithms for market equilibrium computation such as proportional response dynamics face scalability issues with Internet-based applications such as auctions, recommender systems, and fair division, despite having an almost…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
We elaborate the notion of a Ricci curvature lower bound for parametrized statistical models. Following the seminal ideas of Lott-Strum-Villani, we define this notion based on the geodesic convexity of the Kullback-Leibler divergence in a…
In this article we introduce a new operator representing the three-dimensional scalar curvature in loop quantum gravity. Our construction does not apply to the entire kinematical Hilbert space of loop quantum gravity; instead, the operator…
We present an efficient quantum algorithm aiming to find the negative curvature direction for escaping the saddle point, which is the critical subroutine for many second-order non-convex optimization algorithms. We prove that our algorithm…
The quantum approximate optimisation algorithm was proposed as a heuristic method for solving combinatorial optimisation problems on near-term quantum computers and may be among the first algorithms to perform useful computations in the…
We explore the near-term intersection of quantum computing with the transport sector. To support near-term integration, we introduce a framework for assessing the suitability of transport optimization problems for obtaining potential…
The use of vectorial parameterization to create geometrical representations in computational models has a large number of applications. One particular application is the calculation of the 3D rotational motion of rigid bodies, that could be…
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…