Related papers: Universal Quantum Speedup for Branch-and-Bound, Br…
We present a new method that efficiently solves TO problems and provides a practical pathway to leverage quantum computing to exploit potential quantum advantages. This work targets on large-scale, multi-material TO challenges for…
Quantified Integer Programming (QIP) bridges multiple domains by extending Quantified Boolean Formulas (QBF) to incorporate general integer variables and linear constraints while also generalizing Integer Programming through variable…
This paper presents a novel algorithm integrating global and robust optimization methods to solve continuous non-convex quadratic problems under convex uncertainty sets. The proposed Robust spatial branch-and-bound (RsBB) algorithm combines…
Quantum algorithms based on variational approaches are one of the most promising methods to construct quantum solutions and have found a myriad of applications in the last few years. Despite the adaptability and simplicity, their…
Quantum algorithms can potentially solve a handful of problems more efficiently than their classical counterparts. In that context, it has been discussed that Markov chains problems could be solved significantly faster using quantum…
Among classical search algorithms with the same heuristic information, with sufficient memory A* is essentially as fast as possible in finding a proven optimal solution. However, in many situations optimal solutions are simply infeasible,…
We develop fast approximation algorithms for the minimum-cost version of the Bounded-Degree MST problem (BD-MST) and its generalization the Crossing Spanning Tree problem (Crossing-ST). We solve the underlying LP to within a $(1+\epsilon)$…
In topologically-protected quantum computation, quantum gates can be carried out by adiabatically braiding two-dimensional quasiparticles, reminiscent of entangled world lines. Bonesteel et al. [Phys. Rev. Lett. 95, 140503 (2005)], as well…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
As the most central and computationally intensive component of deep neural networks, the execution efficiency of matrix multiplication directly determines the training and inference performance of models. Harnessing the parallel processing…
Distributed quantum computation is often proposed to increase the scalability of quantum hardware, as it reduces cooperative noise and requisite connectivity by sharing quantum information between distant quantum devices. However, such…
Brand\~ao and Svore very recently gave quantum algorithms for approximately solving semidefinite programs, which in some regimes are faster than the best-possible classical algorithms in terms of the dimension $n$ of the problem and the…
Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step…
Mixed Integer Linear Programming (MILP) is a pillar of mathematical optimization that offers a powerful modeling language for a wide range of applications. During the past decades, enormous algorithmic progress has been made in solving…
We propose fast and practical quantum-inspired classical algorithms for solving linear systems. Specifically, given sampling and query access to a matrix $A\in\mathbb{R}^{m\times n}$ and a vector $b\in\mathbb{R}^m$, we propose classical…
In this paper, we introduce a quantum-enhanced algorithm for simulation-based optimization. Simulation-based optimization seeks to optimize an objective function that is computationally expensive to evaluate exactly, and thus, is…
We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst-case running time $n^{\frac{1}{2}} m^{\frac{1}{2}} s^2 \text{poly}(\log(n), \log(m), R, r, 1/\delta)$, with $n$ and $s$ the dimension and row-sparsity of the…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
The MaxCut problem is a fundamental problem in Combinatorial Optimization, with significant implications across diverse domains such as logistics, network design, and statistical physics. The algorithm represents innovative approaches that…