Related papers: An Improved Approximation Algorithm for Quantum Ma…
MaxCut is a key NP-Hard combinatorial optimization graph problem with extensive theoretical and industrial applications, including the Ising model and chip design. While quantum computing offers new solutions for such combinatorial…
We initiate the study of approximating the largest induced expander in a given graph $G$. Given a $\Delta$-regular graph $G$ with $n$ vertices, the goal is to find the set with the largest induced expansion of size at least $\delta \cdot…
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 give a new $(1+\epsilon)$-approximation for sparsest cut problem on graphs where small sets expand significantly more than the sparsest cut (sets of size $n/r$ expand by a factor $\sqrt{\log n\log r}$ bigger, for some small $r$; this…
Quantum annealing is a heuristic optimization algorithm that exploits quantum evolution to approximately find lowest energy states. Quantum annealers have scaled up in recent years to tackle increasingly larger and more highly connected…
In this article we report on the application of the Quantum Approximate Optimization Algorithm (QAOA) to solve the unweighted MaxCut problem on tree-structured graphs. Specifically, we utilize the Nauty (No Automorphisms, Yes?) package to…
This paper presents a quantum algorithm for solving the fractional Poisson equation \((-\Delta)^s u = f\) with \(s \in (0,1)\) on bounded domains. The proposed approach combines rational approximation techniques with quantum linear system…
This work shows that minimizing the depth of a quantum circuit composed of commuting operations reduces to a vertex coloring problem on an appropriately constructed graph, where gates correspond to vertices and edges encode…
The weighted MAX k-CUT problem consists of finding a k-partition of a given weighted undirected graph G(V,E) such that the sum of the weights of the crossing edges is maximized. The problem is of particular interest as it has a multitude of…
Proposed hybrid algorithms encode a combinatorial cost function into a problem Hamiltonian and optimize its energy by varying over a set of states with low circuit complexity. Classical processing is typically only used for the choice of…
It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time…
Finite-sum optimization has wide applications in machine learning, covering important problems such as support vector machines, regression, etc. In this paper, we initiate the study of solving finite-sum optimization problems by quantum…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…
The quantum circuit layout (QCL) problem is to map a quantum circuit such that the constraints of the device are satisfied. We introduce a quantum circuit mapping heuristic, QXX, and its machine learning version, QXX-MLP. The latter infers…
The current noisy intermediate-scale quantum (NISQ) era is characterized by substantial errors and noise, which limit the practical feasibility of deep, many-qubit circuits. To address these constraints, quantum circuit cutting has emerged…
We give a quantum algorithm to exactly solve certain problems in combinatorial optimization, including weighted MAX-2-SAT as well as problems where the objective function is a weighted sum of products of Ising variables, all terms of the…
We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and…
We introduce a method for solving the Max-Cut problem using a variational algorithm and a continuous-variables quantum computing approach. The quantum circuit consists of two parts: the first one embeds a graph into a circuit using the…
The Graph Pricing problem is among the fundamental problems whose approximability is not well-understood. While there is a simple combinatorial 1/4-approximation algorithm, the best hardness result remains at 1/2 assuming the Unique Games…