Related papers: Almost optimal classical approximation algorithms …
Motivated by applications in wireless communications, this paper develops semidefinite programming (SDP) relaxation techniques for some mixed binary quadratically constrained quadratic programs (MBQCQP) and analyzes their approximation…
B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto…
We study a generalization of entanglement testing which we call the "hidden cut problem." Taking as input copies of an $n$-qubit pure state which is product across an unknown bipartition, the goal is to learn precisely where the state is…
Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…
We describe a new approximation algorithm for Max Cut. Our algorithm runs in $\tilde O(n^2)$ time, where $n$ is the number of vertices, and achieves an approximation ratio of $.531$. On instances in which an optimal solution cuts a…
Graph partitioning is one of an important set of well-known compute-intense (NP-hard) graph problems that devolve to discrete constrained optimization. We sampled solutions to the problem via two different quantum-ready methods to…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
We present randomized approximation algorithms for multi-criteria Max-TSP. For Max-STSP with k > 1 objective functions, we obtain an approximation ratio of $1/k - \eps$ for arbitrarily small $\eps > 0$. For Max-ATSP with k objective…
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…
We consider the graph $k$-partitioning problem under the min-max objective, termed as Minmax $k$-cut. The input here is a graph $G=(V,E)$ with non-negative edge weights $w:E\rightarrow \mathbb{R}_+$ and an integer $k\geq 2$ and the goal is…
We study the problem of finding a (pure) product state with optimal fidelity to an unknown $n$-qubit quantum state $\rho$, given copies of $\rho$. This is a basic instance of a fundamental question in quantum learning: is it possible to…
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, i.e., the set of all Pareto optimal solutions, where no objective can be improved without…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the…
The Lasserre Hierarchy is a set of semidefinite programs which yield increasingly tight bounds on optimal solutions to many NP-hard optimization problems. The hierarchy is parameterized by levels, with a higher level corresponding to a more…
The Traveling Salesperson Problem (TSP) is a fundamental NP-hard optimisation challenge with widespread applications in logistics, operations research, and network design. While classical algorithms effectively solve small to medium-sized…
In this paper we propose and study a new complexity model for approximation algorithms. The main motivation are practical problems over large data sets that need to be solved many times for different scenarios, e.g., many multicast trees…
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…
Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the…