Related papers: An Improved Approximation Algorithm for Quantum Ma…
Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter…
Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their…
This paper is devoted to the distributed complexity of finding an approximation of the maximum cut in graphs. A classical algorithm consists in letting each vertex choose its side of the cut uniformly at random. This does not require any…
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…
Quadratic Programming (QP) is the well-studied problem of maximizing over {-1,1} values the quadratic form \sum_{i \ne j} a_{ij} x_i x_j. QP captures many known combinatorial optimization problems, and assuming the unique games conjecture,…
Trevisan [SICOMP 2012] presented an algorithm for Max-Cut based on spectral partitioning techniques. This is the first algorithm for Max-Cut with an approximation guarantee strictly larger than 1/2 that is not based on semidefinite…
There is a strong interest in finding challenging instances of NP-hard problems, from the perspective of showing quantum advantage. Due to the limits of near-term NISQ devices, it is moreover useful if these instances are small. In this…
The "exact subgraph" approach was recently introduced as a hierarchical scheme to get increasingly tight semidefinite programming relaxations of several NP-hard graph optimization problems. Solving these relaxations is a computational…
The input to the Multiway Cut problem is a weighted undirected graph, with nonnegative edge weights, and $k$ designated terminals. The goal is to partition the vertices of the graph into $k$ parts, each containing exactly one of the…
Gate model quantum computers with too many qubits to be simulated by available classical computers are about to arrive. We present a strategy for programming these devices without error correction or compilation. This means that the number…
It is well-known in physics that the limit of large quantum spin $S$ should be understood as a semiclassical limit. This raises the question of whether such emergent classicality facilitates the approximation of computationally hard quantum…
The EPR Hamiltonian is a family of 2-local quantum Hamiltonians introduced by King (arXiv:2209.02589). We introduce a polynomial time $\frac{1+\sqrt{5}}{4}\approx 0.809$-approximation algorithm for the problem of computing the ground energy…
We study the MaxCut problem for graphs $G=(V,E)$. The problem is NP-hard, there are two main approximation algorithms with theoretical guarantees: (1) the Goemans \& Williamson algorithm uses semi-definite programming to provide a…
We give an efficient 0.8395-approximation algorithm for the EPR Hamiltonian. Our improvement comes from a new nonlinear monogamy-of-entanglement bound on star graphs and a refined parameterization of a shallow quantum circuit from previous…
The technique of semidefinite programming (SDP) relaxation can be used to obtain a nontrivial bound on the optimal value of a nonconvex quadratically constrained quadratic program (QCQP). We explore concave quadratic inequalities that hold…
Goemans and Williamson designed a 0.878-approximation algorithm for Max-Cut in undirected graphs [JACM'95]. Khot, Kindler, Mosel, and O'Donnel showed that the approximation ratio of the Goemans-Williamson algorithm is optimal assuming…
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…
Quantum approximate optimization algorithms are hybrid quantum-classical variational algorithms designed to approximately solve combinatorial optimization problems such as the MAX-CUT problem. In spite of its potential for near-term quantum…
Quantum algorithms for binary optimization problems have been the subject of extensive study. However, the application of quantum algorithms to integer optimization problems remains comparatively unexplored. In this paper, we study the…
We study the Max-Cut semidefinite programming (SDP) relaxation in the regime where a near-optimal solution admits a low-dimensional realization. While the Goemans--Williamson hyperplane rounding achieves the worst-case optimal approximation…