Relaxations and exact solutions to quantum Max Cut via the algebraic structure of swap operators
Abstract The Quantum Max Cut (QMC) problem has emerged as a test-problem for
designing approximation algorithms for local Hamiltonian problems. In this paper we attack …
designing approximation algorithms for local Hamiltonian problems. In this paper we attack …
An Improved Quantum Max Cut Approximation via Maximum Matching
E Lee, O Parekh - 51st International Colloquium on Automata …, 2024 - drops.dagstuhl.de
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to
gain a provable and practical quantum advantage. A line of recent studies focuses on …
gain a provable and practical quantum advantage. A line of recent studies focuses on …
Monogamy of highly symmetric states
We study the question of how highly entangled two particles can be when also entangled in
a similar way with other particles on the complete graph for the case of Werner, isotropic and …
a similar way with other particles on the complete graph for the case of Werner, isotropic and …
Guest Column: The 7 faces of quantum NP
S Gharibian - ACM SIGACT News, 2024 - dl.acm.org
When it comes to NP, its natural definition, its wide applicability across scientific disciplines,
and its timeless relevance, the writing is on the wall: There can be only one. Quantum NP …
and its timeless relevance, the writing is on the wall: There can be only one. Quantum NP …
An improved Quantum Max Cut approximation via matching
E Lee, O Parekh - arxiv preprint arxiv:2401.03616, 2024 - arxiv.org
Finding a high (or low) energy state of a given quantum Hamiltonian is a potential area to
gain a provable and practical quantum advantage. A line of recent studies focuses on …
gain a provable and practical quantum advantage. A line of recent studies focuses on …
Rapidly mixing loop representation quantum Monte Carlo for Heisenberg models on star-like bipartite graphs
Quantum Monte Carlo (QMC) methods have proven invaluable in condensed matter
physics, particularly for studying ground states and thermal equilibrium properties of …
physics, particularly for studying ground states and thermal equilibrium properties of …
Hardness of approximation for ground state problems
S Gharibian, C Hecht - arxiv preprint arxiv:2411.04874, 2024 - arxiv.org
After nearly two decades of research, the question of a quantum PCP theorem for quantum
Constraint Satisfaction Problems (CSPs) remains wide open. As a result, proving QMA …
Constraint Satisfaction Problems (CSPs) remains wide open. As a result, proving QMA …
Second order cone relaxations for quantum Max Cut
F Huber, K Thompson, O Parekh… - arxiv preprint arxiv …, 2024 - arxiv.org
Quantum Max Cut (QMC), also known as the quantum anti-ferromagnetic Heisenberg
model, is a QMA-complete problem relevant to quantum many-body physics and computer …
model, is a QMA-complete problem relevant to quantum many-body physics and computer …
Approximation Algorithms for Quantum Max--Cut
We initiate the algorithmic study of the Quantum Max-$ d $-Cut problem, a quantum
generalization of the well-known Max-$ d $-Cut problem. The Quantum Max-$ d $-Cut …
generalization of the well-known Max-$ d $-Cut problem. The Quantum Max-$ d $-Cut …