{"status":"public","year":"2024","abstract":[{"text":"Quantum Max Cut (QMC), also known as the quantum anti-ferromagnetic\r\nHeisenberg model, is a QMA-complete problem relevant to quantum many-body\r\nphysics and computer science. Semidefinite programming relaxations have been\r\nfruitful in designing theoretical approximation algorithms for QMC, but are\r\ncomputationally expensive for systems beyond tens of qubits. We give a second\r\norder cone relaxation for QMC, which optimizes over the set of mutually\r\nconsistent three-qubit reduced density matrices. In combination with Pauli\r\nlevel-$1$ of the quantum Lasserre hierarchy, the relaxation achieves an\r\napproximation ratio of $0.526$ to the ground state energy. Our relaxation is\r\nsolvable on systems with hundreds of qubits and paves the way to\r\ncomputationally efficient lower and upper bounds on the ground state energy of\r\nlarge-scale quantum spin systems.","lang":"eng"}],"external_id":{"arxiv":["2411.04120"]},"_id":"56944","type":"preprint","author":[{"full_name":"Huber, Felix","last_name":"Huber","first_name":"Felix"},{"first_name":"Kevin","last_name":"Thompson","full_name":"Thompson, Kevin"},{"first_name":"Ojas","last_name":"Parekh","full_name":"Parekh, Ojas"},{"last_name":"Gharibian","first_name":"Sevag","id":"71541","orcid":"0000-0002-9992-3379","full_name":"Gharibian, Sevag"}],"language":[{"iso":"eng"}],"date_updated":"2024-11-07T12:10:28Z","user_id":"71541","citation":{"chicago":"Huber, Felix, Kevin Thompson, Ojas Parekh, and Sevag Gharibian. “Second Order Cone Relaxations for Quantum Max Cut.” <i>ArXiv:2411.04120</i>, 2024.","bibtex":"@article{Huber_Thompson_Parekh_Gharibian_2024, title={Second order cone relaxations for quantum Max Cut}, journal={arXiv:2411.04120}, author={Huber, Felix and Thompson, Kevin and Parekh, Ojas and Gharibian, Sevag}, year={2024} }","mla":"Huber, Felix, et al. “Second Order Cone Relaxations for Quantum Max Cut.” <i>ArXiv:2411.04120</i>, 2024.","short":"F. Huber, K. Thompson, O. Parekh, S. Gharibian, ArXiv:2411.04120 (2024).","apa":"Huber, F., Thompson, K., Parekh, O., &#38; Gharibian, S. (2024). Second order cone relaxations for quantum Max Cut. In <i>arXiv:2411.04120</i>.","ieee":"F. Huber, K. Thompson, O. Parekh, and S. Gharibian, “Second order cone relaxations for quantum Max Cut,” <i>arXiv:2411.04120</i>. 2024.","ama":"Huber F, Thompson K, Parekh O, Gharibian S. Second order cone relaxations for quantum Max Cut. <i>arXiv:241104120</i>. Published online 2024."},"title":"Second order cone relaxations for quantum Max Cut","date_created":"2024-11-07T12:09:37Z","publication":"arXiv:2411.04120"}