Work

Approximation Algorithms for Quantum Max-$d$-Cut

Year: 2023

Type: preprint

Abstract: 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 problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. Equivalently, this problem is physically motivated by the $SU(d)$-Heisenberg model, a spin glass model that generalized the well-known Heisenberg model over qudits. We develop a polynomial-time randomized approximation algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees. Moreover, we prove the tightness of our analysis by presenting an algorithmic gap instance for Quantum Max-d-Cut problem with $d \geq 3$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2309.10957

Authors: Carlson, Charlie, Jorquera, Zackary, Kolla, Alexandra, Kordonowy, Steven, Wayland, Stuart

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Simons Institute for the Theory of Computing, University of California Berkeley

OpenAlex ID: W4386942706

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