arXiv subjects

Zackary Jorquera

Publications and source records attributed to Zackary Jorquera.

3 recordsLinked to original sources

arXiv2026

Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians

We prove new monogamy of entanglement bounds for two-local qudit Hamiltonians of rank-one projectors without one-local terms. In particular, we certify the maximum energy in terms of the maximum matching of the underlying interaction graph via low-degree sum-of-squares proofs. Algorithmically, we show that a simple matching-based algorithm approximates the maximum energy to at least $1/d$ for general graphs and to at least $1/d + Θ(1/D)$ for graphs with bounded degree, $D$. This outperforms random assignment, which, in expectation, achieves energy of only $1/d^2$ of the maximum energy for general graphs. Notably, on $D$-regular graphs with degree, $D \leq 5$, and for any local dimension, $d$, we show that this simple matching-based algorithm has an approximation guarantee of $1/2$. Lastly, when $d=2$, we present an algorithm achieving an approximation guarantee of $0.595$, beating that of [PT22, arXiv:2206.08342], which gave an approximation ratio of $1/2$.

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arXiv2024

Approximation Algorithms for Quantum Max-$d$-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 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 $d \geq 3$.

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arXiv2023

A quantum advantage over classical for local max cut

We compare the performance of a quantum local algorithm to a similar classical counterpart on a well-established combinatorial optimization problem LocalMaxCut. We show that a popular quantum algorithm first discovered by Farhi, Goldstone, and Gutmannn [1] called the quantum optimization approximation algorithm (QAOA) has a computational advantage over comparable local classical techniques on degree-3 graphs. These results hint that even small-scale quantum computation, which is relevant to the current state-of the art quantum hardware, could have significant advantages over comparably simple classical computation.

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