Research

My work sits at the intersection of spectral graph theory, quantum Hamiltonian complexity, and randomized algorithms. I focus on classical algorithms for ground-state problems such as Quantum Max-Cut and the antiferromagnetic Heisenberg model, and on the spectral theory of random graphs and expanders.

References

1. [1]
   Classical Algorithms for Bipartite Quantum Max-Cut on Dense Expanders

   Stuart Wayland, Zackary Jorquera, and Alexandra Kolla

   arXiv:2610.03670, 2026. arXivpdf

   › Abstract

   We give a polynomial-time classical randomized algorithm for the spin-½ antiferromagnetic Heisenberg model — equivalently, Quantum Max-Cut — on dense, balanced bipartite expanders. The algorithm estimates the ground energy and edge correlations to additive error $\varepsilon$ in time polynomial in both the system size $n$ and $1/\varepsilon$.

2. [2]
   Monogamy of Entanglement Bounds and Improved Approximation Algorithms for Qudit Hamiltonians

   Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, Juspreet Singh Sandhu, and Stuart Wayland

   arXiv:2410.15544, 2024. arXivpdf

   › Abstract

   We establish new entanglement monogamy bounds for two-local qudit Hamiltonians and certify ground state energy using sum-of-squares proofs. A simple matching-based algorithm achieves better-than-random approximations, including a 0.595 guarantee for qubits, outperforming prior results on bounded-degree graphs.

3. [3]
   Approximation Algorithms for Quantum Max-$d$-Cut

   Charlie Carlson, Zackary Jorquera, Alexandra Kolla, Steven Kordonowy, and Stuart Wayland

   arXiv:2309.10957, 2023. arXivpdf

   › Abstract

   The Quantum Max-$d$-Cut problem seeks quantum states maximizing antisymmetric subspace energy in $d$-dimensional systems, generalizing Max-$d$-Cut. We provide a polynomial-time approximation algorithm with performance guarantees and prove its tightness using a gap instance for $d \geq 3$.