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Documents authored by Lee, Eunou

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.105
An Improved Quantum Max Cut Approximation via Maximum Matching

Authors: Eunou Lee and Ojas Parekh

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
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 Quantum Max Cut, where one is asked to find a high energy state of a given antiferromagnetic Heisenberg Hamiltonian. In this work, we present a classical approximation algorithm for Quantum Max Cut that achieves an approximation ratio of 0.595, outperforming the previous best algorithms of Lee [Eunou Lee, 2022] (0.562, generic input graph) and King [King, 2023] (0.582, triangle-free input graph). The algorithm is based on finding the maximum weighted matching of an input graph and outputs a product of at most 2-qubit states, which is simpler than the fully entangled output states of the previous best algorithms.
Cite as

Eunou Lee and Ojas Parekh. An Improved Quantum Max Cut Approximation via Maximum Matching. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 105:1-105:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lee_et_al:LIPIcs.ICALP.2024.105,
  author =	{Lee, Eunou and Parekh, Ojas},
  title =	{{An Improved Quantum Max Cut Approximation via Maximum Matching}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{105:1--105:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.105},
  URN =		{urn:nbn:de:0030-drops-202482},
  doi =		{10.4230/LIPIcs.ICALP.2024.105},
  annote =	{Keywords: approximation, optimization, local Hamiltonian, rounding, SDP, matching}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2022.48
Optimizing Quantum Circuit Parameters via SDP

Authors: Eunou Lee

Published in: LIPIcs, Volume 248, 33rd International Symposium on Algorithms and Computation (ISAAC 2022)

Abstract
In recent years, parameterized quantum circuits have become a major tool to design quantum algorithms for optimization problems. The challenge in fully taking advantage of a given family of parameterized circuits lies in finding a good set of parameters in a non-convex landscape that can grow exponentially to the number of parameters. We introduce a new framework for optimizing parameterized quantum circuits: round SDP solutions to circuit parameters. Within this framework, we propose an algorithm that produces approximate solutions for a quantum optimization problem called Quantum Max Cut. The rounding algorithm runs in polynomial time to the number of parameters regardless of the underlying interaction graph. The resulting 0.562-approximation algorithm for generic instances of Quantum Max Cut improves on the previously known best algorithms by Anshu, Gosset, and Morenz with a ratio 0.531 and by Parekh and Thompson with a ratio 0.533.
Cite as

Eunou Lee. Optimizing Quantum Circuit Parameters via SDP. In 33rd International Symposium on Algorithms and Computation (ISAAC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 248, pp. 48:1-48:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lee:LIPIcs.ISAAC.2022.48,
  author =	{Lee, Eunou},
  title =	{{Optimizing Quantum Circuit Parameters via SDP}},
  booktitle =	{33rd International Symposium on Algorithms and Computation (ISAAC 2022)},
  pages =	{48:1--48:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-258-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{248},
  editor =	{Bae, Sang Won and Park, Heejin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2022.48},
  URN =		{urn:nbn:de:0030-drops-173330},
  doi =		{10.4230/LIPIcs.ISAAC.2022.48},
  annote =	{Keywords: Quantum algorithm, Optimization, Rounding algorithm, Quantum Circuit, Approximation}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.59
An Approximation Algorithm for the MAX-2-Local Hamiltonian Problem

Authors: Sean Hallgren, Eunou Lee, and Ojas Parekh

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
We present a classical approximation algorithm for the MAX-2-Local Hamiltonian problem. This is a maximization version of the QMA-complete 2-Local Hamiltonian problem in quantum computing, with the additional assumption that each local term is positive semidefinite. The MAX-2-Local Hamiltonian problem generalizes NP-hard constraint satisfaction problems, and our results may be viewed as generalizations of approximation approaches for the MAX-2-CSP problem. We work in the product state space and extend the framework of Goemans and Williamson for approximating MAX-2-CSPs. The key difference is that in the product state setting, a solution consists of a set of normalized 3-dimensional vectors rather than boolean numbers, and we leverage approximation results for rank-constrained Grothendieck inequalities. For MAX-2-Local Hamiltonian we achieve an approximation ratio of 0.328. This is the first example of an approximation algorithm beating the random quantum assignment ratio of 0.25 by a constant factor.
Cite as

Sean Hallgren, Eunou Lee, and Ojas Parekh. An Approximation Algorithm for the MAX-2-Local Hamiltonian Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 59:1-59:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hallgren_et_al:LIPIcs.APPROX/RANDOM.2020.59,
  author =	{Hallgren, Sean and Lee, Eunou and Parekh, Ojas},
  title =	{{An Approximation Algorithm for the MAX-2-Local Hamiltonian Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{59:1--59:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.59},
  URN =		{urn:nbn:de:0030-drops-126629},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.59},
  annote =	{Keywords: approximation algorithm, quantum computing, local Hamiltonian, mean-field theory, randomized rounding}
}
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