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Optimizing Quantum Circuit Parameters via SDP

Author Eunou Lee

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Eunou Lee
  • Sunkyunkwan University, Seoul, South Korea

Acknowledgements

This work was supported by the Postdoctoral Research Program of Sungkyunkwan University (2021).

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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) https://doi.org/10.4230/LIPIcs.ISAAC.2022.48

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
Keywords
  • Quantum algorithm
  • Optimization
  • Rounding algorithm
  • Quantum Circuit
  • Approximation

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References

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