Parity Quantum Optimization: Benchmarks

Michael Fellner, Kilian Ender, Roeland ter Hoeven, and Wolfgang Lechner

Parity Quantum Computing GmbH, A-6020 Innsbruck, Austria
Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria

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Abstract

We present benchmarks of the parity transformation for the Quantum Approximate Optimization Algorithm (QAOA). We analyse the gate resources required to implement a single QAOA cycle for real-world scenarios. In particular, we consider random spin models with higher order terms, as well as the problems of predicting financial crashes and finding the ground states of electronic structure Hamiltonians. For the spin models studied our findings imply a significant advantage of the parity mapping compared to the standard gate model. In combination with full parallelizability of gates this has the potential to boost the race for demonstrating quantum advantage.

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Cited by

[1] Dylan Herman, Cody Googin, Xiaoyuan Liu, Alexey Galda, Ilya Safro, Yue Sun, Marco Pistoia, and Yuri Alexeev, "A Survey of Quantum Computing for Finance", arXiv:2201.02773, (2022).

[2] P. V. Sriluckshmy, Vicente Pina-Canelles, Mario Ponce, Manuel G. Algaba, Fedor Šimkovic, and Martin Leib, "Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates", arXiv:2303.04498, (2023).

[3] Kilian Ender, Roeland ter Hoeven, Benjamin E. Niehoff, Maike Drieb-Schön, and Wolfgang Lechner, "Parity Quantum Optimization: Compiler", arXiv:2105.06233, (2021).

[4] Federico Dominguez, Josua Unger, Matthias Traube, Barry Mant, Christian Ertler, and Wolfgang Lechner, "Encoding-Independent Optimization Problem Formulation for Quantum Computing", arXiv:2302.03711, (2023).

[5] Narendra N. Hegade, Koushik Paul, F. Albarrán-Arriagada, Xi Chen, and Enrique Solano, "Digitized adiabatic quantum factorization", Physical Review A 104 5, L050403 (2021).

[6] Maike Drieb-Schön, Kilian Ender, Younes Javanmard, and Wolfgang Lechner, "Parity Quantum Optimization: Encoding Constraints", arXiv:2105.06235, (2021).

[7] Anita Weidinger, Glen Bigan Mbeng, and Wolfgang Lechner, "Error Mitigation for Quantum Approximate Optimization", arXiv:2301.05042, (2023).

[8] Anette Messinger, Michael Fellner, and Wolfgang Lechner, "Constant Depth Code Deformations in the Parity Architecture", arXiv:2303.08602, (2023).

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