AffiliationDepartment of Electrical and Computer Engineering, University of Arizona
Department of Physics, University of Arizona
James C. Wyant College of Optical Sciences, University of Arizona
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CitationZhang, B., Sone, A., & Zhuang, Q. (2022). Quantum computational phase transition in combinatorial problems. Npj Quantum Information, 8(1).
Journalnpj Quantum Information
RightsCopyright © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License.
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AbstractQuantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical computers, without a proof that bounded-error quantum polynomial time (BQP) ≠ nondeterministic polynomial time (NP), it is necessary to investigate the empirical advantages of QAOA. We identify a computational phase transition of QAOA when solving hard problems such as SAT—random instances are most difficult to train at a critical problem density. We connect the transition to the controllability and the complexity of QAOA circuits. Moreover, we find that the critical problem density in general deviates from the SAT-UNSAT phase transition, where the hardest instances for classical algorithms lies. Then, we show that the high problem density region, which limits QAOA’s performance in hard optimization problems (reachability deficits), is actually a good place to utilize QAOA: its approximation ratio has a much slower decay with the problem density, compared to classical approximate algorithms. Indeed, it is exactly in this region that quantum advantages of QAOA over classical approximate algorithms can be identified. © 2022, The Author(s).
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Except where otherwise noted, this item's license is described as Copyright © The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License.