Quantum 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.
Hybrid Quantum-Classical Algorithms for Solving the Weighted CSP
Many kinds of algorithms have been developed for solving the constraint satisfaction problem (WCSP), a combinatorial optimization problem that frequently appears in AI. Unfortunately, its NP-hardness prohibits the existence of an algorithm for solving it that is universally efficient on classical computers. Therefore, a peek into quantum computers may be imperative for solving the WCSP efficiently. In this paper, we focus on a specific type of quantum computer, called the quantum annealer, which approximately solves quadratic unconstrained binary optimization (QUBO) problems. We propose the first three hybrid quantum-classical algorithms (HQCAs) for the WCSP: one specifically for the binary Boolean WCSP and the other two for the general WCSP. We experimentally show that the HQCA based on simple polynomial reformulation works well on the binary Boolean WCSP, but the HQCA based on the constraint composite graph works best on the general WCSP.
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- Award ID(s):
- 1837779
- NSF-PAR ID:
- 10193993
- Date Published:
- Journal Name:
- Proceedings of the International Symposium on Artificial Intelligence and Mathematics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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