Quantum computational phase transition in combinatorial problems
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.
- Research Organization:
- National Quantum Information Science (QIS) Research Centers (United States). Superconducting Quantum Materials and Systems Center (SQMS)
- Sponsoring Organization:
- National Science Foundation (NSF); USDOE; USDOE Office of Science (SC)
- Grant/Contract Number:
- AC02-07CH11359
- OSTI ID:
- 1877692
- Alternate ID(s):
- OSTI ID: 1982121
- Journal Information:
- npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 8; ISSN 2056-6387
- Publisher:
- Nature Publishing GroupCopyright Statement
- Country of Publication:
- United Kingdom
- Language:
- English