Different adiabatic quantum optimization algorithms
(pp0638-0648)
Vicky
Choi
doi:
https://doi.org/10.26421/QIC11.7-8-7
Abstracts:
One of the most important questions in studying quantum computation is:
whether a quantum computer can solve NP-complete problems more
efficiently than a classical computer? In 2000, Farhi, et al. (Science,
292(5516):472–476, 2001) proposed the adiabatic quantum optimization (AQO),
a paradigm that directly attacks NP-hard optimization problems. How
powerful is AQO? Early on, van Dam and Vazirani claimed that AQO failed
(i.e. would take exponential time) for a family of 3SAT instances they
constructed. More recently, Altshuler, et al. (Proc Natl Acad Sci USA,
107(28): 12446–12450, 2010) claimed that AQO failed also for random
instances of the NP-complete Exact Cover problem. In this paper, we make
clear that all these negative results are only for a specific AQO
algorithm. We do so by demonstrating different AQO algorithms for the
same problem for which their arguments no longer hold. Whether AQO fails
or succeeds for solving the NP-complete problems (either the worst case
or the average case) requires further investigation. Our AQO algorithms
for Exact Cover and 3SAT are based on the polynomial reductions to the
NP-complete Maximum-weight Independent Set (MIS) problem.
Key words:
Adiabatic Quantum Optimization, Adiabatic Quantum
Algorithms, NPComplete, Exact Cover, 3SAT, Maximum Independent Set |