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arXiv:quant-ph/0302027 · Quantum Information Processing

Treating the Independent Set Problem by 2D Ising Interactions with Adiabatic Quantum Computing

Paweł Wocjan, Dominik Janzing, Thomas Beth

Published Aug 1, 2003• 2 citations
arXivHTMLPDF
DOI
10.1023/b:qinp.0000020075.20455.5f

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We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problems in computer science. Our approach is based on coherent manipulation of atom arrays via the excitation into Rydberg atomic states. Specifically, we show that solutions of MIS problems can be efficiently encoded in the ground state of interacting atoms in 2D arrays by utilizing the Rydberg blockade mechanism. By studying the performance of leading classical algorithms, we identify parameter regimes, where computationally hard instances can be tested using near-term experimental systems. Practical implementations of both quantum annealing and variational quantum optimization algorithms beyond the adiabatic principle are discussed.
Adiabatic Quantum Computation (AQC) is a quantum model proposed by Farhi, et al., in 2000, and has been proven to be equivalent to conventional quantum computation (quantum gate model). Unlike classical computation or conventional quantum (gate) model in which an algorithm is discrete, an adiabatic quantum algorithm is continuous. In this talk, I will give an introduction of AQC, in particular, on the design and analysis of adiabatic quantum algorithms for the NP-hard maximum independent set problem. I will also discuss the adiabatic quantum architecture design and minor-embedding problems.
Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.