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Journal of Nanjing University of Posts and Telecommunications

Adiabatic Quantum Computation

Fangmin Song

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

This paper describes and analyses AQC from the perspectives of physics and computer science: firstly,explain the basic principle and the computational power of AQC,and then analysis the advantages of AQC by contrast with GMQC,and then according to the theoretical foundation of AQC,introduce the adiabatic quantum algorithms.Finally,discuss the prospects and further works of AQC and adiabatic quantum computer.

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This paper describes and analyses AQC from the perspectives of physics and computer science: firstly,explain the basic principle and the computational power of AQC,and then analysis the advantages of AQC by contrast with GMQC,and then according to the theoretical foundation of AQC,introduce the adiabatic quantum algorithms.Finally,discuss the prospects and further works of AQC and adiabatic quantum computer.
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.
In this thesis we summarize the principles of quantum computing. We specifically consider adiabatic quantum computing, whose principles are explained and shown on several examples. To explain the principle of adiabatic quantum computing we review the adiabatic theorem. We also outline possibility of using a particular Hamiltonian by Berry, which enables us to evolve system adiabatically in arbitrarily short time. In the final part of this thesis, we explain the concept of quantum phase transitions. We discuss a relationship between quantum phase transitions and adiabatic quantum computing and show that adiabatic quantum computing scales polynomially with the number of qubits only for quantum phase transitions of second or higher order. Powered by TCPDF (www.tcpdf.org)
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.
The model of adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its exact computational power has been unknown. We settle this question and describe an efficient adiabatic simulation of any given quantum algorithm. This implies that the adiabatic computation model and the standard quantum circuit model are polynomially equivalent. We also describe an extension of this result with implications to physical implementations of adiabatic computation. We believe that our result highlights the potential importance of the adiabatic computation model in the design of quantum algorithms and in their experimental realization.
In the recent years, the field of adiabatic quantum computing has gained importance due to the advances in the realisation of such machines, especially by the company D-Wave Systems. These machines are suited to solve discrete optimisation problems which are typically very hard to solve on a classical computer. Due to the quantum nature of the device it is assumed that there is a substantial speedup compared to classical HPC facilities. We explain the basic principles of adiabatic quantum computing as well as its advantages and limitations. By using a quantum computer simulation software we present how discrete optimisation problems, like map colouring and the maximal Clique problem, can be solved. In addition, we investigate the applicability of adiabatic quantum computing to DLR specific problems.
This paper extensively studies classical and quantum computing paradigms, analysing their basic principles, architectural distinctions, computational power, and real-world applications. We introduce a formal mathematical model to define both models of computation and compare their strengths and weaknesses. Through a thorough analysis of computational complexity, we prove the theoretical superiority of quantum algorithms for certain problem domains. Moreover, recent experimental implementations of quantum computer structures are discussed here, and problems and probable development directions are marked. The study shows that, whereas quantum computing promises to be ideal for specific computationally hard issues theoretically, implementation challenges in practice remain vast. This contribution to the argument of next-generation computing architecture further illuminates prospects for future advancement in computational sciences.