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Adiabatic Quantum Computation and Simulation

Vlad Goldenberg, Maciek Sakrejda

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

Adiabatic quantum computation came into the spotlight of quantum information processing researchers several years ago. The idea suggested an alternative approach to quantum computing which can be shown to be equivalent to the

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While adiabatic quantum computation (AQC) possesses some intrinsic robustness to noise, it is expected that a form of error control will be necessary for large scale computations. Error control ideas developed for circuit-model quantum computation do not transfer easily to the AQC model and to date there have been two main proposals to suppress errors during an AQC implementation: energy gap protection and dynamical decoupling. Here we show that these two methods are essentially equivalent and can be analyzed within the same formalism. We analyze the effectiveness of such error suppression techniques and identify critical constraints on the performance of error suppression in AQC, suggesting that error suppression by itself is insufficient for fault-tolerant, large-scale AQC and that a form of error correction is needed.
The basic ideas in quantum information processing (QIP) dates from several decades back, however the research development based on these ideas started only a little more than a decade ago.The initial ideas of quantum information processing emerged from the fundamental difference between quantum physics and classical physics.It was, and still is, hard to analyse quantum systems in general, and in particular when a quantum system gets bigger, it soon becomes intractable even with high performance computers.To analyse a quantum system, Feynman suggested that we should use a computer based on quantum physics.This is the initial idea of quantum information processing.By contrast to quantum computers, all non-quantum-physicsbased computers, that is, all the existing ones including high performance computers, are now called "classical computers" indicating computers based on classical physics.The research on quantum information processing did not take off until 1990s.Until then, the technology to manipulate quantum was yet not ready, and more importantly, the theory for QIP was not developed enough to show the way to efficiently use quantum nature to carry out computation.Quantum key distribution (QKD) was one of the first QIP protocols successfully implemented and developed in 1990s.QKD is a protocol to exchange secure key material between authenticated users at a distance.Thanks to a property that overlapping quantum states cannot be cloned without trace of interaction, the protocol can detect an eavesdropper by measuring the quantum states and post-processing the signals via classical communication between the users.As one-time pad using QKD was proven to be secure against an eavesdropper who has unbounded ability, unlike conventional cryptogra-
Information is physical. Today’s information processing and communication are classical: they are based upon the laws of Newton’s and Maxwell’s classical physics. This assertion holds all the way, from commercial computers and networks, up to their most abstract models, e.g. Turing machines. Research in quantum information was born some twenty five years ago, with the encounter of two major scientific achievements of the 20th century, namely quantum physics and information sciences. A technological motivation for that is an extrapolation of Moore’s law which seems to indicate that the amount of matter needed for one bit will be reduced to one particle sometimes before year 2020. A deeper, scientific driving force of this interdisciplinary research is that of looking for the consequences of having computation and communication based directly upon the laws of quantum physics, i.e. our current ultimate knowledge of the world of elementary particles, as described by quantum mechanics. Breakthroughs in cryptography, communications, information theory and algorithmics have shown that this transplantation from classical to quantum has far reaching consequences, both quantitative and qualitative, and opens new avenues for research within the foundations of computer science and physics. The principles 388 and most striking results and hot topics of this promising way of encoding, processing and communicating information are briefly introduced in this chapter from a mostly computer science point of view, with detailed examples in algorithmics and in cryptography. At the end of the chapter, a short list of some significant articles, textbooks and reports on quantum information are suggested for further reading.