Quantum Circuit Simulation
Recent progress in atomic physics, semiconductors, and optical technologies lead to the need to control matter at an unprecedented scale. However, atoms, electrons and photons do not obey laws of classical physics and instead are governed by quantum mecha
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George F. Viamontes • Igor L. Markov • John P. Hayes
Quantum Circuit Simulation
George Viamontes Department of Electrical Engineering & Computer Science Advanced Computer Architecture Laboratory [email protected] http://www.eecs.umich.edu/~gviamont/
Igor L. Markov Department of Electrical Engineering & Computer Science University of Michigan Ann Arbor, MI 48109-2121 USA [email protected]
John P. Hayes Department of Electrical Engineering & Computer Science University of Michigan Ann Arbor, MI 48109-2121 USA [email protected]
ISBN 978-90-481-3064-1 e-ISBN 978-90-481-3065-8 Springer Dordrecht Heidelberg London New York Library of Congress Control Number: 2009929020 © Springer Science + Business Media B.V. 2009, Corrected printing 2009 No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Recent scientific advances, both experimental and algorithmic, have brought quantum information processing closer to reality. The ability to process information “quantumly” already allows ultra-precise metrology and more secure communication, and quantum algorithms allow computations such as factoring to be done significantly faster than we know how to do them on classical computers. With these advances, quantum simulation has become an increasingly important topic for both theoretical and engineering reasons. On the theoretical front, progress toward defining the class of circuits that can be simulated efficiently on a classical computer has and will continue to lead to a deeper understanding of the power of quantum computation. Even though efficient simulation of all quantum circuits may not be possible, the circuits that will most likely make up the majority of operations on a quantum computer can in fact be simulated efficiently. These are fault-tolerant error-correction circuits; they are composed of only Clifford-group gates, which, as this book demonstrates, can be simulated surprisingly efficiently on a classical computer. Recent results suggest that larger classes of circuits can also be simulated efficiently on classical computers. From a circuit perspective, efficient simulation can result from operating with a restricted set of gates, such as the Clifford-group gates, or from operating with an arbitrary gate set if the circuit has a small treewidth, as Markov and Shi have shown. From a physical perspective, efficient simulation can also result from limiting the amount of entanglement in the intermediate states of the computation. For example, Vidal has shown that one-dimensional many-body systems can be simulated efficiently and more recently,
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