Sc enceLos AlamosL O S A L A M O S N A T I O N A L L A B O R A T O R Y

Number 27 2002 Information, Science, and Technology in a Quantum World

About the CoverA strange-looking cat welcomes you to the rich world of quantum research. Its sphere-like eyes represent the qubit, the quantum version of a classical bit. They point “up” and“down” in a quantum superposition, reminding us of Schrödinger’s famous “cat para-dox.” A cat is trapped in a steel chamber with a “diabolical device”—a flask of cyanic

acid attached to a Geiger countercontaining a tiny bit of verylong-lived radioactive material.The decay of one atom willcause the contraption to shatterthe flask and poison the cat.What is the quantum mechanicalwave function of this systembefore we look inside? It is a strange superposition inwhich the cat is dead and alive at the same time! Clearly,Schrödinger warns us not toascribe too much reality to thewave function.

But perspectives change. Almostseven decades later, scientists are manipulating quantumsuperpositions in ways that makethem seem almost tangible. Incomputation and communication,single qubits and multiple qubitsare presenting new opportunities.

One example is Peter Shor’s famous quantum factoring algorithm. The beginning of therelevant quantum computing network is shown at the lower left. Another example isquantum cryptography, the new wave for communicating secret keys and a remarkabledeparture from the stone cipher wheel of long ago seen in the background.

At upper right is John Wheeler’s drawing of the universe, a giant U, with the observer, a big eye, looking backward in time. The thin upper right end of the U represents theBig Bang, when it all started. Moving down, along the thin right leg, and up, along thethick left leg of the U, symbolically traces the evolution of the universe—from small tolarge. It is by observing single photons from the distant past that the early universebecomes part of our reality. In Wheeler’s view, our reality ultimately derives from meas-urement of individual quanta—“it from bit.”

(The drawing of the abacist at bottom right is used with permission from Cliché Bibliothèque Nationale de France, Paris.Permission for use of the confederate cypher wheel is from the Louis Kruh Collection.)

For past Los Alamos Science issues, see our Web site at the following URL:http://www.lanl.gov/external/science/lascience/index.html

Information, Science,and Technology in a

Quantum World

EditorNecia Grant Cooper

Managing EditorIleana G. Buican

Science WriterJay A. Schecker

DesignerGloria E. Sharp

IllustratorsAndrea J. KronChris D. BrigmanDavid R. Delano

Editorial SupportFaith J. Harp

Composition SupportJoy E. BakerWendy M. BurdittJeanne M. K. Bowles

PhotographersRichard C. RobinsonJohn A. Flower

Printing CoordinationGuadalupe D. Archuleta

Address mail toLos Alamos ScienceMail Stop M711Los Alamos National LaboratoryLos Alamos, NM 87545

lascience@lanl.govFax: 505-665-4408Tel: 505-667-1447

iv

John Wheeler and Richard Feynman on Quantum Theory and Information . . . . . . . . . . . . . . . . . . . . . vi

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x

About This Volume and Quantum Research at Los Alamos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Concepts in Quantum Information Science

Quantum Information Processing—A Hands-on Primer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Emanuel Knill, Raymond Laflamme, Howard N. Barnum, Diego A. Dalvit, Jacek J. Dziarmaga,James E. Gubernatis, Leonid Gurvits, Gerardo Ortiz, Lorenza Viola, and Wojciech H. Zurek

Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

From Factoring to Phase Estimation—A Discussion of Shor’s Algorithm . . . . . . . . . . . . . . . . . 38 Emanuel Knill, Raymond Laflamme, Howard N. Barnum, Diego A. Dalvit, Jacek J. Dziarmaga,James E. Gubernatis, Leonid Gurvits, Gerardo Ortiz, Lorenza Viola, and Wojciech H. Zurek

20 Questions, Quantum Computers, and Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46Mark Ettinger

Quantum State Entanglement—Creation, Characterization, and Application . . . . . . . . . . . . . . . . . . . . . 52Daniel F. V. James and Paul G. Kwiat

A New Face for Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Jane E. Nordholt and Richard J. Hughes

Quantum Science

Decoherence and the Transition from Quantum to Classical—Revisited . . . . . . . . . . . . . . . . . . . . . . . . 86Wojciech H. Zurek

The Emergence of Classical Dynamics in a Quantum World . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs

Quantum Feedback Control—How Can We Control Quantum Systems without Disturbing Them? . . . .126Salman Habib, Kurt Jacobs, and Hideo Mabuchi

Atom-Trap BECs—A New Laboratory for Studying Superfluidity, Quantum Fluctuations,and Other Quantum Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136

Eddy M. E. Timmermans

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Schrödinger Cats in Atom-Trap BECs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .166 Diego A. R. Dalvit and Jacek Dziarmaga

Experiments on Cold Trapped Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .168David J. Vieira and Xinxin Zhao

Quantum Information with Trapped Strontium Ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .178Dana J. Berkeland

Theory of Single-Spin Detection with a Scanning Tunneling Microscope . . . . . . . . . . . . . . . . . . . . . . .184Alexander V. Balatsky and Ivar Martin

Quantum Computation

Introduction to Quantum Error Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .188Emanuel Knill, Raymond Laflamme, Alexei Ashikhmin, Howard N. Barnum, Lorenza Viola,and Wojciech H. Zurek

NMR and Quantum Information Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .226Raymond Laflamme, Emanuel Knill, David G. Cory, Evan M. Fortunato, Timothy F. Havel,Cesar Miquel, Rudy Martinez, Camille J. Negrevergne, Gerardo Ortiz, Marco A. Pravia,Yehuda Sharf, Suddhasattwa Sinha, Rolando Somma, and Lorenza Viola

Realizing a Noiseless Subsystem in an NMR Quantum Information Processor . . . . . . . . . . . . .260Lorenza Viola and Evan M. Fortunato

Ion-Trap Quantum Computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .264Michael H. Holzscheiter

Toward a Silicon-Based Nuclear-Spin Quantum Computer—Developing the Technology for a Scalable Solid-State Quantum Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .284

Robert G. Clark, P. Chris Hammel, Andrew Dzurak, Alexander Hamilton,Lloyd Hollenberg, David Jamieson, and Christopher Pakes as told to Jay Schecker

Fabricating a Qubit Array with a Scanning Tunneling Microscope . . . . . . . . . . . . . . . . . . . . . . . . . . .302 Marilyn E. Hawley, Geoffrey W. Brown, Michele Y. Simmons, and Robert G. Clark

Information, Science, and Technology in a Quantum World