Los Alamos SLc O S A L A M Oence 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 Cover A 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 counter containing a tiny bit of very long-lived radioactive material. The decay of one atom will cause the contraption to shatter the flask and poison the cat. What is the quantum mechanical wave function of this system before we look inside? It is a strange superposition in which the cat is dead and alive at the same time! Clearly, Schrödinger warns us not to ascribe too much reality to the wave function. But perspectives change. Almost seven decades later, scientists are manipulating quantum superpositions in ways that make them seem almost tangible. In computation and communication, single qubits and multiple qubits are presenting new opportunities. One example is Peter Shor’s famous quantum factoring algorithm. The beginning of the relevant quantum computing network is shown at the lower left. Another example is quantum cryptography, the new wave for communicating secret keys and a remarkable departure 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 the Big Bang, when it all started. Moving down, along the thin right leg, and up, along the thick left leg of the U, symbolically traces the evolution of the universe—from small to large. It is by observing single photons from the distant past that the early universe becomes 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 Editor Necia Grant Cooper Managing Editor Ileana G. Buican Science Writer Information, Science, Jay A. Schecker Designer and Technology in a Gloria E. Sharp Illustrators Quantum World Andrea J. Kron Chris D. Brigman David R. Delano Editorial Support Faith J. Harp Composition Support Joy E. Baker Wendy M. Burditt Jeanne M. K. Bowles Photographers Richard C. Robinson John A. Flower Printing Coordination Guadalupe D. Archuleta Address mail to Los Alamos Science Mail Stop M711 Los Alamos National Laboratory Los Alamos, NM 87545 [email protected] Fax: 505-665-4408 Tel: 505-667-1447 Los Alamos Sc ence Number 27 2002 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 . 46 Mark Ettinger Quantum State Entanglement—Creation, Characterization, and Application . 52 Daniel F. V. James and Paul G. Kwiat A New Face for Cryptography . 68 Jane E. Nordholt and Richard J. Hughes Quantum Science Decoherence and the Transition from Quantum to Classical—Revisited . 86 Wojciech H. Zurek The Emergence of Classical Dynamics in a Quantum World . .110 Tanmoy Bhattacharya, Salman Habib, and Kurt Jacobs Quantum Feedback Control—How Can We Control Quantum Systems without Disturbing Them? . .126 Salman 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 iv Information, Science, and Technology in a Quantum World Schrödinger Cats in Atom-Trap BECs . .166 Diego A. R. Dalvit and Jacek Dziarmaga Experiments on Cold Trapped Atoms . .168 David J. Vieira and Xinxin Zhao Quantum Information with Trapped Strontium Ions . .178 Dana J. Berkeland Theory of Single-Spin Detection with a Scanning Tunneling Microscope . .184 Alexander V. Balatsky and Ivar Martin Quantum Computation Introduction to Quantum Error Correction . .188 Emanuel Knill, Raymond Laflamme, Alexei Ashikhmin, Howard N. Barnum, Lorenza Viola, and Wojciech H. Zurek NMR and Quantum Information Processing . .226 Raymond 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 . .260 Lorenza Viola and Evan M. Fortunato Ion-Trap Quantum Computation . .264 Michael 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 v.