Address:
My work consists of developing and applying mathematical and physical
tools to better understand the limitations and utilize the
capabilities of information processing resources. I use ideas and
results from discrete mathematics, linear and multilinear algebra,
information theory, the theory of computation and theoretical physics,
which I have applied to automated reasoning, learning theory,
numerical methods and the human genome project. Since 1996, my focus
has been on quantum information processing, with contributions to
quantum coding theory, models of computation, algorithms and
technology.
Quantum information
processing: The theoretical,
experimental and technological areas covering the use of quantum
mechanics for communication and computation.
Papers are arranged by topic. The bibliographic information is
sometimes followed by
[x], where
x (at least
4) is the total citations as of 02/06/06, according to the Science
Citation Index (SCI). The SCI lists about 60 papers authored or
coauthored by me where my contribution is significant. My papers and
preprints have been cited about 3100 times in total. The number of
papers in quantum information processing listed for 2000 and 2001 in
the SCI are 329 and 406, respectively.1 Unpublished reports are offset and in small
print.
Links are
for electronic versions of papers. The journal versions may require
subscriptions. ArXiv versions are older but may contain additional
information if there were space constraints.
See also: E. Knill, R. Laflamme, and W. H. Zurek.
See also:
G. Ortiz, J. E. Gubernatis, E. Knill, and R. Laflamme.
Document information: Last revised 7 February 2006.
Contents
Education and Employment
1984
MS/BS
Physics
University of Massachusetts at Boston
1984-6
Res. Asst.
Nuclear Physics
Massachusetts Inst. Tech.
1991
Ph.D.
Mathematics
University of Colorado at Boulder
Thesis: ``Generalized Degrees and Densities for Families of Sets''
Adviser: R. Laver
1991-2
Res. Assoc.
Computer Science
Technical University of Nova Scotia
1992-5
Postdoc
Los Alamos Nat. Lab.
1995-7
Team leader
Los Alamos Nat. Lab.
1995-2003
Technical Staff Member
Los Alamos Nat. Lab.
2003-present
Researcher
Nat. Inst. St. & Tech.
Research Areas
Research Papers
Quantum Information Processing: Theory
Models and Schemes
Compiling gate networks on an ising quantum computer.
Phys. Rev. A, 72:032315/1-5, 2005.
Journal version.
Reprint.
Optical pumping of quantum dot nuclear spins.
Phys. Rev. Lett., 91:017402/1-4, 2003.
cond-mat/0303575.
[19]
Journal version.
Reprint.
PrEprint from arXiv.
A scheme for efficient linear optics quantum computation.
Nature, 409:46-52, 2001.
[502]
Journal version.
Reprint.
Quantum gates using linear optics and postselection.
Phys. Rev. A, 66(LAUR-01-5973):052306/1-5, 2002.
[19]
Journal version.
Reprint.
PrEprint from arXiv.
Bounds on the probability of success of postselected non-linear sign
shifts implemented with linear optics.
quant-ph/0307015, 2003.
[7]
Journal version.
Reprint.
PrEprint from arXiv.
Fermionic linear optics and matchgates.
Technical Report LAUR-01-4472, Los Alamos National Laboratory, 2001.
quant-ph/0108033.
PrEprint from arXiv.
Efficient linear optics quantum computation.
Technical Report LAUR-00-2936, Los Alamos National Laboratory, 2000.
quant-ph/0006088.
PrEprint from arXiv.
Thresholds for linear optics quantum computation.
Technical Report LAUR-00-3477, Los Alamos National Laboratory, 2000.
quant-ph/0006120.
PrEprint from arXiv.
Constructing qubits in physical systems.
J. Phys. A, 34:7067-7080, 2001.
[16]
Reprint.
PrEprint from arXiv.
On the power of one bit of quantum information.
Phys. Rev. Lett., 81:5672-5675, 1998.
[44]
Journal version.
Reprint.
PrEprint from arXiv.
Efficient refocussing of one spin and two spin interactions for
NMR.
J. Mag. Res., 141:322-325, 1999.
[43]
Journal version.
Reprint.
PrEprint from arXiv.
Effective pure states for bulk quantum computation.
Phys. Rev. A, 57:3348-3363, 1998.
[108]
Journal version.
Reprint.
PrEprint from arXiv.
Controlling Errors
Quantum computing with realistically noisy devices.
Nature, 434:39-44, 2005.
[6]
Journal version.
Reprint.
PrEprint from arXiv.
Scalable quantum computation in the presence of large detected-error
rates.
Phys. Rev. A, 71:042322/1-7, 2005.
Journal version.
Reprint.
PrEprint from arXiv.
Random decoupling schemes for quantum dynamical control and error
suppression.
Phys. Rev. Lett., 94:060502/1-4, 2005.
Journal version.
Reprint.
PrEprint from arXiv.
Fault-tolerant postselected quantum computation: Threshold analysis.
quant-ph/0404104, 2004.
PrEprint from arXiv.
Fault-tolerant postselected quantum computation: Schemes.
quant-ph/0402171, 2004.
PrEprint from arXiv.
Robust dynamical decoupling of quantum systems with bounded controls.
Phys. Rev. Lett., 90:037901/1-4, 2003.
[17]
Journal version.
Reprint.
PrEprint from arXiv.
Non-binary quantum stabilizer codes.
IEEE Trans. Inf. Theory, 47:3065-3072, 2001.
[23]
Reprint.
PrEprint from arXiv.
Dynamical generation of noiseless quantum subsystems.
Phys. Rev. Lett., 85:3520-3523, 2000.
[45]
Journal version.
Reprint.
PrEprint from arXiv.
Theory of quantum error correction for general noise.
Phys. Rev. Lett., 84:2525-2528, 2000.
[114]
Journal version.
Reprint.
PrEprint from arXiv.
Dynamical decoupling of open quantum systems.
Phys. Rev. Lett., 82:2417-2421, 1999.
[151]
Journal version.
Reprint.
PrEprint from arXiv.
Universal control of decoupled quantum systems.
Phys. Rev. Lett., 83:4888-4891, 1999.
[60]
Journal version.
Reprint.
PrEprint from arXiv.
Quantum error detection I: Statement of the problem.
IEEE Trans. Inf. Theory, 46:778-788, 1999.
quant-ph/9906126.
[8]
Reprint.
PrEprint from arXiv.
Quantum error detection II: Bounds.
IEEE Trans. Inf. Theory, 46:789-800, 1999.
quant-ph/9906131.
[5]
Reprint.
PrEprint from arXiv.
Resilient quantum computation.
Science, 279:342-345, 1998.
[139]
Journal version.
Reprint.
Resilient quantum computation.
Science, 293:2395-2395, 2001.
Erratum to correct a misprinted exponent.
Journal version.
Resilient quantum computation: Error models and thresholds.
Proc. R. Soc. Lond. A, 454:365-384, 1998.
[42]
Journal version.
Reprint.
PrEprint from arXiv.
Non-binary unitary error bases and quantum codes.
Technical Report LAUR-96-2717, Los Alamos National Laboratory, 1996.
quant-ph/9608048.
[35]
PrEprint from arXiv.
Group representations, error bases and quantum codes.
Technical Report LAUR-96-2807, Los Alamos National Laboratory, http://www.c3.lanl.gov/~knill, 1996.
quant-ph/9608049.
[20]
PrEprint from arXiv.
Concatenated quantum codes.
Technical Report LAUR-96-2808, Los Alamos National Laboratory, 1996.
quant-ph/9608012.
[26]
PrEprint from arXiv.
Assumptions for fault tolerant quantum computing.
Technical Report LAUR-96-2718, Los Alamos National Laboratory, 1996.
PrEprint.
Accuracy threshold for quantum computation.
Technical Report LAUR-96-2199, Los Alamos National Laboratory, 1996.
quant-ph/9610011.
PrEprint from arXiv.
A theory of quantum error correcting codes.
Phys. Rev. A, 55:900-911, 1997.
[287]
Journal version.
Reprint.
PrEprint from arXiv.
Quantum Information Theory
Nature and measure of entanglement in quantum phase transitions.
Phys. Rev. A, 70:042311/1-21, 2004.
[7]
Journal version.
PrEprint from arXiv.
A subsystem-independent generalization of entanglement.
Phys. Rev. Lett., 92:107902/1-4, 2004.
[15]
Journal version.
PrEprint from arXiv.
Generalizations of entanglement based on coherent states and convex
sets.
Phys. Rev. A, 68:032308/1-21, 2003.
quant-ph/0207149.
[6]
Journal version.
Reprint.
PrEprint from arXiv.
Quantum dynamics of two coupled qubits.
Phys. Rev. A, 65:032316/1-10, 2003.
[7]
Journal version.
Reprint.
PrEprint from arXiv.
Reversing quantum dynamics with near-optimal quantum and classical
fidelity.
J. Math. Phys., 43:2097-2106, 2002.
quant-ph/0004088.
[4]
Journal version.
Reprint.
PrEprint from arXiv.
On quantum fidelities and channel capacities.
IEEE Trans. Inf. Theory, 46:1317-1329, 2000.
[36]
Reprint.
PrEprint from arXiv.
Complexity and Algorithms
The quantum query complexity of the hidden subgroup problem is
polynomial.
Information Processing Letters, 91(LAUR-02-5088):438-48, 2004.
PrEprint.
Simulating physical phenomena by quantum networks.
Phys. Rev. A, 65:042323/1-17, 2002.
quant-ph/0108146.
[4]
Journal version.
Reprint.
PrEprint from arXiv.
The challenge of quantum computer simulations of physical phenomena.
Nuc. Phys. B-Proc. Supp., 106:151-158, 2002.
Quantum algorithms for fermionic simulations.
Phys. Rev. A, 64:022319/1-14, 2001.
[6]
Journal version.
Reprint.
PrEprint from arXiv.
Quantum algorithms for fermionic simulations.
Phys. Rev. A, 65:029902/1-1, 2002.
Erratum to add omitted term to universal fermionic Hamiltonian PRA 65
029902/1-1 (2002)..
Journal version.
Quantum computation and quadratically signed weight enumerators.
Information Processing Letters, 79:173-179, 2001.
quant-ph/9909094.
Reprint.
PrEprint from arXiv.
Quantum randomness and nondeterminism?
Technical Report LAUR-96-2186, Los Alamos National Laboratory, 1996.
quant/ph/9610012.
PrEprint from arXiv.
Quantum pseudo-code for factor finding and discrete logarithm.
preprint, 1996.
PrEprint.
Conventions for quantum pseudocode.
Technical Report LAUR-96-2724, Los Alamos National Laboratory, 1996.
PrEprint.
Approximation by quantum circuits.
Technical Report LAUR-95-2225, Los Alamos National Laboratory, 1995.
quant-ph/9508006.
[4]
PrEprint from arXiv.
Bounds for approximation in total variation distance by quantum
circuits.
Technical Report LAUR-95-2724, Los Alamos National Laboratory, 1995.
quant-ph/9508007.
PrEprint from arXiv.
An analysis of Bennett's pebble game.
Technical Report LAUR-95-2258, Los Alamos National Laboratory, 1995.
PrEprint.
On Shor's quantum factor finding algorithm: Increasing the
probability of success and tradeoffs involving the Fourier transform
modulus.
Technical Report LAUR-95-3350, Los Alamos National Laboratory, 1995.
PrEprint.
Quantum Information Processing: Experiment
Benchmarking
Verification procedures for quantum noiseless subsystems.
Phys. Rev. A, 68:032311/1-5, 2003.
quant-ph/0303165.
Journal version.
Reprint.
PrEprint from arXiv.
Implementation of the five qubit error correction benchmark.
Phys. Rev. Lett., 86:5811-5814, 2001.
[34]
Journal version.
Reprint.
PrEprint from arXiv.
An algorithmic benchmark for quantum information processing.
Nature, 404:368-370, 2000.
[85]
Journal version.
Reprint.
PrEprint from arXiv.
Experimental quantum error correction.
Phys. Rev. Lett., 81:2152-2155, 1998.
[113]
Journal version.
Reprint.
PrEprint from arXiv.
A study of quantum error correction by geometric algebra and
liquid-state NMR spectroscopy.
Mol. Phys., 98:1347-1363, 2000.
[12]
Journal version.
Reprint.
PrEprint from arXiv.
Ion Trap Demonstrations
Creation of a six-atom``schrödinger cat'' state.
Nature, 438:639-642, 2005.
Journal version.
Reprint.
Enhanced quantum state detection efficiency through quantum
information processing.
Phys. Rev. Lett., 94:010501/1-4, 2005.
Journal version.
Reprint.
Realization of quantum error correction.
Nature, 432:602-605, 2004.
[16]
Journal version.
Reprint.
Deterministic quantum teleportation of atomic qubits.
Nature, 429:737-739, 2004.
[62]
Journal version.
Reprint.
NMR Demonstrations
Liquid-state NMR simulations of quantum many-body problems.
Phys. Rev. A, 71:032344/1-11, 2005.
Journal version.
Reprint.
Exploring noiseless subsystems via nuclear magnetic resonance.
Phys. Rev. A, 67:062303/1-16, 2003.
Journal version.
Reprint.
Interpretation of tomography and spectroscopy as dual forms of
quantum computations.
Nature, 418:59-62, 2002.
quant-ph/0109072.
[26]
Journal version.
Reprint.
PrEprint from arXiv.
Experimental realization of noiseless subsystems for quantum
information processing.
Science, 293:2059-2063, 2001.
[47]
Journal version.
Reprint.
Complete quantum teleportation.
Nature, 396:52-55, 1998.
[141]
Journal version.
Reprint.
PrEprint from arXiv.
Quantum simulation with natural decoherence.
Phys. Rev. A, 62:032309/1-9, 2000.
[17]
Journal version.
Reprint.
Quantum simulation of a three-body interaction Hamiltonian on an
NMR quantum computer.
Phys. Rev. A, 61:012302/1-6, 2000.
[20]
Journal version.
Reprint.
PrEprint from arXiv.
NMR Greenberger-Horne-Zeilinger states.
Phil. Trans. R. Soc. Lond. A, 356:1941-1948, 1997.
[38]
Journal version.
Reprint.
PrEprint from arXiv.
NMR-GHZ.
In Lecture Notes in Computer Science, volume 1509, pages
357-363, 1999.
Evaluation
Decoherence bounds on quantum computation with trapped ions.
Phys. Rev. Lett., 77:3240-3243, 1996.
[40]
Journal version.
Reprint.
PrEprint from arXiv.
Discrete Mathematics
Grouptesting for Molecular Biology
Group testing problems with sequences in experimental molecular
biology.
In B. Carpentieri et al, editor, Compression and Complexity of
SEQUENCES 1997, pages 11-13, Los Alamitos, CA, 1997. IEEE Comput. Soc.
A comparative survey of non-adaptive pooling designs.
In Genetic Mapping and DNA Sequencing, volume 81 of IMA Volumes in Mathematics and its Applications, pages 133-155. Springer
Verlag, 1995.
Lower bounds for identifying subset members with subset queries.
In Proceedings of the Sixth Annual ACM-SIAM Symposium on
Discrete Algorithms, pages 369-377. Association for Computing Machinery &
Society for Industrial and Applied Mathematics, 1995.
[9]
PrEprint.
Interpretation of pooling experiments using the Markov chain Monte
Carlo method.
Journal of Computational Biology, 3(LAUR-95-2402):395-406,
1996.
[6]
PrEprint.
Efficient pooling designs for library screening.
Genomics, 26:21-30, 1995.
[37]
Group testing problems in experimental computational biology.
Technical Report LAUR-95-1503, Los Alamos National Laboratory, 1994.
PrEprint.
Extremal Combinatorics
Extreme k-families.
Europ. J. Combinatorics, 16:23-33, 1995.
PrEprint.
The size of k-pseudotrees.
Discrete Mathematics, 141:185-194, 1995.
Reprint.
PrEprint.
Restricted routing and wide diameter of the cycle prefix network.
In DIMACS Interconnection Networks and Mapping, pages 31-46,
1995.
PrEprint.
Notes on the connectivity of Cayley coset digraphs.
Technical Report LAUR-94-3719, Los Alamos National Laboratory, 1994.
PrEprint.
Invertible families of sets of bounded degree.
Congressus Numerantium, 100-104, 1994.
PrEprint.
Graph generated union-closed families and the union-closed sets
conjecture.
Technical Report LAUR-93-2297, Los Alamos National Laboratory, 1993.
PrEprint.
Inverting sets and the packing problem.
In Conference on Graph Theory, Combinatorics, Algorithms and
Applications, pages 351-366, 1992.
Generalized Degrees and Densities for Families of Sets.
PhD thesis, University of Colorado at Boulder, 1991.
PrEprint.
Other Contributions
Molecular Biology
An integrated physical map of human-chromosome-16.
Nature, 377:335-365, 1995.
[93]
Numerical Methods
Minimal residual method stronger than polynomial preconditioning.
SIAM J. Matrix An. and App., 17:707-729, 1995.
[7]
Journal abstract
PrEprint.
Learning Theory
Some results concerning off-training-set and IID error for the
Gibbs and the Bayes optimal generalizers.
Statistics and Computing, 8:35-54, 1998.
Reprint.
PrEprint.
Computer Logic
Equality and abductive residua for horn clauses.
Theoretical Computer Science, 120:1-44, 1993.
PrEprint.
Abduction in logic programming with equality.
In Proceedings of the International Conference on Fifth
Generation Computer Systems, pages 539-545, 1992.
Transformational methods for clausal theorem proving with equality.
Technical Report LAUR-95-1983, Los Alamos National Laboratory, 1992.
PrEprint.
Completing fault models for abductive diagnosis.
Technical Report LAUR-92-3370, Los Alamos National Laboratory, 1992.
PrEprint.
Miscellaneous
Longitudinal response functions and sum-rules for quasielastic
electron-scattering from H-3 and He-3.
Phys. Rev. Lett., 61:1706-1709, 1988.
[30]
Isoscalar and isovector form-factors of H-3 and He-3 for q below
2.9 fm-1 from electron-scattering measurements.
Phys. Rev. Lett., 59:1537-1540, 1987.
[59]
Survey Papers
Introduction to quantum information processing.
LA Science, 27(LAUR-01-4761):2-45, 2002.
quant-ph/0207171.
Hypertext prEprint.
Introduction to quantum error correction.
LA Science, 27(LAUR-01-6115 and LAUR-02-4311):188-225, 2002.
quant-ph/0207170.
Hypertext prEprint.
Introduction to NMR quantum information processing.
LA Science, 27(LAUR-02-6132):226-259, 2002.
quant-ph/0207172.
Hypertext prEprint.
Quantum information processing.
Technical Report LAUR-00-5265, Los Alamos National Laboratory, 2000.
quant-ph/0010058, accepted for Supplement III, Encyclopedia of
Mathematics, Kluwer.
PrEprint from arXiv.
Theory of quantum computation.
Technical Report LAUR-00-5267, Los Alamos National Laboratory, 2000.
quant-ph/0010057, accepted for Supplement III, Encyclopedia of
Mathematics, Kluwer.
PrEprint from arXiv.
NMR based quantum information processing: Achievements and
prospects.
Fort. Phys., 48:875-907, 2000.
[72]
Journal version
Reprint.
Mathematical Reviews
Access to the following links requires a subscription to Mathematical Reviews.
Invited Lectures
Quantum Information Processing
Fault-tolerant quantum computation workshop,
IBM, Yorktown Heights, New York, Aug 29, 2005.
Visuals of talk at IBM
SPRC Annual Meeting, Stanford, Sept 13, 2004.
Quantum Information and Control Conference, Toronto, July 22, 2004
NIST Gaithersburg, January 22, 2003.
Transparencies and recording of talk (realplayer) from NIST
NIST Boulder, December 3, 2002.
Oregon Center for Optics, U. Oregon, November 11, 2002.
NIST Boulder, December 4, 2002.
NANO2002 Workshop II, IPAM, UCLA, October 21, 2002.
Transparencies from IPAM.
QIP2002, IBM NY, January 15, 2002.
Math Colloquium, Univ. of Cal. at Santa Barbara, November 29, 2001.
Math. Phys and Stat. Mech. Seminar, Univ. of Cal. at Davis, November 27, 2001.
Transparencies.
CS Colloquium, U. of Colorado, Boulder, March 13, 2003.
CS Colloquium, U. Oregon, November 14, 2002.
CS Colloquium, Univ. of Cal. at Santa Barbara, November 19, 2001.
Transparencies.
Mathematics Department Seminar, Univ. of New Mexico, February 27, 2002.
Mathematics Department Colloquium, Univ. of Cal. at Santa Barbara, May 31, 2001.
Transparencies.
CEPI Seminar, Santa Fe Institute, October 4, 2000.
ACS National Meeting, Washington DC, August 24, 2000.
Transparencies.
Mathematics Department Colloquium, University of Nevada at Reno, December 2, 1999.
Transparencies.
DIMACS Workshop, Rutgers University, November 11, 1999.
Complexity, Comp. and the Phys. of Inf., Newton Inst., Cambridge, Eng., July 22, 1999.
Transparencies.
Institute for Mathematics and its Applications, University of Minnesota, July, 1998.
Transparencies from the IMA.
Instituto Superior Tecnico, Lisbon, Portugal, May 20, 1998.
ETH, Zürich, Switzerland, May 18, 1998.
Dagstuhl, Germany, May 14, 1998.
Transparencies.
The Conference on High Speed Computing, Salishan Lodge, Oregon, April 23, 1998.
Transparencies.
Quantum Technologies Seminar, Los Alamos Nat. Lab., April 8, 1998.
Transparencies.
APS Tutorial on Quantum Computation, Los Angeles, March 16, 1998.
APS Tutorial on Quantum Computation, Los Angeles, March 16, 1998.
UNM Physics Colloquium, Albuquerque, May 5/24, 1997.
Workshop on Q. Coh. and Comp., ITP, Univ. of Cal. at Santa Barbara, October, 1996.
Workshop on Quantum Computation, ISI, Torino, Italy, June, 1996.
SQUINT Workshop, Albuquerque, May 1, 1999.
Workshop on Q. Inf. Proc. and NMR, Harvard Smithsonian, February 24, 1999
Transparencies.
Quantum Computation Workshop, ISI, Torino, Italy, July 17, 1997.
Discrete Mathematics
Eight Quadr. Int. Conf. on Gr. Th., Comb., Alg. and App., West. Mich. University, June, 1996.
26'th SE Int. Conf. on Comb., Gr. Th. and Comp., Boca Raton, Florida, March, 1995.
SODA'95, January, 1995.
DIMACS Workshop on Sequencing and Mapping, DIMACS, October, 1994.
DIMACS Computational Biology Colloquium, DIMACS, October, 1994.
Sandia National Lab. Workshop on Comp. Molec. Biology, Albuquerque, NM, June 1994.
Computer Science Colloquium, Ransselaer Polytechnic Institute, September, 1993.
NYU, New York, October, 1994.
7'th SIAM conference on Discrete Mathematics, Albuquerque, NM, June, 1994.
Transparencies.
Others
Colorado Conference on Iterative Methods, Breckenridge, Colorado, April, 1994.
Conference for Fifth Generation Computer Systems, Tokyo, Japan, June, 1992.
Los Alamos National Laboratory, Los Alamos, New Mexico, March, 1992.
Tutorials and Teaching
Univ. of Colorado Physics Dept., One credit course, Spring 2004.
For the ``Coherent Tangles'', 2003.
Transparencies
IAP Seminars, MIT, January 18-25, 2002.
Six tutorial lectures, ITP at the Univ. of Cal. at Santa Barbara, Nov. 14, Dec 3, 2001.
Transparencies from the ITP:
Overview,
I,
II,
III,
IV,
V.
Quantum Computing Summer School, The Fields Institute, Toronto, May 15/16, 2001.
Transparencies from the Fields Institute.
IAP Seminars, MIT, January 21-24, 1999.
3 credit course, Tech. Univ. of Nova Scotia, Spring 1992.
3 credit course, Tech. Univ. of Nova Scotia, Fall 1991.
Advising
Software Development
Language: C++. (2005)
Languages: Mathematica, Octave. (2004)
Languages: Matlab, Perl.
(2000)
Languages: C++. (1994)
Languages: Perl, HTML. (1992)
Miscellaneous
Footnotes
2006-02-07