Progress report and summary of future plans.

Over the last year, we

1. Developed analog quantum error-correcting routines for continuous quantum variables such as position and momentum.

2. Developed microscopic analogs of the Greenberger-Horne-Zeilinger experiment to test aspects of quantum nonlocality. Experiments are planned for the coming year.

3. In collaboration with David Cory and the DARPA NMR quantum computation project, performed an experimental demonstration of a quantum feedback loop. Used NMR techniques to enact a quantum feedback loop and to transfer entanglement from a controller spin to a target spin.

4. In collaboration with Ike Chuang and the DARPA NMR quantum computation initiative, performed an experimental demonstration of an intrinsically quantum algorithm.

5. Developed a quantum theory of information-processing lasers and masers, a la Maxwell's demon. Experiments are planned for the coming year.

6. With S.M. Shahriar P. Hemmer, developed novel techniques for quantum computation by combining spectral hole burning with adiabatic passage {\it a la} Kimble.

7. With T. Orlando and H. Mooij, developed designs for quantum logic devices using superconducting circuits in quantum regime.

8. With L. Viola, designed quantum control methods for enhancing stability and reducing decoherence in quantum optical and magnetic resonance spin systems.

9. With D. Abrams, showed that nonlinear quantum mechanics can be used in conjunction with quantum computation to solve NP-complete problems in polynomial time.

10. With D. Abrams, developed algorithms for determining the eigenvalues and eigenvectors of a quantum systems more rapidly than is possible classically.

11. Organized a conference, `Experimental Realizations of Quantum Logic,' at Harvard, ITAMP, Aug. 1-16th, 1997.

Over the next 6 month period we intend to

1. Develop a method for realizing Kitaev's fault-tolerant quantum computation schemes by quantum simulation.

2. Perform Greenberger-Horne-Zeilinger experiments using NMR.

3. Develop methods of quantum feedback control appropriate for cavity QED quantum computing techniques.

4. Realize quantum Fourier transforms and quantum chaotic maps such as the Baker's map using NMR and evaluate their properties experimentally.

5. Develop protocols for combining NMR with spin polarization and optical pumping methods to extend the range of NMR quantum computing to many bits.

6. Finish book on quantum computation.

Papers:

Lloyd, S., ``Universe as Quantum Computer," Complexity, 3/1, 32-35, 1997.

Lloyd, S., and D. Abrams, ``Simulation of Many-Body Fermi Systems on a Universal Quantum Computer," Physical Review Letters 79, 2586-2589, 1997. {Outgrowth of supervised student research}

Lloyd, S., ``Quantum-Mechanical Maxwell's Demon," Physical Review A 56, 3374-3382, 1997.

Lloyd, S., ``Microscopic Analogs of the Greenberger-Horne-Zeilinger Experiment,'' Physical Review A 57 R1473-1476, 1998.

Lloyd, S., and J.J.-E. Slotine, ``Analog Quantum Error Correction,'' Physical Review Letters, 80, 4088-4091, 1998.

Lloyd, S., and I.L. Chuang, L.M.K. Vandersypen, X. Zhou, D.W. Leung, ``Experimental Realization of a Quantum Algorithm,'' Nature, May, 1998.

Lloyd, S., ``Unconventional Quantum Computing Devices,'' in Unconventional Models of Computation, C.S. Calude, J. Casti, M.J. Dinneen, eds., Springer, Singapore, 1998.

Lloyd, S., and D. Abrams, ``Computational Complexity and Physical Law,'' proceedings of the NASA Conference on Quantum Computation and Quantum Coherence, Palm Springs, February, 1998. Springer, Singapore, 1998.

Lloyd, S., and D. Abrams, ``Nonlinear Quantum Mechanics Allows the Rapid Solution of NP-complete and \#P Problems,'' submitted to Physical Review Letters, January, 1998.

Presentations:

June 1997, ``NMR Realizations of the GHZ Experiment,'' International Workshop on Quantum Coherence, Ventura.

June 1997, ``NMR Quantum Computation,'' Conference on Quantum Computation, Torino.

June 1997, ``Quantum Information Processing,'' Finmeccanica Seminar, Rome.

August 1997, ``What Makes a Good Quantum Logic Device?'' Harvard Workshop on Experimental Realizations of Quantum Logic.

August 1997, ``Microscopic Realizations of the GHZ Experiment,'' Cambridge University, Department of Applied Mathematics and Theoretical Physics seminar.

August 1997, ``What Makes a Good Quantum Logic Device?'' Harvard Workshop on Experimental Realizations of Quantum Logic.

November 1997, ``Quantum Computation,'' National Academy of Sciences Frontiers of Science Meeting, Irvine.

December 1997, ``Quantum Computation and Quantum Control,'' MIT Electrical Engineering and Computer Science Colloquium.

January 1998, ``Quantum Computation,'' Keynote speach, International Workshop on Unconventional Computation Devices, Auckland, New Zealand.

February 1998, Dan Abrams, ``Nonlinear Quantum Mechanics Allows the Rapid Solution of NP-Complete Problems,'' Palm Springs Quantum Computation conference.