J. F. Traub and H. Wozniakowski, Path Integration on a Quantum Computer, Quantum Information Processing, 1(5), 365-388, Oct. 2002. LANL preprint quant-ph/0109113.

David Cory's DARPA presentation, April 2002.

David Cory, Integration via a Quantum Information Processor, 2002.

E. Novak, I. H. Sloan and H. Wozniakowski, Tractability of Approximation for Weighted Korobov Spaces on Classical and Quantum Computers, Journal of Foundations of Computational Mathematics, 4, 121-156, 2004. LANL preprint quant-ph/0206023.

E. M. Fortunato, M. A. Pravia, N. Boulant, G. Teklemarian, T. F. Havel and D. G. Cory, Design of Strongly Modulating Pulses to Implement Precise Effective Hamiltonians for Quantum Information Processing, Journal of Chemical Physics, 116 (17), 7599-7606, 2002. LANL preprint quant-ph/0202065.

Y. S. Weinstein, S. Lloyd, J. V. Emerson and D. G. Cory, Experimental Implementation of the Quantum Baker's Map, Physical Review Letters, 89, 157902, 2002. LANL preprint quant-ph/0201064.

G. Teklemariam, E. M. Fortunato, C. C. Lopez, J. Emerson, J. P. Paz and D. G. Cory, A Method for Modeling Decoherence on a Quantum Information Processor, 2002. (ps)

Y. S. Weinstein, J. V. Emerson and D. G. Cory, Fidelity Decay Saturation Level for Initial Eigenstates, Quantum Information Processing, 6, 439-449, 2002. LANL preprint quant-ph/0210063.

J. Emerson, Y. S. Weinstein, S. Lloyd and D. G. Cory, Fidelity Decay as an Efficient Indicator of Quantum Chaos, Physical Review Letters, 89, 284102, 2002 . LANL preprint quant-ph/0207099.

Y. S. Weinstein, S. Lloyd and C. Tsallis, The Edge of Quantum Chaos, Physical Review Letters, 89, 214101, 2002.

W.M. Kaminsky and S.Lloyd. Scalable Architecture for Adiabatic Quantum Computing of NP-Hard Problems, in Quantum Computing and Quantum Bits in Mesoscraper Systems, Kluwer Academic, 2003. LANL preprint quant-ph/0211152.

M. Kwas and H. Wozniakowski, Sharp Error Bounds on Quantum Boolean Summation in Various Settings, J. Complexity, Vol. 20, No. 5, 669-698,2003, LANL preprint quant-ph/0303049.

S. Lloyd, A.J. Landahl, and J-J.E. Slotine, Universal Quantum Interfaces,  Physical Review Letters, 2003. LANL preprint quant-ph/0303048.

P. Jaksch and A. Papageorgiou, Eigenvector Approximation Leading to Exponential Speedup of Quantum Eigenvalue Calculation, Phys. Rev. Lett., 91, 257902, 2003. LANL preprint quant-ph/0308016.

A. Bessen, The Power of Various Real-Valued Quantum Queries, Journal of Complexity, Vol. 20, No. 5, 2004. LANL preprint quant-ph/0308140.

P. Zanardi, D. Lidar and S. Lloyd, Quantum Tensor Product Structures are Observable-Induced, 2003. LANL preprint quant-ph/0308043.

J. Emerson, S. Lloyd, D. Poulin and D. Cory, Estimation of the Local Density States on a Quantum Computer, Physical Review A, 2004. LANL preprint quant-ph/0308164

M. Pravia, N. Boulant, J. Emerson, A. Faird, E. Fortunato, T. Havel and D. Cory, Robust Control of Quantum Information, Journal of Chemical Physics, 119, 9993-10001, 2003. LANL preprint quant-ph/0307062.

H. Gutman, F. Wilhelm, W. Kaminsky and S. Lloyd, Compensation of Decoherence from Telegraph Noise by Means of Bang-Bang Control, 2003. LANL preprint cond-mat/0308107.

A. Papageorgiou, Average case quantum lower bounds for computing the Boolean mean, J. Complexity, Vol. 20, No. 5, 713-731, 2004. LANL preprint quant-ph/0311007.

S. Heinrich, M. Kwas, and H. Wozniakowski, Quantum Boolean Summation with Repetitions in the Worst-Average Setting, Proceedings of the 5th Intrnational Conference on Monte Carlo and Quasi-Monte Carlo Methods, Pringer-Verlag, 2003. LANL preprint quant-ph/0311036.

G. Teklemarian, E. M. Fortunato, C. Lopez, J. Emerson, J. P. Paz and D. G. Cory, A Methodology to Experimentally Explore Quantum Decoherence, Physical Review A, 67, 062316, 1-11, 2003.

E. M. Fortunato, L. Viola, M. A. Pavia, E. Knill, R. Laflamme, T. F. Havel and D. G. Cory, Exploring Noiseless Subsystems via NMR, Physical Review A, 67, 062303, 1-13, 2003.

J. Emerson, Y. Weinstein, M. Saraceno, S. Lloyd and D. G. Cory, Random Circuits for Quantum Information Science, Science, 302, 2089-2100, 2003.

P. Giorda, P. Zanardi and S. Lloyd, Universal Quantum Control in Irreducible State-Space Sectors: Application to Bosonic and Spin-Boson Systems, Physical Review A (to appear).

L. Tian, S. Lloyd and T. P. Orlando, Projective Measurement Scheme for Solid-State Qubits, Physical Review B, 67, R220505, 2003.

S. Sinha, J. Emerson, N. Boulant, E. Fortunato, C. Ramanathan, T. Havel and D. G. Cory, Experimental Implementation of Squeezing Using NMR, Quantum Information Processing, 2003.

N. Boulant, J. Emerson, T. F. Havel and D. G. Cory, Incoherent Processes and Quantum Control, Journal of Chemical Processes, 121, 2955-2961, 2004.

M. Kwas and Y. Li, Worst Case Complexity of Multivariate Feynman-Kac Path Integration, J. Complexity, 19, 730-743, 2003.

G. Boutis, H. Cho, D. Greenbaum, D. G. Cory and C. Ramanathan, Measurement of the Spin Diffusion Rate of Dipolar Order in Single Crystal Calcium Fluoride, Physical Review Letters (to appear).

Y. Weinstein, T. Havel, J. Emerson, N. Boulant, M. Saraceno, S. Lloyd and D. G. Cory, Quantum Process Tomography of the Quantum Fourier Transform, Journal of Chemical Physics, 2004.

P. Zanardi, D. Lidar and S. Lloyd, Quantum Tensor Product Structures are Observable-Induced, Physical Review Letters, 92, 060402, 2004.

J. Emerson, S. Lloyd, D. Poulin and D. G. Cory, Estimation of the Local Density of States on a Quantum Computer, Physical Review A, 2004.

J. M. Fernandez, S. Lloyd, T. Mor and V. Roychowdhury, Algorithmic Cooling of Spins: A Practicable Model for Increasing Polarization, 2004. LANL preprint quant-ph/0401135.

P. Zanardi and S. Lloyd, Universal Control of Quantum Subspaces and Subsystems, Physical Review A, 2003. LANL preprint quant-ph/03050013.

P, Cappellaro, J. Emerson, N. Boulant, C. Ramanathan, S. Lloyd, Entanglement Assisted Metrology, Physical review Letters, 2004.

N. Boulant, Z. Chen, I. Chuang, D. G. Cory, C. Ramanathan, M. Steffen,NMR Quantum Information Processing, Quantum Information Processing, 2004.

D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, O. Regev, Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation, 2004. LANL preprint quant-ph/0405098.

W. M. Kaminsky, S. Lloyd, T. Orlando, Scalable Superconducting Architecture for Adiabatic Quantum computation, submitted to Physical review Letters, 2004.

T. G. Draper, S. A. Kutin, E. M. Rains, K. M. Svore, A Logarithmic-depth Quantum Carry-lookahead Adder, 2004. LANL preprint quant-ph/0406142.

M. Kwas, Complexity of multivariate Feynman-Kac Path Integration in Randomized and Quantum Settings, 2004, LANL preprint quant-ph/0410134.

A. Papageorgiou, H. Wozniakowski, Classical and Quantum Complexity of the Sturm-Liouville Eigenvalue Problem, Quantum Information Processing, Vol. 4, 87-127, 2005. LANL preprint quant-ph/0502054.

A. Bessen, A Lower Bound for Phase Estimation, Physical Review A, Vol. 71, No. 4,2005. LANL preprint quant-ph/0412008.

V. Giovanneti, S. lloyd, L. Maccone, Quantum-enhanced Measurements: Beating the Standard Quantum Limit, Science, 306, 1330, 2004.

J. Emerson, E. Livine, S. Lloyd, Convergence Conditions for Random Quantum Circuits, 2005, LANL preprint quant-ph/0503210.

A. Papageorgiou, H. Wozniakowski, The Sturm-Liouville eigenvalue problem in the quantum setting with queries, 2005, LANL preprint quant-ph/0504194.

S. Lloyd, A Theory of Quantum Gravity Based on Quantum Computation, 2005, LANL preprint quant-ph/0501135.

S. Lloyd, S. Pirandola, P. Tombesi, D. Vitali, Macroscopic Entanglement Swapping, 2005, LANL preprint quant-ph/0509119.

J. Baugh, O. Moussa, C. A. Ryan, R. Laflame, C. Ramanathan, T. F. Havel, D. G. Cory, A Solid-State NMR Three-Qubit homnuclear system for Quantum Information Processing: Control and Characterization, 2005, LANL preprint quant-ph/0510115.

A. Bessen, A Lower Bound for the Sturm-Liouville Eigenvalue Problem on a Quantum Computer, 2005, LANL preprint quant-ph/0512109.

A. Papageorgiou, J. F. Traub, Qubit Complexity of Continuous Problems, 2005, LANL preprint quant-ph/0512082.

H. Wozniakowski, The Quantum Setting with Randomized Queries for Continuous Problems, Quantum Information Processing, 2006 (to appear), LANL preprint quant-ph/0601196.

Related Publications

 D. S. Abrams and C. P. Williams, Fast quantum algorithms for numerical integrals and stochastic processes. LANL preprint quant-ph/9908083.

 G. Brassard, P. Hoyer, M. Mosca, Quantum amplitude amplification and estimation, 2000. LANL preprint quant-ph/0005055.

 L. Grover, A fast quantum mechanical algorithm for database search, Physical Review Letters, 79, 325-328, 1996. LANL preprint quant-ph/9706033.

 L. Grover, A framework for fast quantum mechanical algorithms, Proc. 30 Annual ACM Symp. on the Theory of Computing, ACM Press, New York. Physical Review Letters, 80, 4329-4332, 1998. LANL preprint quant-ph/9711043.

 S. Heinrich, Quantum summation with an application to integration, J. Complexity, 18 (1), 1-50, 2002. LANL preprint quant-ph/0105116.

 S. Heinrich and E. Novak, Optimal summation and integration by deterministic, randomized, and quantum algorithms, to appear in Proceedings of the 4th International Conference on Monte Carlo and Quasi-Monte Carlo Methods, Hong Kong 2000, eds. F. Hickernell and H. Niederreiter, Springer Verlag, New York. LANL preprint quant-ph/0105114.

 S. Heinrich and E. Novak, On a problem in quantum summation, J. Complexity, 19(1), 1-18, 2003. LANL preprint quant-ph/0109038.

 A. Nayak and F. Wu, The quantum query complexity of approximating the median and related statistics, STOC, May 1999, 384-393. LANL preprint quant-ph/9804066.

 E. Novak, Quantum complexity of integration, J. Complexity, 17, 2-16, 2001. LANL preprint quant-ph/0008124.

S. Heinrich, Quantum integration in Sobolev classes, J. Complexity, 19(1), 19-42, 2003. LANL preprint quant-ph/0112153.