Quantum information processing by nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance (NMR) is a direct macroscopic manifestation of the quantum mechanics of the intrinsic angular momentum of atomic nuclei. It is best known for its extraordinary range of applications, which include molecular structure determination, medical imaging, and measurements of flow and diffusion rates. Most recently, liquid-state NMR spectroscopy has been found to provide a powerful experimental tool for the development and evaluation of the coherent control techniques needed for quantum information processing. This burgeoning new interdisciplinary field has the potential to achieve cryptographic, communications, and computational feats far beyond what is possible with known classical physics. Indeed, NMR has made the demonstration of many of these feats sufficiently simple to be carried out by high school summer interns working in our laboratory (see the last two authors). In this paper the basic principles of quantum information processing by NMR spectroscopy are described, along with ...

[1]  Timothy F. Havel,et al.  NMR analog of the quantum disentanglement eraser. , 2001, Physical Review Letters.

[2]  S. Lloyd,et al.  Implementation of the quantum Fourier transform. , 1999, Physical review letters.

[3]  Richard Jozsa,et al.  Quantum factoring, discrete logarithms, and the hidden subgroup problem , 1996, Comput. Sci. Eng..

[4]  H. K. Cummins,et al.  Nuclear magnetic resonance: A quantum technology for computation and spectroscopy , 2000 .

[5]  Timothy F. Havel,et al.  Quantum simulation with natural decoherence , 2000 .

[6]  Timothy F. Havel,et al.  Multiqubit logic gates in NMR quantum computing , 2000 .

[7]  Timothy F. Havel,et al.  Spatially encoded pseudopure states for NMR quantum-information processing , 2000, quant-ph/0005076.

[8]  Timothy F. Havel,et al.  Quantum codes for controlling coherent evolution , 2000, quant-ph/0004029.

[9]  Timothy F. Havel,et al.  A study of quantum error correction by geometric algebra and liquid-state NMR spectroscopy , 2000, quant-ph/0004030.

[10]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[11]  Timothy F. Havel,et al.  Generalized methods for the development of quantum logic gates for an NMR quantum information processor , 1999 .

[12]  Timothy F. Havel,et al.  Construction and implementation of NMR quantum logic gates for two spin systems. , 1999, Journal of magnetic resonance.

[13]  Timothy F. Havel,et al.  Quantum simulation of a three-body-interaction Hamiltonian on an NMR quantum computer , 1999, quant-ph/9908012.

[14]  Timothy F. Havel,et al.  Quantum Simulations on a Quantum Computer , 1999, quant-ph/9905045.

[15]  R. Jozsa,et al.  SEPARABILITY OF VERY NOISY MIXED STATES AND IMPLICATIONS FOR NMR QUANTUM COMPUTING , 1998, quant-ph/9811018.

[16]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[17]  N. Gershenfeld,et al.  Quantum Computing with Molecules , 1998 .

[18]  Jonathan A. Jones,et al.  Implementation of a quantum search algorithm on a quantum computer , 1998, Nature.

[19]  R. Jozsa,et al.  Quantum algorithms: entanglement–enhanced information processing , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  D. Leung,et al.  Bulk quantum computation with nuclear magnetic resonance: theory and experiment , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[21]  Timothy F. Havel,et al.  Expressing the operations of quantum computing in multiparticle geometric algebra , 1998 .

[22]  Timothy F. Havel,et al.  Nuclear magnetic resonance spectroscopy: an experimentally accessible paradigm for quantum computing , 1997, quant-ph/9709001.

[23]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[24]  R. Jozsa Quantum algorithms and the Fourier transform , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[25]  R. Schack Using a quantum computer to investigate quantum chaos , 1997, quant-ph/9705016.

[26]  Warren S. Warren,et al.  The Usefulness of NMR Quantum Computing , 1997 .

[27]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[28]  J. Raimond,et al.  Quantum Computing: Dream or Nightmare? , 1996 .

[29]  S. Lloyd Quantum-Mechanical Computers , 1995 .

[30]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[31]  W. Zurek The Environment, Decoherence and the Transition from Quantum to Classical , 1991 .

[32]  R. Landauer,et al.  The Fundamental Physical Limits of Computation. , 1985 .

[33]  Richard R. Ernst,et al.  Product operator formalism for the description of NMR pulse experiments , 1984 .

[34]  R. Feynman Simulating physics with computers , 1999 .