NMR Based Quantum Information Processing: Achievements and Prospects

Nuclear magnetic resonance (NMR) provides an experimental setting to explore physical implementations of quantum information processing (QIP). Here we introduce the basic background for understanding applications of NMR to QIP and explain their current successes, limitations and potential. NMR spectroscopy is well known for its wealth of diverse coherent manipulations of spin dynamics. Ideas and instrumentation from liquid state NMR spectroscopy have been used to experiment with QIP. This approach has carried the field to a complexity of about 10 qubits, a small number for quantum computation but large enough for observing and better understanding the complexity of the quantum world. While liquid state NMR is the only present-day technology about to reach this number of qubits, further increases in complexity will require new methods. We sketch one direction leading towards a scalable quantum computer using spin 1/2 particles. The next step of which is a solid state NMR-based QIP capable of reaching 10-30 qubits.

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

[2]  R. Schumann.  Quantum Information Theory , 2000, quant-ph/0010060.

[3]  Andris Ambainis,et al.  Computing with highly mixed states (extended abstract) , 2000, STOC '00.

[4]  R. Martinez,et al.  An algorithmic benchmark for quantum information processing , 2000, Nature.

[5]  Isaac L. Chuang,et al.  Demonstration of quantum logic gates in liquid crystal nuclear magnetic resonance , 2000 .

[6]  J. A. Jones,et al.  NMR Quantum Computation: A Critical Evaluation , 2000, quant-ph/0002085.

[7]  D. DiVincenzo,et al.  The Physical Implementation of Quantum Computation , 2000, quant-ph/0002077.

[8]  Jonathan A. Jones,et al.  Geometric quantum computation using nuclear magnetic resonance , 2000, Nature.

[9]  Kikkawa,et al.  All-optical magnetic resonance in semiconductors , 2000, Science.

[10]  M. B. Plenio,et al.  Efficient factorization with a single pure qubit , 2000 .

[11]  David Collins,et al.  NMR quantum computation with indirectly coupled gates , 2000 .

[12]  Viola,et al.  Theory of quantum error correction for general noise , 1996, Physical review letters.

[13]  M. Feng,et al.  Experimental implementation of dense coding using nuclear magnetic resonance , 1999, quant-ph/9906041.

[14]  Arvind,et al.  Implementing quantum-logic operations, pseudopure states, and the Deutsch-Jozsa algorithm using noncommuting selective pulses in NMR , 1999, quant-ph/9906027.

[15]  Kang L. Wang,et al.  Electron-spin-resonance transistors for quantum computing in silicon-germanium heterostructures , 1999, quant-ph/9905096.

[16]  S. Lloyd,et al.  Experimental demonstration of greenberger-horne-zeilinger correlations using nuclear magnetic resonance , 1999, quant-ph/9905028.

[17]  G. Castagnoli,et al.  Geometric quantum computation with NMR , 1999, quant-ph/9910052.

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

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

[20]  Raymond Laflamme,et al.  Quantum Computation and Quadratically Signed Weight Enumerators , 1999, ArXiv.

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

[22]  Dolores C. Miller,et al.  NUCLEAR MAGNETIC RESONANCE QUANTUM COMPUTING USING LIQUID CRYSTAL SOLVENTS , 1999, quant-ph/9907063.

[23]  N. Linden,et al.  NMR quantum logic gates for homonuclear spin systems , 1999, quant-ph/9907003.

[24]  D. Leung,et al.  Quantum algorithms which accept hot qubit inputs , 1999, quant-ph/9906112.

[25]  S. Glaser,et al.  Realization of a 5-bit nmr quantum computer using a new molecular architecture , 1999, quant-ph/9905087.

[26]  Jun Luo,et al.  Experimental realization of discrete fourier transformation on NMR quantum computers , 1999, quant-ph/9905083.

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

[28]  G. Bodenhausen,et al.  Average Liouvillian theory revisited: cross-correlated relaxation between chemical shift anisotropy and dipolar couplings in the rotating frame in nuclear magnetic resonance , 1999 .

[29]  Lov K. Grover,et al.  Quantum computation , 1999, Proceedings Twelfth International Conference on VLSI Design. (Cat. No.PR00013).

[30]  D. Leung,et al.  Experimental realization of a two-bit phase damping quantum code , 1998, quant-ph/9811068.

[31]  E. Knill,et al.  Dynamical Decoupling of Open Quantum Systems , 1998, Physical Review Letters.

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

[33]  D. Aharonov.  Quantum Computation , 1998, quant-ph/9812037.

[34]  E. Knill,et al.  Complete quantum teleportation using nuclear magnetic resonance , 1998, Nature.

[35]  Timothy F. Havel,et al.  The effective Hamiltonian of the Pound-Overhauser controlled-NOT gate , 1998, quant-ph/9809045.

[36]  David G. Cory,et al.  A generalized k-space formalism for treating the spatial aspects of a variety of NMR experiments , 1998 .

[37]  N. Linden,et al.  An implementation of the Deutsch-Jozsa algorithm on a three-qubit NMR quantum computer , 1998, quant-ph/9808039.

[38]  Raymond Laflamme,et al.  NMR Greenberger–Horne–Zeilinger states , 1998, Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[39]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

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

[41]  David P. DiVincenzo,et al.  Real and realistic quantum computers , 1998, Nature.

[42]  B. E. Kane.  A silicon-based nuclear spin quantum computer , 1998, Nature.

[43]  U. Vazirani,et al.  Scalable NMR Quantum Computation , 1998, quant-ph/9804060.

[44]  S. Glaser,et al.  Unitary control in quantum ensembles: maximizing signal intensity in coherent spectroscopy , 1998, Science.

[45]  N. Gershenfeld,et al.  Experimental Implementation of Fast Quantum Searching , 1998 .

[46]  S. Lloyd,et al.  DYNAMICAL SUPPRESSION OF DECOHERENCE IN TWO-STATE QUANTUM SYSTEMS , 1998, quant-ph/9803057.

[47]  E. Knill,et al.  Power of One Bit of Quantum Information , 1998, quant-ph/9802037.

[48]  D. G. Cory,et al.  FIRST DIRECT MEASUREMENT OF THE SPIN DIFFUSION RATE IN A HOMOGENOUS SOLID , 1998 .

[49]  Timothy F. Havel,et al.  EXPERIMENTAL QUANTUM ERROR CORRECTION , 1998, quant-ph/9802018.

[50]  D. Leung,et al.  Experimental realization of a quantum algorithm , 1998, Nature.

[51]  E. Knill,et al.  Resilient Quantum Computation , 1998 .

[52]  Jonathan A. Jones,et al.  Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer , 1998, quant-ph/9801027.

[53]  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.

[54]  Timothy F. Havel,et al.  Expressing the operations of quantum computing in multiparticle geometric algebra , 1998, quant-ph/9801002.

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

[56]  J. Preskill.  Reliable quantum computers , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[57]  A. Kitaev.  Quantum computations: algorithms and error correction , 1997 .

[58]  E. Knill,et al.  EFFECTIVE PURE STATES FOR BULK QUANTUM COMPUTATION , 1997, quant-ph/9706053.

[59]  P. Zanardi,et al.  Noiseless Quantum Codes , 1997, quant-ph/9705044.

[60]  N. Gershenfeld,et al.  Bulk Spin-Resonance Quantum Computation , 1997, Science.

[61]  M. Ben-Or,et al.  Fault-tolerant quantum computation with constant error , 1996, STOC '97.

[62]  Schumacher,et al.  Sending entanglement through noisy quantum channels. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[63]  Gil Navon,et al.  Enhancement of Solution NMR and MRI with Laser-Polarized Xenon , 1996, Science.

[64]  A. Steane.  Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[65]  Barenco,et al.  Approximate quantum Fourier transform and decoherence. , 1996, Physical Review A. Atomic, Molecular, and Optical Physics.

[66]  David P. DiVincenzo,et al.  Towards an engineering era? , 1995, Nature.

[67]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

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

[69]  E. Knill.  Approximation by Quantum Circuits , 1995, quant-ph/9508006.

[70]  Lloyd,et al.  Almost any quantum logic gate is universal. , 1995, Physical review letters.

[71]  DiVincenzo,et al.  Two-bit gates are universal for quantum computation. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[72]  Unruh,et al.  Maintaining coherence in quantum computers. , 1994, Physical review. A, Atomic, molecular, and optical physics.

[73]  S Lloyd,et al.  A Potentially Realizable Quantum Computer , 1993, Science.

[74]  E. Charnaya,et al.  Direct measurement of the lattice and impurity components of nuclear spin-lattice relaxation under magnetic-saturation conditions , 1992 .

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

[76]  D. Cory,et al.  Time-suspension multiple-pulse sequences: applications to solid-state imaging , 1990 .

[77]  K. Mueller,et al.  Dynamic-Angle Spinning of Quadrupolar Nuclei , 1990 .

[78]  O. W. Sørensen.  A universal bound on spin dynamics , 1990 .

[79]  D. Longmore.  The principles of magnetic resonance. , 1989, British medical bulletin.

[80]  O. W. Sørensen,et al.  Polarization transfer experiments in high-resolution NMR spectroscopy , 1989 .

[81]  M. Munowitz,et al.  Coherence and NMR , 1988 .

[82]  A. Pines,et al.  Principles and Applications of Multiple‐Quantum Nmr , 2007 .

[83]  G. Bodenhausen,et al.  Principles of nuclear magnetic resonance in one and two dimensions , 1987 .

[84]  Alexander Pines,et al.  Lectures on pulsed NMR , 1986 .

[85]  Pines,et al.  Indirect phase detection of NMR spinor transitions. , 1986, Physical review letters.

[86]  U. Haeberlen.  Multiple pulse techniques in solid state NMR , 1985 .

[87]  A. Pines,et al.  Zero field NMR and NQR , 1985 .

[88]  A. Pines,et al.  Multiple‐quantum dynamics in solid state NMR , 1985 .

[89]  R. Wind,et al.  Applications of dynamic nuclear polarization in 13C NMR in solids , 1985 .

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

[91]  K. J. Packer,et al.  The use of single-spin operator basis sets in the N.M.R. spectroscopy of scalar-coupled spin systems , 1983 .

[92]  C. Hilbers,et al.  A simple formalism for the description of multiple-pulse experiments. Application to a weakly coupled two-spin ( I = {1}/{2}) system , 1983 .

[93]  A. Redfield,et al.  Nuclear Magnetism: Order and Disorder , 1982 .

[94]  John S. Waugh,et al.  Theory of broadband spin decoupling , 1982 .

[95]  D. T. Pegg,et al.  Distortionless enhancement of NMR signals by polarization transfer , 1982 .

[96]  I. Pykett,et al.  NMR imaging in medicine. , 1982, Scientific American.

[97]  J. Jeener.  Superoperators in Magnetic Resonance , 1982 .

[98]  R. Freeman,et al.  Composite pulse decoupling , 1981 .

[99]  A. Bax,et al.  An NMR technique for tracing out the carbon skeleton of an organic molecule , 1981 .

[100]  A. N. Garroway,et al.  Zero quantum NMR in the rotating frame: J cross polarization in AXN systems , 1981 .

[101]  Warren S. Warren,et al.  Theory of selective excitation of multiple‐quantum transitions , 1980 .

[102]  R. R. Ernst,et al.  Net polarization transfer via a J-ordered state for signal enhancement of low-sensitivity nuclei , 1980 .

[103]  Warren S. Warren,et al.  Selective Excitation of Multiple-Quantum Coherence in Nuclear Magnetic Resonance , 1979 .

[104]  Gareth A. Morris,et al.  Enhancement of nuclear magnetic resonance signals by polarization transfer , 1979 .

[105]  M. E. Stoll,et al.  Explicit demonstration of spinor character for a spin-1/2 nucleus via NMR interferometry. Technical report , 1977 .

[106]  R. R. Ernst,et al.  Two‐dimensional spectroscopy. Application to nuclear magnetic resonance , 1976 .

[107]  A. Pines,et al.  NEW APPROACH TO HIGH RESOLUTION PROTON NMR IN SOLIDS: DEUTERIUM SPIN-DECOUPLING BY MULTIPLE-QUANTUM TRANSITIONS , 1976 .

[108]  Haeberlen Ulrich,et al.  High resolution NMR in solids : selective averaging , 1976 .

[109]  W. Boer,et al.  Dynamic polarization of protons, deuterons, and carbon-13 nuclei: Thermal contact between nuclear spins and an electron spin-spin interaction reservoir , 1974 .

[110]  S. Meiboom,et al.  Theory of proton NMR with deuteron decoupling in nematic liquid crystalline solvents , 1973 .

[111]  A. Pines,et al.  Violation of the Spin-Temperature Hypothesis , 1970 .

[112]  U. Haeberlen,et al.  Coherent Averaging Effects in Magnetic Resonance , 1968 .

[113]  U. Haeberlen,et al.  Approach to High-Resolution nmr in Solids , 1968 .

[114]  C. Jeffries,et al.  Proton Spin-Lattice Relaxation in (Nd, La) 2 Mg 3 (NO 3 ) 12 .24H 2 O in High Fields and Low Temperatures , 1967 .

[115]  R. Wilcox.  Exponential Operators and Parameter Differentiation in Quantum Physics , 1967 .

[116]  T. Schmugge,et al.  High dynamic polarization of protons , 1965 .

[117]  A. Saupe.  Das Protonenresonanzspektrum von orientiertem Benzol in nematisch-kristallinflüssiger Lösung , 1965 .

[118]  C. Slichter.  Principles of magnetic resonance , 1963 .

[119]  C. Jeffries.  Dynamic nuclear orientation , 1963 .

[120]  E. Hahn,et al.  Nuclear Double Resonance in the Rotating Frame , 1962 .

[121]  H. Carr,et al.  The Principles of Nuclear Magnetism , 1961 .

[122]  E. R. Andrew,et al.  Removal of Dipolar Broadening of Nuclear Magnetic Resonance Spectra of Solids by Specimen Rotation , 1959, Nature.

[123]  R. L. Garwin,et al.  Spin Echo Serial Storage Memory , 1955 .

[124]  W. G. Proctor,et al.  SATURATION OF NUCLEAR ELECTRIC QUADRUPOLE ENERGY LEVELS BY ULTRASONIC EXCITATION , 1955 .

[125]  Nicolaas Bloembergen,et al.  Radiation Damping in Magnetic Resonance Experiments , 1954 .

[126]  N. Bloembergen,et al.  On the interaction of nuclear spins in a crystalline lattice , 1949 .

[127]  E. Purcell,et al.  Resonance Absorption by Nuclear Magnetic Moments in a Solid , 1946 .

[128]  A..  An NMR Technique for Tracing Out the Carbon Skeleton of an Organic Molecule , 2022 .

[129]  G.,et al.  On the Theory of Relaxation Processes * , 2022 .