Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer

Quantum computing shows great promise for the solution of many difficult problems, such as the simulation of quantum systems and the factorization of large numbers. While the theory of quantum computing is fairly well understood, it has proved difficult to implement quantum computers in real physical systems. It has recently been shown that nuclear magnetic resonance (NMR) can be used to implement small quantum computers using the spin states of nuclei in carefully chosen small molecules. Here we demonstrate the use of a NMR quantum computer based on the pyrimidine base cytosine, and the implementation of a quantum algorithm to solve Deutsch’s problem (distinguishing between constant and balanced functions). This is the first successful implementation of a quantum algorithm on any physical system.

[1]  T. Toffoli,et al.  Proceedings of the fourth workshop on Physics and computation , 1998 .

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

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

[4]  Jonathan A. Jones,et al.  Fast Searches with Nuclear Magnetic Resonance Computers , 1998, Science.

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

[6]  Raymond Laflamme,et al.  Nmr Ghz , 1997, QCQC.

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

[8]  Lov K. Grover Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[9]  Timothy F. Havel,et al.  Ensemble quantum computing by NMR spectroscopy , 1997, Proc. Natl. Acad. Sci. USA.

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

[11]  A. Steane Active Stabilization, Quantum Computation, and Quantum State Synthesis , 1996, quant-ph/9611027.

[12]  P. Knight,et al.  Decoherence limits to quantum computation using trapped ions , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[13]  Anthony J. G. Hey,et al.  Feynman Lectures on Computation , 1996 .

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

[15]  R. Jozsa,et al.  Quantum Computation and Shor's Factoring Algorithm , 1996 .

[16]  Lov K. Grover A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[17]  G. Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

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

[19]  Knight,et al.  Realistic lower bounds for the factorization time of large numbers on a quantum computer. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[20]  King,et al.  Demonstration of a fundamental quantum logic gate. , 1995, Physical review letters.

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

[22]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[23]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[24]  P. Shor,et al.  Quantum Computers, Factoring, and Decoherence , 1995, Science.

[25]  R. Freeman,et al.  Techniques for Multisite Excitation , 1993 .

[26]  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.

[27]  D. Deutsch Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[28]  R. Freeman,et al.  Selective excitation at two arbitrary frequencies. The double-DANTE sequence , 1989 .

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

[30]  R. Penrose,et al.  Quantum Concepts in Space and Time , 1986 .

[31]  D. Deutsch Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

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

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

[34]  Ray Freeman,et al.  Composite Z pulses , 1981 .

[35]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .