51
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Preparation and addressability of molecular vibrational qubit states in the presence of anharmonic resonance. Chem Phys Lett 2003. [DOI: 10.1016/s0009-2614(03)01266-1] [Citation(s) in RCA: 54] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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52
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Jones JA. Robust quantum information processing with techniques from liquid-state NMR. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2003; 361:1429-1440. [PMID: 12869319 DOI: 10.1098/rsta.2003.1212] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
While nuclear-magnetic-resonance (NMR) techniques are unlikely to lead to a large-scale quantum computer, they are well suited to investigating basic phenomena and developing new techniques. Indeed, it is likely that many existing NMR techniques will find uses in quantum information processing. Here I describe how the composite-rotation (composite-pulse) method can be used to develop quantum logic gates which are robust against systematic errors.
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Affiliation(s)
- Jonathan A Jones
- Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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53
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Gulde S, Häffner H, Riebe M, Lancaster G, Becher C, Eschner J, Schmidt-Kaler F, Chuang IL, Blatt R. Quantum information processing with trapped Ca(+) ions. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2003; 361:1363-1374. [PMID: 12869313 DOI: 10.1098/rsta.2003.1206] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Quantum information processing is performed with single trapped Ca(+) ions, stored in a linear Paul trap and laser-cooled to the ground state of their harmonic quantum motion. Composite laser-pulse sequences were used to implement SWAP gate, phase gate and controlled-NOT gate operations. Stark shifts on the quantum-bit transitions were precisely measured and compensated. For a demonstration of quantum information processing, a Deutsch-Jozsa algorithm has been implemented using two quantum bits encoded on a single ion.
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Affiliation(s)
- S Gulde
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, 6020 Innsbruck, Austria
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54
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Ermakov VL, Fung BM. Nuclear magnetic resonance implementation of the Deutsch–Jozsa algorithm using different initial states. J Chem Phys 2003. [DOI: 10.1063/1.1574802] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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55
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Brainis E, Lamoureux LP, Cerf NJ, Emplit P, Haelterman M, Massar S. Fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms with three qubits. PHYSICAL REVIEW LETTERS 2003; 90:157902. [PMID: 12732071 DOI: 10.1103/physrevlett.90.157902] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/06/2003] [Indexed: 05/24/2023]
Abstract
We report on a fiber-optics implementation of the Deutsch-Jozsa and Bernstein-Vazirani quantum algorithms for 8-point functions. The measured visibility of the 8-path interferometer is about 97.5%. Potential applications of our setup to quantum communication or cryptographic protocols using several qubits are discussed.
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Affiliation(s)
- E Brainis
- Optique et Acoustique, CP 194/5, Université Libre de Bruxelles, Avenue F. D. Roosevelt 50, 1050 Brussels, Belgium
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56
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57
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Gulde S, Riebe M, Lancaster GPT, Becher C, Eschner J, Häffner H, Schmidt-Kaler F, Chuang IL, Blatt R. Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer. Nature 2003; 421:48-50. [PMID: 12511949 DOI: 10.1038/nature01336] [Citation(s) in RCA: 354] [Impact Index Per Article: 16.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2002] [Accepted: 11/27/2002] [Indexed: 11/09/2022]
Abstract
Determining classically whether a coin is fair (head on one side, tail on the other) or fake (heads or tails on both sides) requires an examination of each side. However, the analogous quantum procedure (the Deutsch-Jozsa algorithm) requires just one examination step. The Deutsch-Jozsa algorithm has been realized experimentally using bulk nuclear magnetic resonance techniques, employing nuclear spins as quantum bits (qubits). In contrast, the ion trap processor utilises motional and electronic quantum states of individual atoms as qubits, and in principle is easier to scale to many qubits. Experimental advances in the latter area include the realization of a two-qubit quantum gate, the entanglement of four ions, quantum state engineering and entanglement-enhanced phase estimation. Here we exploit techniques developed for nuclear magnetic resonance to implement the Deutsch-Jozsa algorithm on an ion-trap quantum processor, using as qubits the electronic and motional states of a single calcium ion. Our ion-based implementation of a full quantum algorithm serves to demonstrate experimental procedures with the quality and precision required for complex computations, confirming the potential of trapped ions for quantum computation.
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Affiliation(s)
- Stephan Gulde
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstrasse 25, A-6020 Innsbruck, Austria
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58
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Tesch CM, De Vivie-Riedle R. Quantum computation with vibrationally excited molecules. PHYSICAL REVIEW LETTERS 2002; 89:157901. [PMID: 12366025 DOI: 10.1103/physrevlett.89.157901] [Citation(s) in RCA: 116] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/27/2001] [Indexed: 05/23/2023]
Abstract
A new physical implementation for quantum computation is proposed. The vibrational modes of molecules are used to encode qubit systems. Global quantum logic gates are realized using shaped femtosecond laser pulses which are calculated applying optimal control theory. The scaling of the system is favorable; sources for decoherence can be eliminated. A complete set of one- and two-quantum gates is presented for a specific molecule. Detailed analysis regarding experimental realization shows that the structural resolution of today's pulse shapers is easily sufficient for pulse formation.
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59
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Xiao L, Long GL, Yan HY, Sun Y. Experimental realization of the Brüschweiler’s algorithm in a homonuclear system. J Chem Phys 2002. [DOI: 10.1063/1.1494784] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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60
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Bihary Z, Glenn DR, Lidar DA, Ara Apkarian V. An implementation of the Deutsch–Jozsa algorithm on molecular vibronic coherences through four-wave mixing: a theoretical study. Chem Phys Lett 2002. [DOI: 10.1016/s0009-2614(02)00808-4] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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61
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Cummins HK, Jones C, Furze A, Soffe NF, Mosca M, Peach JM, Jones JA. Approximate quantum cloning with nuclear magnetic resonance. PHYSICAL REVIEW LETTERS 2002; 88:187901. [PMID: 12005722 DOI: 10.1103/physrevlett.88.187901] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/19/2001] [Indexed: 05/23/2023]
Abstract
Here we describe a nuclear magnetic resonance (NMR) experiment that uses a three qubit NMR device to implement the one-to-two approximate quantum cloning network of Buzek et al. [Phys. Rev. A 56, 3446 (1997)]. As expected the experimental results indicate that the network clones all input states with similar fidelities, but as a result of decoherence and incoherent evolution arising from B(1) inhomogeneity the total fidelity achieved does not exceed the measurement bound.
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Affiliation(s)
- Holly K Cummins
- Centre for Quantum Computation, Clarendon Laboratory, University of Oxford, Parks Road, OX1 3PU, United Kingdom
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62
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Fortunato EM, Pravia MA, Boulant N, Teklemariam G, Havel TF, Cory DG. Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing. J Chem Phys 2002. [DOI: 10.1063/1.1465412] [Citation(s) in RCA: 185] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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63
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64
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Unanyan RG, Vitanov NV, Bergmann K. Preparation of entangled states by adiabatic passage. PHYSICAL REVIEW LETTERS 2001; 87:137902. [PMID: 11580627 DOI: 10.1103/physrevlett.87.137902] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/08/2001] [Indexed: 05/23/2023]
Abstract
We propose a novel technique for the creation of entangled pairs of two-state systems based upon adiabatic passage induced by a suitably crafted time-dependent external field.
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Affiliation(s)
- R G Unanyan
- Fachbereich Physik der Universität Kaiserslautern, 67653 Kaiserslautern, Germany
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65
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Xiang-Bin W, Keiji M. Nonadiabatic conditional geometric phase shift with NMR. PHYSICAL REVIEW LETTERS 2001; 87:097901. [PMID: 11531598 DOI: 10.1103/physrevlett.87.097901] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2001] [Indexed: 05/23/2023]
Abstract
A conditional geometric phase shift gate, which is fault tolerant to certain types of errors due to its geometric nature, was realized recently via nuclear magnetic resonance (NMR) under adiabatic conditions. However, in quantum computation, everything must be completed within the decoherence time. The adiabatic condition makes any fast conditional Berry phase (cyclic adiabatic geometric phase) shift gate impossible. Here we show that by using a newly designed sequence of simple operations with an additional vertical magnetic field, the conditional geometric phase shift gate can be run nonadiabatically. Therefore geometric quantum computation can be done at the same rate as usual quantum computation.
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Affiliation(s)
- W Xiang-Bin
- Imai Quantum Computation and Information Project, ERATO, Japan Science and Technology Corporation, Dani Hongo White Building 201, 5-28-3, Hongo Bunkyo, Tokyo 113-0033, Japan.
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66
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Chen P, Piermarocchi C, Sham LJ. Control of exciton dynamics in nanodots for quantum operations. PHYSICAL REVIEW LETTERS 2001; 87:067401. [PMID: 11497860 DOI: 10.1103/physrevlett.87.067401] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2001] [Indexed: 05/23/2023]
Abstract
We present a theory to further a new perspective of proactive control of exciton dynamics in the quantum limit. Circularly polarized optical pulses in a semiconductor nanodot are used to control the dynamics of two interacting excitons of opposite polarizations. Shaping of femtosecond laser pulses keeps the quantum operation within the decoherence time. Computation of the fidelity of the operations and application to the complete solution of a minimal quantum computing algorithm demonstrate in theory the feasibility of quantum control.
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Affiliation(s)
- P Chen
- Department of Physics, University of California-San Diego, La Jolla, California 92093-0319, USA
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67
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Tesch CM, Kurtz L, de Vivie-Riedle R. Applying optimal control theory for elements of quantum computation in molecular systems. Chem Phys Lett 2001. [DOI: 10.1016/s0009-2614(01)00748-5] [Citation(s) in RCA: 96] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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68
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Mozyrsky D, Privman V, Glasser ML. Indirect interaction of solid-state qubits via two-dimensional electron gas. PHYSICAL REVIEW LETTERS 2001; 86:5112-5115. [PMID: 11384434 DOI: 10.1103/physrevlett.86.5112] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/02/2001] [Indexed: 05/23/2023]
Abstract
We propose a mechanism of long-range coherent coupling between nuclear spin qubits in semiconductor-heterojunction quantum information processing devices. The coupling is via localized donor electrons which interact with the two-dimensional electron gas. An effective interaction Hamiltonian is derived and the coupling strength is evaluated. We also discuss mechanisms of decoherence and consider gate control of the interaction between qubits. The resulting quantum computing scheme retains all the control and measurement aspects of earlier approaches, but allows qubit spacing at distances of the order of 100 nm, attainable with the present-day semiconductor device technologies.
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Affiliation(s)
- D Mozyrsky
- Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA
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69
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70
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Cummins HK, Jones JA. Resonance offset tailored composite pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2001; 148:338-342. [PMID: 11237639 DOI: 10.1006/jmre.2000.2247] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We describe novel composite pulse sequences which act as general rotors and thus are particularly suitable for nuclear magnetic resonance quantum computation. The resonance offset tailoring to enhance nutations approach permits perfect compensation of off-resonance errors at two selected frequencies placed symmetrically around the frequency of the radiofrequency source.
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Affiliation(s)
- H K Cummins
- Oxford Centre for Quantum Computation, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom.
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71
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72
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73
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74
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Mahesh TS, Dorai K, Kumar A. Implementing logic gates and the Deutsch-Jozsa quantum algorithm by two-dimensional NMR using spin- and transition-selective pulses. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2001; 148:95-103. [PMID: 11133281 DOI: 10.1006/jmre.2000.2225] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Quantum logical operations using two-dimensional NMR have recently been described using the scalar coupling evolution technique [J. Chem. Phys. 109, 10603 (1998)]. In the present paper, we describe the implementation of quantum logical operations using two-dimensional NMR, with the help of spin- and transition-selective pulses. A number of logic gates are implemented using two and three qubits with one extra observer spin. Some many-in-one gates (or Portmanteau gates) are also implemented. Toffoli gate (or AND/NAND gate) and OR/NOR gates are implemented on three qubits. The Deutsch-Jozsa quantum algorithm for one and two qubits, using one extra work qubit, has also been implemented using spin- and transition-selective pulses after creating a coherent superposition state in the two-dimensional methodology.
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Affiliation(s)
- T S Mahesh
- Department of Physics, Indian Institute of Science, Bangalore, 560012, India
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75
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Vandersypen LM, Steffen M, Breyta G, Yannoni CS, Cleve R, Chuang IL. Experimental realization of an order-finding algorithm with an NMR quantum computer. PHYSICAL REVIEW LETTERS 2000; 85:5452-5455. [PMID: 11136019 DOI: 10.1103/physrevlett.85.5452] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2000] [Indexed: 05/23/2023]
Abstract
We report the realization of a nuclear magnetic resonance quantum computer which combines the quantum Fourier transform with exponentiated permutations, demonstrating a quantum algorithm for order finding. This algorithm has the same structure as Shor's algorithm and its speed-up over classical algorithms scales exponentially. The implementation uses a particularly well-suited five quantum bit molecule and was made possible by a new state initialization procedure and several quantum control techniques.
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Affiliation(s)
- L M Vandersypen
- Solid State and Photonics Laboratory, Stanford University, Stanford, California 94305-4075, USA.
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76
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Hollenberg LC. Fast quantum search algorithms in protein sequence comparisons: quantum bioinformatics. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 2000; 62:7532-5. [PMID: 11102126 DOI: 10.1103/physreve.62.7532] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/28/2000] [Indexed: 11/07/2022]
Abstract
Quantum search algorithms are considered in the context of protein sequence comparison in bioinformatics. Given a sample protein sequence of length m (i.e., m residues), the problem considered is to find an optimal match in a large database containing N residues. Initially, Grover's quantum search algorithm is applied to a simple illustrative case-namely, where the database forms a complete set of states over the 2(m) basis states of a m qubit register, and thus is known to contain the exact sequence of interest. This example demonstrates explicitly the typical O(square root of [N]) speedup on the classical O(N) requirements. An algorithm is then presented for the (more realistic) case where the database may contain repeat sequences, and may not necessarily contain an exact match to the sample sequence. In terms of minimizing the Hamming distance between the sample sequence and the database subsequences the algorithm finds an optimal alignment, in O(square root of [N]) steps, by employing an extension of Grover's algorithm, due to Boyer et al. for the case when the number of matches is not a priori known.
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Affiliation(s)
- L C Hollenberg
- Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, Heidelberg D-69117, Germany
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77
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Hübler P, Bargon J, Glaser SJ. Nuclear magnetic resonance quantum computing exploiting the pure spin state of para hydrogen. J Chem Phys 2000. [DOI: 10.1063/1.482015] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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78
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Abstract
In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.
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79
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Abstract
A significant development in computing has been the discovery that the computational power of quantum computers exceeds that of Turing machines. Central to the experimental realization of quantum information processing is the construction of fault-tolerant quantum logic gates. Their operation requires conditional quantum dynamics, in which one sub-system undergoes a coherent evolution that depends on the quantum state of another sub-system; in particular, the evolving sub-system may acquire a conditional phase shift. Although conventionally dynamic in origin, phase shifts can also be geometric. Conditional geometric (or 'Berry') phases depend only on the geometry of the path executed, and are therefore resilient to certain types of errors; this suggests the possibility of an intrinsically fault-tolerant way of performing quantum gate operations. Nuclear magnetic resonance techniques have already been used to demonstrate both simple quantum information processing and geometric phase shifts. Here we combine these ideas by performing a nuclear magnetic resonance experiment in which a conditional Berry phase is implemented, demonstrating a controlled phase shift gate.
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80
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Jones JA, Knill E. Efficient refocusing of one-spin and two-spin interactions for NMR quantum computation. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 1999; 141:322-325. [PMID: 10579955 DOI: 10.1006/jmre.1999.1890] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
The use of spin echoes to refocus one-spin interactions (chemical shifts) and two-spin interactions (spin-spin couplings) plays a central role in both conventional NMR experiments and NMR quantum computation. Here we describe schemes for efficient refocusing of such interactions in both fully and partially coupled spin systems.
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Affiliation(s)
- J A Jones
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom
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81
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82
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Linden N, Barjat H, Kupče Ē, Freeman R. How to exchange information between two coupled nuclear spins: the universal SWAP operation. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)00516-3] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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83
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Pulse sequences for NMR quantum computers: how to manipulate nuclear spins while freezing the motion of coupled neighbours. Chem Phys Lett 1999. [DOI: 10.1016/s0009-2614(99)00339-5] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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84
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85
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Pravia M, Fortunato E, Weinstein Y, Price MD, Teklemariam G, Nelson RJ, Sharf Y, Somaroo S, Tseng CH, Havel TF, Cory DG. Observations of quantum dynamics by solution-state NMR spectroscopy. ACTA ACUST UNITED AC 1999. [DOI: 10.1002/(sici)1099-0534(1999)11:4<225::aid-cmr3>3.0.co;2-e] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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86
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Jones JA, Hansen RH, Mosca M. Quantum logic gates and nuclear magnetic resonance pulse sequences. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 1998; 135:353-360. [PMID: 9878463 DOI: 10.1006/jmre.1998.1606] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
There has recently been considerable interest in the use of nuclear magnetic resonance (NMR) as a technology for the implementation of small quantum computers. These computers operate by the laws of quantum mechanics, rather than classical mechanics and can be used to implement new quantum algorithms. Here we describe how NMR in principle can be used to implement all the elements required to build quantum computers, and draw comparisons between the pulse sequences involved and those of more conventional NMR experiments.
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Affiliation(s)
- J A Jones
- OCMS, New Chemistry Laboratory, South Parks Road, Oxford, OX1 3QT, United Kingdom.
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87
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88
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Linden N, Barjat H, Freeman R. An implementation of the Deutsch–Jozsa algorithm on a three-qubit NMR quantum computer. Chem Phys Lett 1998. [DOI: 10.1016/s0009-2614(98)01015-x] [Citation(s) in RCA: 100] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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89
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Fahmy AF. Quantum Computing. Science 1998. [DOI: 10.1126/science.281.5385.1961e] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Amr F. Fahmy
- Department of Biological Chemistry and Molecular Pharmacology, Harvard Medical School, Boston, MA 02115-5718, USA
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