量子计算中的新计算模式和新物理实现体系研究
|
摘要
量子计算研究的最终目标是建造实用的高性能量子计算机——一台以量子力学为基本原理对信息进行编码和计算的新型计算机。它在理论上被证明能够完全模拟当前的经典计算机,并且在一些特殊问题上更具有经典计算机无可比拟的优势。量子计算是近十多年来物理学研究中最热门的领域之一,已形成了集量子物理学、数学、材料科学和工程科学等多学科交叉研究的局面,吸引了大量的科研人员投身其中。然而,关于量子计算机最终以何种方式(模式)以及在何种物理体系中实现的问题,目前尚没有定论,仍处于多种途径并行研究的阶段。
本文介绍了我们在量子计算新模式和新的物理实现体系上的工作。使用液体核磁共振技术,我们在核磁共振体系中第一次实验模拟了one-way量子计算模式的全过程,包括确定性地制备图态和实现one-way模式下的Deutsch-Josza算法。我们的工作验证了one-way量子计算模式的可行性,同时也将为其它物理体系开展one-way量子计算提供有益经验。在新的物理实现体系上,我们重点关注基于掺杂富勒烯的量子计算物理体系。我们提出了在掺杂富勒烯体系中构筑普适量子逻辑门集合的方案。通过电子自旋为媒介实现相邻核自旋之间的两量子比特逻辑门,这与核自旋上可进行的单量子比特逻辑门一起构成普适量子逻辑门集合。我们的方案将电子自旋3／2及其跃迁存在简并的特点和难点考虑在内,解决了前人方案中遗留的问题,为掺杂富勒烯量子计算的普适性提供了基础。进一步,我们提出了一个以电子自旋为辅助的基于掺杂富勒烯的普适和可扩展量子计算方案。充分利用掺杂富勒烯中电子自旋与核自旋并存的特点,使电子自旋在核自旋量子比特的寻址、初始化、量子逻辑门和读出上都起到重要的作用。与前人的方案相比,该方案在核自旋的寻址和量子逻辑门上具有明显的优势。此外,针对当前掺杂富勒烯仍属于系综实验研究的特点,我们给出了可在当前实验谱仪(含ENDOR功能的脉冲式电子自旋共振谱仪)上完成的自旋量子态重构技术,这为在掺杂富勒烯系综实验平台上开展少数量子比特的量子计算研究提供了方便。
我们的工作力图展示将量子计算模式和物理实现这两个量子计算的不同层面紧密结合在一起的特点。我们提出的普适量子逻辑门集合实现方案,不仅是基于逻辑网络的量子计算模式的重要组成部分,也为在掺杂富勒烯体系中应用one-way量子计算模式提供了基础(建立图态)。以电子自旋为辅助的掺杂富勒烯量子计算方案中,我们通过综合使用基于逻辑网络和基于整体控制这两种量子计算模式,解决了核自旋的寻址问题,避开了原先存在的技术难点。我们预期最终量子计算机的实现将有赖于多种量子计算模式和物理实现体系的综合使用,而我们的工作初步展示了这一特征。
The ultimate goal of quantum computation research is to build a powerful quantum computer, which is a new type computer based on quantum mechanics. It has been proved in theory that a quantum computer can fully simulate the classical computer, and further it can solve specific problems efficiently which classical computer cannot. Quantum computation research has the multidisciplinary character that combines quantum physics, mathematics, material science, and engineering etc. It has become one of the most active areas in physical research, and attracted lots of the most brilliant brains in the world. However, it is still not clear today that the ultimate quantum computer would be built in which mode and in which physical system. Many possible ways are under research.
In this thesis we summarize our researches on the new quantum computation mode and new physical realization system. We experimentally simulated the one-way quantum computation mode in nuclear magnetic resonance (NMR) system for the first time, utilizing the liquid-state NMR technologies. We deterministically prepared a four-particle graph state, and demonstrated the Deutsch-Josza algorithm on it in the one-way manner. The results of our experiment verified the feasibility of the one-way mode, and would be helpful to other physical systems for future scalable one-way quantum computation. For the new physical realization system, we concentrate on the endohedral fullerenes. We proposed a scheme to realize the universal quantum gates in endohedral fullerenes. It solved the problem which due to the electron spin 3/2 and its transition degeneracy. Our scheme is a fundamental contribution to the endohedral fullerene based quantum computation. Further, we suggested a new quantum computation proposal based on endohedral fullerenes, in which the electron spins are used as auxiliary. Utilizing these auxiliary spins, it has more convenience in qubit (the nuclear spin) addressing, initialization, quantum gates, and read out, than previous proposals. Besides, we also provided a spin state tomography technology for the endohedral fullerene ensemble, which is feasible for the current electron spin resonance spectrometer with ENDOR (electron-nuclear double resonance) part.
We anticipate that the ultimate realization of quantum computer would rely on the integrated system with different computation modes and even different physical realization systems. Our work have shown this distinguish feature in a primary step. The two-qubit gates which we proposed to construct the universal quantum gates in endohedral fullerenes, is not only an essential part of the logic circuit mode, but also could be used to prepare the graph state onto the nuclear spins which is the unique resource of the one-way mode. We also integrated the logic circuit mode and the global control mode in our electron spin assisted endohedral fullerene quantum computation scheme, according to which we solved the addressing problem of the nuclear spins. This reduces largely the technical requirements.
本文介绍了我们在量子计算新模式和新的物理实现体系上的工作。使用液体核磁共振技术,我们在核磁共振体系中第一次实验模拟了one-way量子计算模式的全过程,包括确定性地制备图态和实现one-way模式下的Deutsch-Josza算法。我们的工作验证了one-way量子计算模式的可行性,同时也将为其它物理体系开展one-way量子计算提供有益经验。在新的物理实现体系上,我们重点关注基于掺杂富勒烯的量子计算物理体系。我们提出了在掺杂富勒烯体系中构筑普适量子逻辑门集合的方案。通过电子自旋为媒介实现相邻核自旋之间的两量子比特逻辑门,这与核自旋上可进行的单量子比特逻辑门一起构成普适量子逻辑门集合。我们的方案将电子自旋3／2及其跃迁存在简并的特点和难点考虑在内,解决了前人方案中遗留的问题,为掺杂富勒烯量子计算的普适性提供了基础。进一步,我们提出了一个以电子自旋为辅助的基于掺杂富勒烯的普适和可扩展量子计算方案。充分利用掺杂富勒烯中电子自旋与核自旋并存的特点,使电子自旋在核自旋量子比特的寻址、初始化、量子逻辑门和读出上都起到重要的作用。与前人的方案相比,该方案在核自旋的寻址和量子逻辑门上具有明显的优势。此外,针对当前掺杂富勒烯仍属于系综实验研究的特点,我们给出了可在当前实验谱仪(含ENDOR功能的脉冲式电子自旋共振谱仪)上完成的自旋量子态重构技术,这为在掺杂富勒烯系综实验平台上开展少数量子比特的量子计算研究提供了方便。
我们的工作力图展示将量子计算模式和物理实现这两个量子计算的不同层面紧密结合在一起的特点。我们提出的普适量子逻辑门集合实现方案,不仅是基于逻辑网络的量子计算模式的重要组成部分,也为在掺杂富勒烯体系中应用one-way量子计算模式提供了基础(建立图态)。以电子自旋为辅助的掺杂富勒烯量子计算方案中,我们通过综合使用基于逻辑网络和基于整体控制这两种量子计算模式,解决了核自旋的寻址问题,避开了原先存在的技术难点。我们预期最终量子计算机的实现将有赖于多种量子计算模式和物理实现体系的综合使用,而我们的工作初步展示了这一特征。
The ultimate goal of quantum computation research is to build a powerful quantum computer, which is a new type computer based on quantum mechanics. It has been proved in theory that a quantum computer can fully simulate the classical computer, and further it can solve specific problems efficiently which classical computer cannot. Quantum computation research has the multidisciplinary character that combines quantum physics, mathematics, material science, and engineering etc. It has become one of the most active areas in physical research, and attracted lots of the most brilliant brains in the world. However, it is still not clear today that the ultimate quantum computer would be built in which mode and in which physical system. Many possible ways are under research.
In this thesis we summarize our researches on the new quantum computation mode and new physical realization system. We experimentally simulated the one-way quantum computation mode in nuclear magnetic resonance (NMR) system for the first time, utilizing the liquid-state NMR technologies. We deterministically prepared a four-particle graph state, and demonstrated the Deutsch-Josza algorithm on it in the one-way manner. The results of our experiment verified the feasibility of the one-way mode, and would be helpful to other physical systems for future scalable one-way quantum computation. For the new physical realization system, we concentrate on the endohedral fullerenes. We proposed a scheme to realize the universal quantum gates in endohedral fullerenes. It solved the problem which due to the electron spin 3/2 and its transition degeneracy. Our scheme is a fundamental contribution to the endohedral fullerene based quantum computation. Further, we suggested a new quantum computation proposal based on endohedral fullerenes, in which the electron spins are used as auxiliary. Utilizing these auxiliary spins, it has more convenience in qubit (the nuclear spin) addressing, initialization, quantum gates, and read out, than previous proposals. Besides, we also provided a spin state tomography technology for the endohedral fullerene ensemble, which is feasible for the current electron spin resonance spectrometer with ENDOR (electron-nuclear double resonance) part.
We anticipate that the ultimate realization of quantum computer would rely on the integrated system with different computation modes and even different physical realization systems. Our work have shown this distinguish feature in a primary step. The two-qubit gates which we proposed to construct the universal quantum gates in endohedral fullerenes, is not only an essential part of the logic circuit mode, but also could be used to prepare the graph state onto the nuclear spins which is the unique resource of the one-way mode. We also integrated the logic circuit mode and the global control mode in our electron spin assisted endohedral fullerene quantum computation scheme, according to which we solved the addressing problem of the nuclear spins. This reduces largely the technical requirements.
引文
[1]G. E. Moore, Gramming more components onto integrated circuits, Electronics 38,114-117 (1965).
[2]P. Benioff, The computer as a physical system:A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, J. Sta. Phys.22,563-591 (1980).
[3]R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys.21,467-488 (1982).
[4]D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. A 439,553-558 (1985).
[5]D. Deutsch, and R. Jozsa, Rapid Solution of Problems by Quantum Computation, Proc. R. Soc. A 439,553-558(1992).
[6]P. Shor, Polynomial-time algorithms for prime factorization and discrete algorithms on a quantum computer, Proceedings of the 35th annual symposium on the foundation of computer science, IEEE press,124-133 (1994).
[7]L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett.79,325 (1997).
[8]M. Scholz, T. Aichele, S. Ramelow, and O. Benson, Deutsch-Jozsa Algorithm-Using Triggered Single Photons from a Single Quantum Dot, Phys. Rev. Lett.96,180501 (2006).
[9]E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman et al., Fiber-Optics Implementation of the Deutsch-Jozsa and Bernstein-Vazirani Quantum Algorithms with Three Qubits, Phys. Rev. Lett.90,157902 (2003).
[10]S. Guide, M. Riebe, G. P. T. Lancaster, C. Becher, J. Eschner et al., Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer, Nature 421,48 (2003).
[11]L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood et al., Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance, Nature 414,883 (2001).
[12]I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett.80,3408 (1998).
[13]M. A. Nielsen, E. Knill, and R. Laflamme, Complete quantum teleportation using nuclear magnetic resonance, Nature 396,52 (1998).
[14]J. A. Jones, M. Mosca, and R. H. Hansen, Implementation of a quantumsearch algorithm on a quantum computer, Nature 393,344 (1998).
[15]I. L. Chuang, L. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, Experimental realization of a quantum algorithm, Nature 393,143 (1998).
[16]D. P. DiVincenzo, The Physical Implementation of Quantum Computation, Fortsch. Phys.48, 771-783 (2000).
[17]T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe et al., Quantum computers, Nature 464,45 (2010).
[18]L. M. K. Vandersypen, and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys.76,1037 (2004).
[19]B. E. Kane, A silicon-based nuclear spin quantum computer, Nature 393,133 (1998).
[20]J. I. Cirac, and P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett.74, 4091-4094(1995).
[21]C. Wunderlich, C. Balzer, T. Hannemann, F. Mintert, W. Neuhauser et al., Spin resonance with trapped ions, Journal of Physics B:Atomic, Molecular and Optical Physics 36,1063 (2003).
[22]J. L. O'Brien, Optical quantum computing, Science 318,1567-1570 (2007).
[23]E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409,46-52 (2001).
[24]R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys.79,1217-1265 (2007).
[25]A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss et al., Quantum Information Processing Using Quantum Dot Spins and Cavity QED, Phys. Rev. Lett.83, 4204-4207(1999).
[26]T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, Spin-based all-optical quantum computation with quantum dots:Understanding and suppressing decoherence, Phys. Rev. A 68, 012310(2003).
[27]I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, Coherent quantum dynamics of a superconducting flux qubit, Science 299,1869-1871 (2003).
[28]J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, Rabi oscillations in a large Josephson-junction qubit, Phys. Rev. Lett.89,117901 (2002).
[29]J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal et al., Josephson Persistent-Current Qubit, Science 285,1036 (1999).
[30]Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Coherent control of macroscopic quantum states in a single-Cooper-pair box, Nature 398,786-788 (1999).
[31]D. Deutsch, Quantum Computational Networks, Proc. R. Soc. A 425,73-90 (1989).
[32]A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus et al., Elementary gates for quantum computation, Phys. Rev. A 52,3457-3467 (1995).
[33]A. Barenco, D. Deutsch, and A. Ekert, Conditional Quantum Dynamics and Logic Gates, Phys. Rev. Lett.74,4083-4086 (1995).
[34]A. Barenco, A Universal Two-Bit Gate for Quantum Computation, Proc. R. Soc. A 449, 679-683 (1995).
[35]D. Deutsch, A. Barenco, and A. Ekert, Universality in Quantum Computation, Proc. R. Soc. A 449,669-677(1995).
[36]S. Lloyd, Almost Any Quantum Logic Gate is Universal, Phys. Rev. Lett.75,346-349 (1995).
[37]D. P. DiVincenzo, Two-bit gates are universal for quantum computation, Phys. Rev. A 51, 1015-1022 (1995).
[38]S. Lloyd, A Potentially Realizable Quantum Computer, Science 261,1569-1571 (1993).
[39]S. C. Benjamin, Schemes for parallel quantum, computation without local control of qubits, Phys. Rev. A 61,020301(R) (2000).
[40]S. C. Benjamin, Quantum Computing Without Local Control of Qubit-Qubit Interactions, Phys. Rev. Lett.88,017904 (2001).
[41]S. C. Benjamin, Multi-qubit gates in arrays coupled by'always-on'interactions, New J. Phys. 6,61 (2004).
[42]S. C. Benjamin, and S. Bose, Quantum Computing with an Always-On Heisenberg Interaction, Phys. Rev. Lett.90,247901 (2003).
[43]S. C. Benjamin, and S. Bose, Quantum computing in arrays coupled by "always-on" interactions, Phys. Rev. A 70,032314 (2004).
[44]S. C. Benjamin, Simple pulses for universal quantum computation with a Heisenberg ABAB chain, Phys. Rev. A 64,054303 (2001).
[45]D. Aharonov, W. Dam, J. Kempe, Z. Landau, S. Lloyd et al., Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation, SIAM J. Comp.37,166-194 (2007).
[46]J. Roland, and N. J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65, 042308 (2002).
[47]R. Raussendorf, and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett.86,5188 (2001).
[48]R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68,022312 (2003).
[49]H. J. Briegel, and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett.86,910 (2001).
[50]M. Van-den-Nest, A. Miyake, W. Dur, and H. J. Briegel, Universal Resources for Measurement-Based Quantum Computation, Phys. Rev. Lett.97,150504 (2006).
[51]P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter et al., Experimental one-way quantum computing, Nature 434,169 (2005).
[52]M. S. Tame, R. Prevedel, M. Paternostro, P. Bohi, M. S. Kim et al., Experimental Realization ofDeutsch's Algorithm in a One-Way Quantum Computer, Phys. Rev. Lett.98,140501 (2007).
[53]N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne et al., Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett.95,210502 (2005).
[54]P. Walther, M. Aspelmeyer, K. J. Resch, and A. Zeilinger, Experimental Violation of a Cluster State Bell Inequality, Phys. Rev. Lett.95,020403 (2005).
[55]A. N. Zhang, C. Y. Lu, X. Q. Zhou, Y. A. Chen, Z. Zhao et al., Experimental construction of optical multiqubit cluster states from Bell states, Phys. Rev. A 73,022330 (2006).
[56]C. Y. Lu, X. Q. Zhou, O. Guhne, W. B. Gao, J. Zhang et al., Experimental entanglement of six photons in graph states, Nature Phys.3,91 (2007).
[57]R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek et al., High-speed linear optics quantum computing using active feed-forward, Nature 445,65 (2007).
[58]X. Su, A. Tan, X. Jia, J. Zhang, C. Xie et al., Experimental Preparation of Quadripartite Cluster and Greenberger-Horne-Zeilinger Entangled States for Continuous Variables, Phys. Rev. Lett.98,070502 (2007).
[59]G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, Active One-Way Quantum Computation with Two-Photon Four-Qubit Cluster States, Phys. Rev. Lett.100,160502 (2008).
[60]K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel et al., Experimental Realization of One-Way Quantum Computing with Two-Photon Four-Qubit Cluster States, Phys. Rev. Lett.99, 120503 (2007).
[61]C. Ju, J. Zhu, X. Peng, B. Chong, X. Zhou et al., Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer, Phys. Rev. A 81,012322 (2010).
[62]D. G. Cory, M. D. Price, and T. F. Havel, Nuclear magnetic resonance spectroscopy:An experimentally accessible paradigm for quantum computing, Physica D 120,82-101 (1998).
[63]N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbruggen, and S. J. Glaser, Optimal control of coupled spin dynamics:design of NMR pulse sequences by gradient ascent algorithms, J. Mag. Reson.172,296-305 (2005).
[64]J. S. Lee, The quantum state tomography on an NMR system, Phys. Lett. A 305,349-353 (2002).
[65]G. Toth, and O. Guhne, Entanglement detection in the stabilizer formalism, Phys. Rev. A 72, 022340 (2005).
[66]G. Teklemariam, E. M. Fortunato, M. A. Pravia, T. F. Havel, and D. G. Cory, NMR Analog of the Quantum Disentanglement Eraser, Phys. Rev. Lett.86,5845 (2001).
[67]D. Suter, and K. Lim, Scalable architecture for spin-based quantum computers with a single type of gate, Phys. Rev. A 65,052309 (2002).
[68]W. Harneit, Fullerene-based electron-spin quantum computer, Phys. Rev. A 65,032322 (2002).
[69]P. Jakes, K. Dinse, C. Meyer, W. Harneit, and A. Weidinger, Purification and optical spectroscopy of N@C60, Phys. Chem. Chem. Phys.5,4080-4083 (2003).
[70]B. Naydenov, C. Spudat, M. Scheloske, H. I. Suess, J. Hulliger et al., N@C60 and N@C70 oriented in a single-crystalline matrix, Phys. Stat. Sol. (b) 243,2995-2998 (2006).
[71]B. Naydenov, C. Spudat, W. Harneit, H. I. Suss, J. Hulliger et al., Ordered inclusion of endohedral fullerenes N@C60 and P@C60 in a crystalline matrix, Chem. Phys. Lett.424,327-332 (2006).
[72]C. Meyer, Endohedral Fullerenes for Quantum Computing (Ph.D. thesis, Universitat Berlin, 2003).
[73]G. W. Morley, J. V. Tol, A. Ardavan, K. Porfyrakis, J. Zhang et al., Efficient Dynamic Nuclear Polarization at High Magnetic Fields, Phys. Rev. Lett.98,220501 (2007).
[74]M. Mehring, W. Scherer, and A. Weidinger, Pseudoentanglement of Spin States in the Multilevel 15N@C60 System, Phys. Rev. Lett.93,206603 (2004).
[75]G. W. Morley, Designing a Quantum Computer based on Pulsed Electron Spin Resonance (Ph.D. thesis, University of Oxford,2005).
[76]J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, K. Porfyrakis, S. A. Lyon et al., Environmental effects on electron spin relaxation in N@C60, Phys. Rev. B 76,085418 (2007).
[77]J. J. L. Morton, A. M. Tyryshkin, K. Porfyrakis, S. A. Lyon, and G. A. D. Briggs, Electron spin relaxation of N@C60 in CS2, J. Chem. Phys 124,014508 (2006).
[78]A. M. Tyryshkin, J. J. L. Morton, A. Ardavan, and S. A. Lyon, Davies electron-nuclear double resonance revisited:Enhanced sensitivity and nuclear spin relaxation, J. Chem. Phys 124, 234508 (2006).
[79]J. J. L. Morton, Electron Spins in Fullerenes as Prospective Qubits (Ph.D. thesis, University of Oxford,2005).
[80]J. Twamley, Quantum-cellular-automata quantum computing with endohedral fullerenes, Phys. Rev. A 67,052318 (2003).
[81]K. M. Lee, L. S. Dang, and G. D. Watkins, Optically detected magnetic resonance study of SiC:Ti, Phys. Rev. B 32,2273-2284 (1985).
[82]F. Jelezko, and J. Wrachtrup, Read-out of single spins by optical spectroscopy, J. Phys.: Condens. Matter 16, R1089-R1104 (2004).
[83]K. Huebener, R. S. Schoenfeld, J. Kniepert, C. Oelmueller, and W. Hameit, ODMR of NV centers in nano-diamonds covered with N@C60, Phys. Stat. Sol. (b) 245,2013-2017 (2008).
[84]S. C. Benjamin, A. Ardavan, G. A. D. Briggs, D. A. Britz, D. Gunlycke et al., Towards a fullerene-based quantum computer, J. Phys.:Condens. Matter 18, S867-S883 (2006).
[85]W. Harneit, C. Boehme, S. Schaefer, K. Huebener, K. Fostiropoulos et al., Room Temperature Electrical Detection of Spin Coherence in C60, Phys. Rev. Lett.98,216601 (2007).
[86]D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, Single spin detection by magnetic resonance force microscopy, Nature 430,329-332 (2004).
[87]M. Xiao, I. Martin, E. Yablonovitch, and H. W. Jiang, Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor, Nature 430,435-439 (2004).
[88]C. I. Pakes, P. W. Josephs-Franks, R. P. Reed, S. G. Corner, and M. S. Colclough, Development of miniature DC SQUID devices for the detection of single atomic spin-flips, IEEE Trans. Instrum. Meas.50,310 (2001).
[89]C. Durkan, and M. E. Welland, Electronic spin detection in molecules using scanning-tunneling-microscopy-assisted electron-spin resonance, Appl. Phys. Lett.80,458 (2002).
[90]J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, S. C. Benjamin, K. Porfyrakis et al., Bang-bang control of fullerene qubits using ultrafast phase gates, Nature Phys.2,40 (2006).
[91]S. Toth, D. Quintavalle, B. Nafradi, L. Korecz, L. Forro et al., Enhanced thermal stability and spin-lattice relaxation rate of N@ C60 inside carbon nanotubes, Phys. Rev. B 77,214409 (2008).
[92]W. Harneit, K. Huebener, B. Naydenov, S. Schaefer, and M. Scheloske, N@C60 quantum bit engineering, Phys. Stat. Sol. (b) 244,3879-3884 (2007).
[93]C. Ju, D. Suter, and J. Du, Two-qubit gates between noninteracting qubits in endohedral-fullerene-based quantum computation, Phys. Rev. A 75,012318 (2007).
[94]C. A. Perez-Delgado, and P. Kok, What is a quantum computer, and how do we build one?, arXiv:0906.4344v1 [quant-ph] (2009).
[2]P. Benioff, The computer as a physical system:A microscopic quantum mechanical Hamiltonian model of computers as represented by Turing machines, J. Sta. Phys.22,563-591 (1980).
[3]R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys.21,467-488 (1982).
[4]D. Deutsch, Quantum theory, the Church-Turing principle and the universal quantum computer, Proc. R. Soc. A 439,553-558 (1985).
[5]D. Deutsch, and R. Jozsa, Rapid Solution of Problems by Quantum Computation, Proc. R. Soc. A 439,553-558(1992).
[6]P. Shor, Polynomial-time algorithms for prime factorization and discrete algorithms on a quantum computer, Proceedings of the 35th annual symposium on the foundation of computer science, IEEE press,124-133 (1994).
[7]L. K. Grover, Quantum mechanics helps in searching for a needle in a haystack, Phys. Rev. Lett.79,325 (1997).
[8]M. Scholz, T. Aichele, S. Ramelow, and O. Benson, Deutsch-Jozsa Algorithm-Using Triggered Single Photons from a Single Quantum Dot, Phys. Rev. Lett.96,180501 (2006).
[9]E. Brainis, L. P. Lamoureux, N. J. Cerf, P. Emplit, M. Haelterman et al., Fiber-Optics Implementation of the Deutsch-Jozsa and Bernstein-Vazirani Quantum Algorithms with Three Qubits, Phys. Rev. Lett.90,157902 (2003).
[10]S. Guide, M. Riebe, G. P. T. Lancaster, C. Becher, J. Eschner et al., Implementation of the Deutsch-Jozsa algorithm on an ion-trap quantum computer, Nature 421,48 (2003).
[11]L. M. K. Vandersypen, M. Steffen, G. Breyta, C. S. Yannoni, M. H. Sherwood et al., Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance, Nature 414,883 (2001).
[12]I. L. Chuang, N. Gershenfeld, and M. Kubinec, Experimental Implementation of Fast Quantum Searching, Phys. Rev. Lett.80,3408 (1998).
[13]M. A. Nielsen, E. Knill, and R. Laflamme, Complete quantum teleportation using nuclear magnetic resonance, Nature 396,52 (1998).
[14]J. A. Jones, M. Mosca, and R. H. Hansen, Implementation of a quantumsearch algorithm on a quantum computer, Nature 393,344 (1998).
[15]I. L. Chuang, L. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, Experimental realization of a quantum algorithm, Nature 393,143 (1998).
[16]D. P. DiVincenzo, The Physical Implementation of Quantum Computation, Fortsch. Phys.48, 771-783 (2000).
[17]T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe et al., Quantum computers, Nature 464,45 (2010).
[18]L. M. K. Vandersypen, and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys.76,1037 (2004).
[19]B. E. Kane, A silicon-based nuclear spin quantum computer, Nature 393,133 (1998).
[20]J. I. Cirac, and P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett.74, 4091-4094(1995).
[21]C. Wunderlich, C. Balzer, T. Hannemann, F. Mintert, W. Neuhauser et al., Spin resonance with trapped ions, Journal of Physics B:Atomic, Molecular and Optical Physics 36,1063 (2003).
[22]J. L. O'Brien, Optical quantum computing, Science 318,1567-1570 (2007).
[23]E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, Nature 409,46-52 (2001).
[24]R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, Spins in few-electron quantum dots, Rev. Mod. Phys.79,1217-1265 (2007).
[25]A. Imamoglu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss et al., Quantum Information Processing Using Quantum Dot Spins and Cavity QED, Phys. Rev. Lett.83, 4204-4207(1999).
[26]T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, Spin-based all-optical quantum computation with quantum dots:Understanding and suppressing decoherence, Phys. Rev. A 68, 012310(2003).
[27]I. Chiorescu, Y. Nakamura, C. J. P. M. Harmans, and J. E. Mooij, Coherent quantum dynamics of a superconducting flux qubit, Science 299,1869-1871 (2003).
[28]J. M. Martinis, S. Nam, J. Aumentado, and C. Urbina, Rabi oscillations in a large Josephson-junction qubit, Phys. Rev. Lett.89,117901 (2002).
[29]J. E. Mooij, T. P. Orlando, L. Levitov, L. Tian, C. H. van der Wal et al., Josephson Persistent-Current Qubit, Science 285,1036 (1999).
[30]Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Coherent control of macroscopic quantum states in a single-Cooper-pair box, Nature 398,786-788 (1999).
[31]D. Deutsch, Quantum Computational Networks, Proc. R. Soc. A 425,73-90 (1989).
[32]A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus et al., Elementary gates for quantum computation, Phys. Rev. A 52,3457-3467 (1995).
[33]A. Barenco, D. Deutsch, and A. Ekert, Conditional Quantum Dynamics and Logic Gates, Phys. Rev. Lett.74,4083-4086 (1995).
[34]A. Barenco, A Universal Two-Bit Gate for Quantum Computation, Proc. R. Soc. A 449, 679-683 (1995).
[35]D. Deutsch, A. Barenco, and A. Ekert, Universality in Quantum Computation, Proc. R. Soc. A 449,669-677(1995).
[36]S. Lloyd, Almost Any Quantum Logic Gate is Universal, Phys. Rev. Lett.75,346-349 (1995).
[37]D. P. DiVincenzo, Two-bit gates are universal for quantum computation, Phys. Rev. A 51, 1015-1022 (1995).
[38]S. Lloyd, A Potentially Realizable Quantum Computer, Science 261,1569-1571 (1993).
[39]S. C. Benjamin, Schemes for parallel quantum, computation without local control of qubits, Phys. Rev. A 61,020301(R) (2000).
[40]S. C. Benjamin, Quantum Computing Without Local Control of Qubit-Qubit Interactions, Phys. Rev. Lett.88,017904 (2001).
[41]S. C. Benjamin, Multi-qubit gates in arrays coupled by'always-on'interactions, New J. Phys. 6,61 (2004).
[42]S. C. Benjamin, and S. Bose, Quantum Computing with an Always-On Heisenberg Interaction, Phys. Rev. Lett.90,247901 (2003).
[43]S. C. Benjamin, and S. Bose, Quantum computing in arrays coupled by "always-on" interactions, Phys. Rev. A 70,032314 (2004).
[44]S. C. Benjamin, Simple pulses for universal quantum computation with a Heisenberg ABAB chain, Phys. Rev. A 64,054303 (2001).
[45]D. Aharonov, W. Dam, J. Kempe, Z. Landau, S. Lloyd et al., Adiabatic Quantum Computation is Equivalent to Standard Quantum Computation, SIAM J. Comp.37,166-194 (2007).
[46]J. Roland, and N. J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65, 042308 (2002).
[47]R. Raussendorf, and H. J. Briegel, A One-Way Quantum Computer, Phys. Rev. Lett.86,5188 (2001).
[48]R. Raussendorf, D. E. Browne, and H. J. Briegel, Measurement-based quantum computation on cluster states, Phys. Rev. A 68,022312 (2003).
[49]H. J. Briegel, and R. Raussendorf, Persistent Entanglement in Arrays of Interacting Particles, Phys. Rev. Lett.86,910 (2001).
[50]M. Van-den-Nest, A. Miyake, W. Dur, and H. J. Briegel, Universal Resources for Measurement-Based Quantum Computation, Phys. Rev. Lett.97,150504 (2006).
[51]P. Walther, K. J. Resch, T. Rudolph, E. Schenck, H. Weinfurter et al., Experimental one-way quantum computing, Nature 434,169 (2005).
[52]M. S. Tame, R. Prevedel, M. Paternostro, P. Bohi, M. S. Kim et al., Experimental Realization ofDeutsch's Algorithm in a One-Way Quantum Computer, Phys. Rev. Lett.98,140501 (2007).
[53]N. Kiesel, C. Schmid, U. Weber, G. Toth, O. Guhne et al., Experimental Analysis of a Four-Qubit Photon Cluster State, Phys. Rev. Lett.95,210502 (2005).
[54]P. Walther, M. Aspelmeyer, K. J. Resch, and A. Zeilinger, Experimental Violation of a Cluster State Bell Inequality, Phys. Rev. Lett.95,020403 (2005).
[55]A. N. Zhang, C. Y. Lu, X. Q. Zhou, Y. A. Chen, Z. Zhao et al., Experimental construction of optical multiqubit cluster states from Bell states, Phys. Rev. A 73,022330 (2006).
[56]C. Y. Lu, X. Q. Zhou, O. Guhne, W. B. Gao, J. Zhang et al., Experimental entanglement of six photons in graph states, Nature Phys.3,91 (2007).
[57]R. Prevedel, P. Walther, F. Tiefenbacher, P. Bohi, R. Kaltenbaek et al., High-speed linear optics quantum computing using active feed-forward, Nature 445,65 (2007).
[58]X. Su, A. Tan, X. Jia, J. Zhang, C. Xie et al., Experimental Preparation of Quadripartite Cluster and Greenberger-Horne-Zeilinger Entangled States for Continuous Variables, Phys. Rev. Lett.98,070502 (2007).
[59]G. Vallone, E. Pomarico, F. D. Martini, and P. Mataloni, Active One-Way Quantum Computation with Two-Photon Four-Qubit Cluster States, Phys. Rev. Lett.100,160502 (2008).
[60]K. Chen, C. M. Li, Q. Zhang, Y. A. Chen, A. Goebel et al., Experimental Realization of One-Way Quantum Computing with Two-Photon Four-Qubit Cluster States, Phys. Rev. Lett.99, 120503 (2007).
[61]C. Ju, J. Zhu, X. Peng, B. Chong, X. Zhou et al., Experimental demonstration of deterministic one-way quantum computation on a NMR quantum computer, Phys. Rev. A 81,012322 (2010).
[62]D. G. Cory, M. D. Price, and T. F. Havel, Nuclear magnetic resonance spectroscopy:An experimentally accessible paradigm for quantum computing, Physica D 120,82-101 (1998).
[63]N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbruggen, and S. J. Glaser, Optimal control of coupled spin dynamics:design of NMR pulse sequences by gradient ascent algorithms, J. Mag. Reson.172,296-305 (2005).
[64]J. S. Lee, The quantum state tomography on an NMR system, Phys. Lett. A 305,349-353 (2002).
[65]G. Toth, and O. Guhne, Entanglement detection in the stabilizer formalism, Phys. Rev. A 72, 022340 (2005).
[66]G. Teklemariam, E. M. Fortunato, M. A. Pravia, T. F. Havel, and D. G. Cory, NMR Analog of the Quantum Disentanglement Eraser, Phys. Rev. Lett.86,5845 (2001).
[67]D. Suter, and K. Lim, Scalable architecture for spin-based quantum computers with a single type of gate, Phys. Rev. A 65,052309 (2002).
[68]W. Harneit, Fullerene-based electron-spin quantum computer, Phys. Rev. A 65,032322 (2002).
[69]P. Jakes, K. Dinse, C. Meyer, W. Harneit, and A. Weidinger, Purification and optical spectroscopy of N@C60, Phys. Chem. Chem. Phys.5,4080-4083 (2003).
[70]B. Naydenov, C. Spudat, M. Scheloske, H. I. Suess, J. Hulliger et al., N@C60 and N@C70 oriented in a single-crystalline matrix, Phys. Stat. Sol. (b) 243,2995-2998 (2006).
[71]B. Naydenov, C. Spudat, W. Harneit, H. I. Suss, J. Hulliger et al., Ordered inclusion of endohedral fullerenes N@C60 and P@C60 in a crystalline matrix, Chem. Phys. Lett.424,327-332 (2006).
[72]C. Meyer, Endohedral Fullerenes for Quantum Computing (Ph.D. thesis, Universitat Berlin, 2003).
[73]G. W. Morley, J. V. Tol, A. Ardavan, K. Porfyrakis, J. Zhang et al., Efficient Dynamic Nuclear Polarization at High Magnetic Fields, Phys. Rev. Lett.98,220501 (2007).
[74]M. Mehring, W. Scherer, and A. Weidinger, Pseudoentanglement of Spin States in the Multilevel 15N@C60 System, Phys. Rev. Lett.93,206603 (2004).
[75]G. W. Morley, Designing a Quantum Computer based on Pulsed Electron Spin Resonance (Ph.D. thesis, University of Oxford,2005).
[76]J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, K. Porfyrakis, S. A. Lyon et al., Environmental effects on electron spin relaxation in N@C60, Phys. Rev. B 76,085418 (2007).
[77]J. J. L. Morton, A. M. Tyryshkin, K. Porfyrakis, S. A. Lyon, and G. A. D. Briggs, Electron spin relaxation of N@C60 in CS2, J. Chem. Phys 124,014508 (2006).
[78]A. M. Tyryshkin, J. J. L. Morton, A. Ardavan, and S. A. Lyon, Davies electron-nuclear double resonance revisited:Enhanced sensitivity and nuclear spin relaxation, J. Chem. Phys 124, 234508 (2006).
[79]J. J. L. Morton, Electron Spins in Fullerenes as Prospective Qubits (Ph.D. thesis, University of Oxford,2005).
[80]J. Twamley, Quantum-cellular-automata quantum computing with endohedral fullerenes, Phys. Rev. A 67,052318 (2003).
[81]K. M. Lee, L. S. Dang, and G. D. Watkins, Optically detected magnetic resonance study of SiC:Ti, Phys. Rev. B 32,2273-2284 (1985).
[82]F. Jelezko, and J. Wrachtrup, Read-out of single spins by optical spectroscopy, J. Phys.: Condens. Matter 16, R1089-R1104 (2004).
[83]K. Huebener, R. S. Schoenfeld, J. Kniepert, C. Oelmueller, and W. Hameit, ODMR of NV centers in nano-diamonds covered with N@C60, Phys. Stat. Sol. (b) 245,2013-2017 (2008).
[84]S. C. Benjamin, A. Ardavan, G. A. D. Briggs, D. A. Britz, D. Gunlycke et al., Towards a fullerene-based quantum computer, J. Phys.:Condens. Matter 18, S867-S883 (2006).
[85]W. Harneit, C. Boehme, S. Schaefer, K. Huebener, K. Fostiropoulos et al., Room Temperature Electrical Detection of Spin Coherence in C60, Phys. Rev. Lett.98,216601 (2007).
[86]D. Rugar, R. Budakian, H. J. Mamin, and B. W. Chui, Single spin detection by magnetic resonance force microscopy, Nature 430,329-332 (2004).
[87]M. Xiao, I. Martin, E. Yablonovitch, and H. W. Jiang, Electrical detection of the spin resonance of a single electron in a silicon field-effect transistor, Nature 430,435-439 (2004).
[88]C. I. Pakes, P. W. Josephs-Franks, R. P. Reed, S. G. Corner, and M. S. Colclough, Development of miniature DC SQUID devices for the detection of single atomic spin-flips, IEEE Trans. Instrum. Meas.50,310 (2001).
[89]C. Durkan, and M. E. Welland, Electronic spin detection in molecules using scanning-tunneling-microscopy-assisted electron-spin resonance, Appl. Phys. Lett.80,458 (2002).
[90]J. J. L. Morton, A. M. Tyryshkin, A. Ardavan, S. C. Benjamin, K. Porfyrakis et al., Bang-bang control of fullerene qubits using ultrafast phase gates, Nature Phys.2,40 (2006).
[91]S. Toth, D. Quintavalle, B. Nafradi, L. Korecz, L. Forro et al., Enhanced thermal stability and spin-lattice relaxation rate of N@ C60 inside carbon nanotubes, Phys. Rev. B 77,214409 (2008).
[92]W. Harneit, K. Huebener, B. Naydenov, S. Schaefer, and M. Scheloske, N@C60 quantum bit engineering, Phys. Stat. Sol. (b) 244,3879-3884 (2007).
[93]C. Ju, D. Suter, and J. Du, Two-qubit gates between noninteracting qubits in endohedral-fullerene-based quantum computation, Phys. Rev. A 75,012318 (2007).
[94]C. A. Perez-Delgado, and P. Kok, What is a quantum computer, and how do we build one?, arXiv:0906.4344v1 [quant-ph] (2009).