An exact effective two-qubit gate in a chain of three spins

Quantum Information and Computation

Volumn 4, Issue 3, 2004, Pages 174-185

  Yung, Man Hong ^a,b   Leung, Debbie W ^b   Bose, Sougato ^b,c  

^a CHINESE UNIVERSITY OF HONG KONG   (Hong Kong)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Entanglement; Quantum gate; Spin chain; State transfer

Indexed keywords

LOGIC GATES; MOLECULAR PHYSICS; QUBITS; SPIN DYNAMICS;

ARBITRARY QUANTUM STATE; ENTANGLEMENT; LOCAL MAGNETIC FIELD; NEAREST NEIGHBORS; QUANTUM GATES; QUANTUM STATE TRANSFERS; SPIN CHAINS; STATE TRANSFER;

QUANTUM ENTANGLEMENT;

EID: 4143130013     PISSN: 15337146     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (24)

1. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
2. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
3. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
4. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
5. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
6. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
7. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
8. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
9. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
10. N. Linden, H. Barjat, R. Carbajo, and R. Freeman (1999), Chem. Phys. Lett. 305 28, ; D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Phys. Rev. A 61, 042310 ; J. Jones and E. Knill (1999), J. of Mag. Res. 141, 322 ; J. L. Dodd, M. A. Nielsen, M. J. Bremner, R. T. Thew (2002), Phys. Rev. A 65, 040301 (R); P. Wocjan, D. Janzing, Th. Beth (2002), Quant. Inf. Comp. 2, 117; D. Leung (2002), J. Mod. Opt. 49, 1199; M. Stollsteimer and G. Mahler (2001), Phys. Rev. A 64, 052301; N. Khaneja, R. Brockett, and S. J. Glaser (2001), Phys. Rev. A. 63, 032308; P. Wocjan, M. Roetteler, D. Janzing, and Th. Beth (2002), Phys. Rev. A 65, 042309 ; M. A. Nielsen, M. J. Bremner, J. L. Dodd, A. M. Childs, C. M. Dawson (2002), Phys. Rev. A 66, 022317.
11. D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto (2000), Efficient implementation of coupled logic gates for quantum computation, Phys. Rev. A, 61 042310.
12. J. Jones and E. Knill (1999), Efficient refocusing of one-spin and two-spin interactions for NMR quantum computation, J. of Mag. Res., 141 322-5.
13. S. Bose (2003), Quantum Communication through an Unmodulated Spin Chain, Phys. Rev. Lett 91, 207901.
14. V. Subrahmanyam (2004), Entanglement dynamics and quantum state transport in spin chains, Phys. Rev. A, 69 034304.
15. M. Christandl, N. Datta, A. Ekert and A.J. Landahl (2003), Perfect state transfer in quantum spin networks, quant-ph/0309131.
16. N. Khaneja, S. J. Glaser and R. W. Brockett (2002), Sub-Riemannian geometry and time optimal control of three spin systems: Quantum gates and coherence transfer, Phys. Rev. A, 65, 032301.
17. T. S. Cubitt, F. Verstraete, W. Dür and J.I. Cirac (2003), Separable states can be used to distribute entanglement, Phys. Rev. Lett. 91, 037902
18. S. C. Benjamin and S. Bose (2003), Quantum Computing with an Always-On Heisenberg Interaction, Phys. Rev. Lett. 90, 247901.
19. C. Bennett, A. Harrow, D. Leung, and J. Smolin (2002), Quantum data hiding, IEEE Trans. Inf. Theory, 48 580.
20. W. Dür, G. Vidal and J. I. Cirac (2000), Three qubits can be entangled in two inequivalent ways, Phys. Rev. A 62 062314.
21. A. Childs, E. Farhi, J. Goldstone, and S. Gutmann (2002), Finding cliques by quantum adiabatic evolution, Quant. Inf. Comp. 2, 181.
22. G. Arfken and H. Weber (2001), Mathematical Methods for Physicists (Harcourt, San Diego).
23. Weisstein Mathematics, http://mathworld.wolfram.com
24. M. Abramowitz and I. A. Stegun (1972), Handbook of Mathematical Functions (Dover, New York).