Abstract

We present two different (but from a performance point of view) equivalent physical implementations for a programmable-state discriminator in terms of quantum circuits. The circuits that perform a positive-operator valued measure are built entirely of known logical quantum gates. The first, more-complicated circuit leads to a simpler readout, whereas the second, simpler circuit requires an extra measurement at the output. The performance of both implementations is good; it is not optimal but comes close to the optimal success probability. In the latter part of the paper we show how the necessary quantum gates can be realized in ion traps using state-of-the-art technology.

© 2007 Optical Society of America

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  1. J. A. Bergou and M. Hillery, "Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states," Phys. Rev. Lett. 94, 160501 (2005).
    [CrossRef] [PubMed]
  2. A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
    [CrossRef]
  3. A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
    [CrossRef]
  4. J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
    [CrossRef]
  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Information (Cambridge U. Press, 2000).
  6. J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
    [CrossRef]
  7. P. Blackburn and M. Orszag, "A single ion stochastic quantum processor," Int. J. Mod. Phys. B 20, 1679-1689 (2006).
    [CrossRef]
  8. M. Orszag and F. Larrain, "Generation of a C-NOT gate using a trapped ion," J. Opt. B 7, S754-S756 (2005).
    [CrossRef]
  9. M. Feng and X. Wang, "Implementation of quantum gates and preparation of quantum states in cavity QED with cold trapped ions," J. Opt. B 4, 283-288 (2002).
    [CrossRef]
  10. X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
    [CrossRef]
  11. J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
    [CrossRef] [PubMed]
  12. Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
    [CrossRef]
  13. C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
    [CrossRef] [PubMed]
  14. C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
    [CrossRef] [PubMed]
  15. D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
    [CrossRef] [PubMed]
  16. D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
    [CrossRef]
  17. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
    [CrossRef]
  18. M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).
  19. F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
    [CrossRef] [PubMed]
  20. Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
    [CrossRef]

2006 (3)

A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
[CrossRef]

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

P. Blackburn and M. Orszag, "A single ion stochastic quantum processor," Int. J. Mod. Phys. B 20, 1679-1689 (2006).
[CrossRef]

2005 (3)

M. Orszag and F. Larrain, "Generation of a C-NOT gate using a trapped ion," J. Opt. B 7, S754-S756 (2005).
[CrossRef]

J. A. Bergou and M. Hillery, "Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states," Phys. Rev. Lett. 94, 160501 (2005).
[CrossRef] [PubMed]

A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
[CrossRef]

2003 (1)

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

2002 (2)

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

M. Feng and X. Wang, "Implementation of quantum gates and preparation of quantum states in cavity QED with cold trapped ions," J. Opt. B 4, 283-288 (2002).
[CrossRef]

2001 (1)

X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
[CrossRef]

2000 (1)

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

1999 (1)

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

1998 (1)

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

1997 (1)

J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
[CrossRef]

1996 (2)

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

1995 (2)

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

1989 (1)

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Beall, J.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Ben-Kish, A.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Bergou, J. A.

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

J. A. Bergou and M. Hillery, "Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states," Phys. Rev. Lett. 94, 160501 (2005).
[CrossRef] [PubMed]

Bergquist, J. C.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Blackburn, P.

P. Blackburn and M. Orszag, "A single ion stochastic quantum processor," Int. J. Mod. Phys. B 20, 1679-1689 (2006).
[CrossRef]

Blatt, R.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Bollinger, J. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Britton, J.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Buzek, V.

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Information (Cambridge U. Press, 2000).

DeMarco, B.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Diedrich, F.

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Eschner, J.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Feldman, E.

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

Feng, M.

M. Feng and X. Wang, "Implementation of quantum gates and preparation of quantum states in cavity QED with cold trapped ions," J. Opt. B 4, 283-288 (2002).
[CrossRef]

Hashimoto, T.

A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
[CrossRef]

A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
[CrossRef]

Hayashi, A.

A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
[CrossRef]

A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
[CrossRef]

Heinzen, D. J.

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Herzog, U.

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

Hillery, M.

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

J. A. Bergou and M. Hillery, "Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states," Phys. Rev. Lett. 94, 160501 (2005).
[CrossRef] [PubMed]

Horibe, M.

A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
[CrossRef]

A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
[CrossRef]

Hughes, J.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Itano, W. M.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Jefferts, S. R.

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

Jelencovic, B.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Kielpinski, D.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Kim, J.

X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
[CrossRef]

King, B. E.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Knight, P. L.

J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
[CrossRef]

Langer, C.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Larrain, F.

M. Orszag and F. Larrain, "Generation of a C-NOT gate using a trapped ion," J. Opt. B 7, S754-S756 (2005).
[CrossRef]

Lee, H.-W.

X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
[CrossRef]

Leibfried, D.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

Meekhof, D. M.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Meyer, V.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Monroe, C.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

Myatt, C.

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

Myatt, C. J.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Nägerl, H. C.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Information (Cambridge U. Press, 2000).

Orszag, M.

P. Blackburn and M. Orszag, "A single ion stochastic quantum processor," Int. J. Mod. Phys. B 20, 1679-1689 (2006).
[CrossRef]

M. Orszag and F. Larrain, "Generation of a C-NOT gate using a trapped ion," J. Opt. B 7, S754-S756 (2005).
[CrossRef]

Rohde, H.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Roos, Ch.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Rosenband, T.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Rowe, M.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Rowe, M. A.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Sackett, C. A.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Schmidt-Kaler, F.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Steinbach, J.

J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
[CrossRef]

Turchette, Q. A.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Twamley, J.

J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
[CrossRef]

Wang, X.

M. Feng and X. Wang, "Implementation of quantum gates and preparation of quantum states in cavity QED with cold trapped ions," J. Opt. B 4, 283-288 (2002).
[CrossRef]

Wineland, D.

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

Wineland, D. J.

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Wood, C.

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

Wood, C. S.

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

Zeiger, Th.

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Zou, X.-B.

X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
[CrossRef]

Fortschr. Phys. (1)

D. J. Wineland, C. Monroe, W. M. Itano, B. E. King, D. Leibfried, D. M. Meekhof, C. Myatt, and C. Wood, "Experimental primer on the trapped ion quantum computer," Fortschr. Phys. 46, 363-390 (1998).
[CrossRef]

Int. J. Mod. Phys. B (1)

P. Blackburn and M. Orszag, "A single ion stochastic quantum processor," Int. J. Mod. Phys. B 20, 1679-1689 (2006).
[CrossRef]

J. Opt. B (2)

M. Orszag and F. Larrain, "Generation of a C-NOT gate using a trapped ion," J. Opt. B 7, S754-S756 (2005).
[CrossRef]

M. Feng and X. Wang, "Implementation of quantum gates and preparation of quantum states in cavity QED with cold trapped ions," J. Opt. B 4, 283-288 (2002).
[CrossRef]

Phys. Rev. A (7)

X.-B. Zou, J. Kim, and H.-W. Lee, "Generation of two-mode non-classical motional state and a Fredkin gate operation in a two dimensional ion trap," Phys. Rev. A 63, 065801 (2001).
[CrossRef]

J. J. Bollinger, W. M. Itano, D. J. Wineland, and D. J. Heinzen, "Optimal frequency measurements with maximally correlated states," Phys. Rev. A 54, R4649-R4652 (1996).
[CrossRef] [PubMed]

Q. A. Turchette, D. Kielpinski, B. E. King, D. Leibfried, D. M. Meekhof, C. J. Myatt, M. A. Rowe, C. A. Sackett, C. S. Wood, W. M. Itano, C. Monroe, and D. J. Wineland, "Heating of trapped ions from the ground state," Phys. Rev. A 61, 063418 (2000).
[CrossRef]

J. Steinbach, J. Twamley, and P. L. Knight, "Engineering two-mode interactions for ion traps," Phys. Rev. A 56, 4815-4825 (1997).
[CrossRef]

A. Hayashi, M. Horibe, and T. Hashimoto, "Quantum pure-state identification," Phys. Rev. A 72, 052306 (2005).
[CrossRef]

A. Hayashi, M. Horibe, and T. Hashimoto, "Unambiguous pure-state identification without classical knowledge," Phys. Rev. A 73, 012328 (2006).
[CrossRef]

J. A. Bergou, V. Buzek, E. Feldman, U. Herzog, and M. Hillery, "Programmable quantum-state discriminators with simple programs," Phys. Rev. A 73, 062334 (2006).
[CrossRef]

Phys. Rev. Lett. (6)

J. A. Bergou and M. Hillery, "Universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states," Phys. Rev. Lett. 94, 160501 (2005).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, W. M. Itano, and D. J. Wineland, "Demonstration of a fundamental quantum logic gate," Phys. Rev. Lett. 75, 4714-4717 (1995).
[CrossRef] [PubMed]

C. Monroe, D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, and D. J. Wineland, "Resolved sideband Raman cooling of a bound atom to the 3-D zero point energy," Phys. Rev. Lett. 75, 4011-4014 (1995).
[CrossRef] [PubMed]

D. M. Meekhof, C. Monroe, B. E. King, W. M. Itano, and D. J. Wineland, "Generation of nonclassical motional states of a trapped atom," Phys. Rev. Lett. 76, 1796-1799 (1996).
[CrossRef] [PubMed]

F. Diedrich, J. C. Bergquist, W. M. Itano, and D. J. Wineland, "Laser cooling to zero point energy of motion," Phys. Rev. Lett. 62, 403-406 (1989).
[CrossRef] [PubMed]

Ch. Roos, Th. Zeiger, H. Rohde, H. C. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, and R. Blatt, "Quantum state engineering on an optical transition and decoherence in a Paul trap," Phys. Rev. Lett. 83, 4713-4716 (1999).
[CrossRef]

Quantum Inf. Comput. (1)

M. Rowe, A. Ben-Kish, B. DeMarco, D. Leibfried, V. Meyer, J. Beall, J. Britton, J. Hughes, W. M. Itano, B. Jelencovic, C. Langer, T. Rosenband, and D. J. Wineland, "Transport of quantum states and separation of ions in a dual RF ion trap," Quantum Inf. Comput. 2, 257-271 (2002).

Rev. Mod. Phys. (1)

D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, "Quantum dynamics of single trapped ions," Rev. Mod. Phys. 75, 281-324 (2003).
[CrossRef]

Other (1)

M. A. Nielsen and I. L. Chuang, Quantum Computation and Information (Cambridge U. Press, 2000).

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Figures (6)

Fig. 1
Fig. 1

Quantum circuit for comparing two qubits probabilistically. If, at the output, we receive ∣11⟩, the qubits are not in the same state. All other outputs correspond to inconclusive results. The average probability of receiving the conclusive output is 1 4 .

Fig. 2
Fig. 2

Quantum circuit for conditional splitting of the data between two qubits. If, at the output, the state of the control bit is ∣0⟩, the data is stored in the upper qubit. If, at the output, the state of the control bit is ∣1⟩, the data is stored in the middle qubit. The probability of each alternative is 1 2 .

Fig. 3
Fig. 3

Quantum circuit for the full implementation of the programmable state discriminator. If, at the output, the reading in the qubits 1 and 3 is 11 13 , the data state is ψ 2 . If, at the output, the reading in the qubits 2 and 4 is 11 24 , the data state is ψ 1 . The average probability of either alternative is 1 8 .

Fig. 4
Fig. 4

Simplified quantum circuit for the full implementation of the programmable state discriminator. If, at the output, the reading in the program qubit 1, data qubit 3, and control bit 5 is 010 135 , the data state is ψ 2 . If, at the output, the reading in the program qubit 2, data qubit 4, and control bit 5 is 011 245 , the data state is ψ 1 . The average probability of either alternative is 1 8 .

Fig. 5
Fig. 5

Energy-level scheme for our setup. Classical lasers E 1 and E 2 of frequencies ω 12 and ω 23 , detuned from resonance by Δ 12 and Δ 23 , respectively, induce a two-mode Raman transition, coupling the ion’s three-dimensional center-of-mass motion in the trap to the electronic state.

Fig. 6
Fig. 6

Ion in a three-dimensional asymmetrical harmonic trap of frequencies ν x , ν y , and ν z is illuminated by two lasers E 1 and E 2 , both in arbitrary directions but sharing the same polarization vector.

Equations (41)

Equations on this page are rendered with MathJax. Learn more.

ψ in = ψ 1 ψ 2 = ( α 1 0 + β 1 1 ) ( α 2 0 + β 2 1 ) = α 1 α 2 00 + α 1 β 2 01 + α 2 β 1 10 + β 1 β 2 11 ,
ψ in = α 1 α 2 00 + α 1 β 2 + α 2 β 1 2 Ψ + + α 1 β 2 α 2 β 1 2 Ψ + β 1 β 2 11 ,
Ψ ± 01 ± 10 2 ,
± = 0 ± 1 2 .
( CNOT ) Ψ 1 ,
( HAD ) 1 , 1 , 1 .
( HAD ) ( CNOT ) ψ in = ( HAD ) ( CNOT ) ψ 1 ψ 2 = α 1 α 2 + β 1 β 2 2 00 + α 1 α 2 β 1 β 2 2 01 + α 1 β 2 + α 2 β 1 2 10 α 1 β 2 α 2 β 1 2 11 .
p = 1 2 α 1 β 2 α 2 β 1 2 = 1 2 ( 1 ψ 1 ψ 2 2 ) ,
ψ in = ψ 0 0 .
( HAD ) 3 ψ 0 0 ψ 1 0 0 + 1 2 .
( CSWAP ) ψ 0 0 + 1 2 ψ 0 0 + 0 ψ 1 2 .
ψ in = ψ 1 ψ 2 ψ 0 0 1 ,
ψ 1 = ( α 1 0 + β 1 1 ) ,
ψ 2 = ( α 2 0 + β 2 1 ) ,
ψ = ( γ 0 + δ 1 ) .
( CSWAP ) 345 ( HAD ) 5 ψ 1 ψ 2 ψ 0 0 1 = ψ 1 ψ 2 ψ 0 0 + 0 ψ 1 1 2 1 .
( CNOT ) 56 ψ 1 ψ 2 ψ 0 0 + 0 ψ 1 2 1 = ψ 1 ψ 2 ψ 0 0 1 + 0 ψ 1 0 2 .
( CHAD 54 ) ( CHAD 63 ) ( T ) 542 ( T ) 631 ( CNOT ) 56 ( CSWAP ) 345 ( HAD ) 5 ψ in = 1 2 { α 1 γ + β 1 δ 2 00 13 + α 1 γ β 1 δ 2 01 13 + α 1 δ + β 1 γ 2 10 13 α 1 δ β 1 γ 2 11 13 } ψ 2 2 001 456 + 1 2 { α 2 γ + β 2 δ 2 00 24 + α 2 γ β 2 δ 2 01 24 + α 2 δ + β 2 γ 2 10 24 α 2 δ β 2 γ 2 11 24 } ψ 1 1 010 356 ,
ψ in = ψ 1 ψ 2 ψ 0 0 ,
( HAD 4 ) ( HAD 3 ) ( CNOT ) 42 ( CNOT ) 31 ( CSWAP ) 345 ( HAD ) 5 ψ in = 1 2 { α 1 γ + β 1 δ 2 00 13 + α 1 γ β 1 δ 2 01 13 + α 1 δ + β 1 γ 2 10 13 α 1 δ β 1 γ 2 11 13 } ψ 2 2 + 4 0 5 + 1 2 { α 2 γ + β 2 δ 2 00 24 + α 2 γ β 2 δ 2 01 24 + α 2 δ + β 2 γ 2 10 24 α 2 δ β 2 γ 2 11 24 } ψ 1 1 + 3 1 5 .
p 1 = α 1 2 + β 1 2 4 α 1 β 2 α 2 β 1 2 = 1 4 [ 1 ψ 2 ψ 1 2 ] .
P = η 1 p 1 + η 2 p 2 = 1 4 [ 1 ψ 2 ψ 1 2 ] .
E 1 = e [ E 1 e i ( k 1 r ω 12 t ) + H.c. ] ,
E 2 = e [ E 2 e i ( k 2 r ω 23 t ) + H.c. ] ,
H 1 C = Ω 1 C ( a σ + a σ + ) ,
H 2 C = Ω 2 C ( a b σ + a b σ + ) ,
Ω 1 C = Ω 13 η x exp [ 1 2 ( η x 2 + η y 2 ) ] ,
Ω 2 C = Ω 13 η x η y exp [ 1 2 ( η x 2 + η y 2 ) ] ,
Δ 13 = ω 12 ω 23 ( ω ̃ 3 ω ̃ 1 ) ,
g l a cos ( l Ω 1 C t ) g l a i sin ( l Ω 1 C t ) e l 1 a ,
e l a cos ( l + 1 Ω 1 C t ) e l a i sin ( l + 1 Ω 1 C t ) g l + 1 a ,
g l a m b cos ( l m Ω 2 C t ) g l a m b i sin ( l m Ω 2 C t ) e l 1 a m 1 b ,
e l a m b cos ( ( l + 1 ) ( m + 1 ) Ω 2 C t ) e l a m b i sin ( ( l + 1 ) ( m + 1 ) Ω 2 C t ) g l + 1 a m + 1 b .
g 1 00 a b g 1 00 a b g 1 00 a b g 1 00 a b ,
g 1 01 a b g 1 01 a b g 1 01 a b g 1 01 a b ,
g 1 10 a b g 1 10 a b i e 3 00 a b g 1 11 a b ,
g 1 11 a b i e 3 00 a b g 1 10 a b g 1 10 a b ,
H 1 = G ( σ + + σ ) .
H 2 = Ω 2 ( a b + a b ) σ x ,
H 3 = Ω 3 ( a b + a b ) ,
Ω 2 t = Ω 3 t = π 4 ,

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