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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 3 — Jan. 31, 2011
  • pp: 2037–2045
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Implementation of Deutsch-Jozsa algorithm and determination of value of function via Rydberg blockade

Aixi Chen  »View Author Affiliations


Optics Express, Vol. 19, Issue 3, pp. 2037-2045 (2011)
http://dx.doi.org/10.1364/OE.19.002037


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Abstract

We propose an efficient scheme in which the Deutsch-Jozsa algorithm can be realized via Rydberg blockade interaction. Deutsch-Jozsa algorithm can fast determine whether function is constant or balanced, but this algorithm does not give the concrete value of function. Using the Rydberg blockade, value of function may be determined in our scheme. According to the quantitative calculation of Rydberg blockade, we discuss the experimental feasibility of our scheme.

© 2011 OSA

1. Introduction

Quantum algorithm, which is made up of a fixed sequence of quantum logic gates, is applied in the process of quantum computation. Quantum algorithm uses some essential feature of quantum mechanics such as quantum superposition or quantum entanglement, so it can solve some problems those cannot be solved by classical algorithm, or it might be able to solve some problems faster than classical algorithm. The most well known algorithm includes Shor’s algorithm for factoring [1

1. P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26(5), 1484–1509 (1997). [CrossRef]

], Grover’s algorithm for searching an unstructured database or unordered list [2

2. L. K. Grover, “Quantum Computers Can Search Rapidly by Using Almost Any Transformation,” Phys. Rev. Lett. 80(19), 4329–4332 (1998). [CrossRef]

], and Deutsch-Jozsa algorithm for solving a black-box problem [3

3. D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992). [CrossRef]

].

For Deutsch-Jozsa algorithm, a black box problem can be done with one query, but, for deterministic classical computers, one requires exponentially many queries to solve the black box problem. Taking the two-qubit Deutsch-Jozsa algorithm (Deutsch algorithm) as an example, we know quantum black box is designed to distinguish between the constant and balanced function on two qubits. The Deutsch question is: supposing f(x) is a function about variable x, where x=0 or 1 and its value of function for each input is either 0 or 1. If f(0)=f(1), f(x) is called the constant function; If f(0)f(1), it is the balanced function. The Deutsch algorithm only needs one query to determine whether the f(x) is constant or balanced, that is, this algorithm can fast know the global property of the function f(x). The experimental realization of Deutsch-Jozsa algorithm is firstly reported in the nuclear magnetic resonance system by two research groups [4

4. I. L. Chuang, I. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, “Experimental realization of a quantum algorithm,” Nature 393(6681), 143–146 (1998). [CrossRef]

,5

5. J. A. Jones and M. Mosca, “Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer,” J. Chem. Phys. 109(5), 1648–1653 (1998). [CrossRef]

]. Subsequently, some researchers realize Deutsch-Jozsa algorithm in ion trap and the linear optical system [6

6. M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91(18), 187903 (2003). [CrossRef] [PubMed]

]. With a single electronic spin in diamond [7

7. F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105(4), 040504 (2010). [CrossRef] [PubMed]

] or QED technique [8

8. S.-B. Zheng, “Scheme for implementing the Deutsch-Jozsa algorithm in cavity QED,” Phys. Rev. A 70(3), 034301 (2004). [CrossRef]

], Deutsch-Jozsa algorithm is also investigated.

Neutral atom qubits are considered a very promising approach to a scalable quantum computer [9

9. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]

16

16. Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69(6), 063803 (2004). [CrossRef]

]. With neutral atoms using Rydberg blockade interactions, the demonstration of two-qubit controlled-NOT gate [9

9. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]

], preparation of two-particle or multiparticle entanglement [10

10. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010). [CrossRef] [PubMed]

,11

11. M. Saffman and K. Mølmer, “Efficient multiparticle entanglement via asymmetric Rydberg blockade,” Phys. Rev. Lett. 102(24), 240502 (2009). [CrossRef] [PubMed]

], implementation of a multiqubit quantum phase gate [12

12. H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Implementation of a multiqubit quantum phase gate in a neutral atomic ensemble via the asymmetric Rydberg blockade,” Phys. Rev. A 82(3), 034307 (2010). [CrossRef]

], and an efficient quantum repeater architecture with mesoscopic atomic ensembles [13

13. B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. Lett. 81, 052329 (2010).

] are proposed in the latest results of research. In this Rydberg blockade effect, the first excited atom shifts the Rydberg levels of nearby atoms and prevents any further excitation of them, resulting in the production of singly excited collective states [17

17. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009). [CrossRef]

]. Being an attractive system for quantum information processing, the Rydberg approach has its own advantages [9

9. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]

]: it does not require cooling of the atoms to the ground state of the confining potentials, it can be operated on μs time scales due to the long lifetime of Rydberg atoms, it permits large interaction distance and does not require precise control of the interaction strength between two-atom, and it is easy to scale to multiqubit system.

2. Implementation of two-qubit Deutsch-Jozsa Algorithm

We consider two atoms are trapped by the confining potentials and two trapping regions might be separated by z=10μm [17

17. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009). [CrossRef]

]. Internal states of each atom can be expressed as |0, |1 and |r, where |0, |1 stand for qubit states, and |r is Rydberg state. Levels and transitions between levels are shown in Fig. 1
Fig. 1 Level scheme and transitions between levels.
.

For D-J algorithm, we consider a quantum black box and it can perform a two-qubit transformation:
Uf:|xi|ya|xi|yf(x)a,
(1)
where x, y{0,1}, ⊕ is addition modulo two, and i and a stand for an input query qubit and an auxiliary qubit, respectively. Considering the transition between internal levels |0 and |1, in the rotating-wave approximation, the evolution of each atom is described by the interaction Hamiltonian [18

18. M. O. Scully, and M. S. Zubairy, Quantum Optics (Cambridge: Cambridge University Press,1997), Chap.5.

] H=ΩR2(|10|+|01|), where ΩR is the Rabi frequency. Assuming the initial state of two atoms is in state |0, we choose ΩRt=π/2, and ΩRt=3π/2 for input qubit and auxiliary qubit, respectively, then |0i12(|0i+|1i), and |0a12(|0a|1a). The state of two-atom can be expressed as
|Ψ1=12(|0i+|1i)(|0a|1a).
(2)
We send this state into a quantum black box. According to the value of function f(x), the quantum black box performs four different kinds of operations Ufj (j=1,2,3,4), where Uf1 corresponding to f(0)=f(1)=0, Uf2 corresponding to f(0)=f(1)=1, Uf3 corresponding to f(0)=1 and f(1)=0, and Uf4 corresponding to f(0)=0 and f(1)=1. After the operations Ufjare performed, the state |Ψ1 becomes
|Ψ1Uf1|Ψ2=12(|0i+|1i)(|0a|1a),
(3a)
|Ψ1Uf2|Ψ2=12(|0i+|1i)(|0a|1a),
(3b)
|Ψ1Uf3|Ψ2=12(|0i|1i)(|0a|1a),
(3c)
|Ψ1Uf4|Ψ2=12(|0i|1i)(|0a|1a).
(3d)
Now we investigate how to perform operations Ufj via Rydberg blockade.

For the case f(0)=f(1)=0, quantum black box does not perform any operations on input and auxiliary qubits, that is, Uf1=IiIa.

If the value of f(0) is 1 and f(1)=0, the level scheme and the sequence of operations for Uf3 are shown in Fig. 3
Fig. 3 Level scheme and sequence of operations for Uf3.
. Here we apply the Rydberg blockade: for step 2, under the drive by laser, the state of the input atom is transferred from |1i to Rydberg state |ri. Due to the strong Rydberg interaction energy Δrr|ri|raar|ir|, the excitation between |1a and Rydberg state |ra is blocked. The interaction Hamiltonian [19

19. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Many-body theory of excitation dynamics in an ultracold Rydberg gas,” Phys. Rev. A 76(1), 013413 (2007). [CrossRef]

] for two atoms can be expressed as H=Δrr|ri|raar|ir|+ΩR2(|raa1|+|rii1|+h.c.), where considering the coupling between states |1a and Rydberg state |ra. For step 3, the dipole-dipole interaction |ri|ra shifts the Rydberg level |ra so that it is blockade and |1a2π|1a. After the operation Uf3, the state |Ψ1 can be expressed as
|Ψ1Uf3|Ψ2=12(|0i|1i)(|0a|1a).
(5)
For the case f(0)=0, and f(1)=1, we first perform σx operation on the input qubit. Implementation of σx includes two steps: application of a 2π pulse between states |1i and |ri of the input atom results in |1i|1i, and coupling between states |1i and |0i by using a π pulse leads to |0i|1i and |1i|0i. Next, sequential operations shown in Fig. 3 are performed on the input and the auxiliary atoms. Finally, we re-perform a σx operation on the input qubit. The final state of two-atom system becomes
|Ψ1Uf4|Ψ2=12(|0i|1i)(|0a|1a).
(6)
After performing the operation Ufj, the final state of two-atom system can be expressed as
|Ψ2=12((1)f(0)|0i+(1)f(1)|1i)12(|0a|1a).
(7)
Next, a π/2 pulse is applied between states |0i and |1i of the input qubit, which leads to 12(|0i+|1i|1i, and 12(|0i|1i|0i. Finally, we only take a measurement on the input qubit with basis {|0i,|1i}. If the outcome of measurement is |1i, the function f(x) is constant; If the outcome of measurement is |0i, the function f(x) is balanced. Thus, one measurement is sufficient to determine whether the function f(x) is constant or balanced, that is, we realize the two-qubit D-J algorithm via Rydberg blockade.

3. Determination of value of function

This is very indeed: the D-J algorithm has given us the ability to determine a global property of f(x). However, D-J algorithm cannot give the concrete value of function f(x). For example, f(0)=f(1) means f(x) is the constant function. But either f(0)=f(1)=0 or f(0)=f(1)=1 is unknown to us. Now we propose a scheme in which the value of function may be determined.

In order to get the value of function f(x), we need a two-atom entangled state
|Ψia1=12(|0i|0a+|1i|1a),
(8)
whose preparation is shown in Ref [10

10. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010). [CrossRef] [PubMed]

].

After the D-J algorithm is completed, let this entangled state Eq. (8) cross the quantum black box. For the constant function, if f(0)=f(1)=0, two atoms are in the entangled state |Ψia1, i.e.
|Ψia1Uf1|Ψia2=|Ψia1.
(9)
If f(0)=f(1)=1, the state of two-atom undergoes the unitary operation Uf2, and evolves as
|Ψia1Uf2|Ψia2=12(|0i|1a+|1i|0a).
(10)
Next, we perform sequential operations shown in Fig. 3 on the state |Ψia2. For the case f(0)=f(1)=0, the state |Ψia2 (expression (9)) evolves as 12(|0i+|1i)|1a, and for the case f(0)=f(1)=1, the state |Ψia2 (expression (10)) becomes 12(|0i+|1i)|0a. Then, performing a measurement on the auxiliary atom with basis {|0a,|1a}. If the outcome of measurement is |0a, f(x) is equal to 1; If the outcome shows |1a, f(x) is equal to 0. For the constant function, we have determined the value of function f(x).

For the balanced function, the entangled state Eq. (8) is sent into quantum black box. For the case f(0)=1 and f(1)=0, the entangled state |Ψia1 undergoes unitary operation Uf3, and becomes 12(|0i+|1i)|1a. For the case f(0)=0 and f(1)=1, unitary operation Uf4 is applied on the entangled state, and we obtain 12(|0i+|1i)|0a. Next, single particle measurement is performed on the auxiliary atom in basis {|0a,|1a}, which is sufficient to determine whether the values of function f(x) are f(0)=0 and f(1)=1 or f(0)=1 and f(1)=0.

Our scheme can be extended to multi-qubit system. Here, we consider the three-qubit Deutsch-Jozsa question. The state of two input qubits and an auxiliary qubit can be expressed as
12(|0i1+|1i1)12(|0i2+|1i2)12(|0a|1a).
(11)
This state are sent into a quantum black box. For different possible values of the function f(x) (x=00,01,10,11), we only take measurement on the input qubits with basis { |0i1|0i2, |0i1|1i2, |1i1|0i2, |1i1|1i2 }, and can determine the global property of f(x).

For constant function, outcomes of measurement are |0i1|0i2, corresponding values of f(x) are f(00)=f(01)=f(10)=f(11)=0, or f(00)=f(01)=f(10)=f(11)=1.

For balanced function, measurements include three different outcomes. If outcomes of measurement are |0i1|1i2, values of f(x) are f(00)=f(10)=1, f(01)=f(11)=0, or f(00)=f(10)=0, f(01)=f(11)=1.

If outcomes of measurement are |1i1|0i2, values of f(x) are f(00)=f(01)=0, f(10)=f(11)=1, or f(00)=f(01)=1, f(10)=f(11)=0.

If outcomes are |1i1|1i2, values of f(x) are f(00)=f(11)=0, f(01)=f(10)=1, or f(00)=f(11)=1, f(01)=f(10)=0.

In the process of two-qubit D-J algorithm, single qubit gates and a two-qubit controlled-NOT gate are proposed via Rydberg blockade. Based on a complete set of universal gates, the three-atom D-J algorithm and extraction of the values of f(x) might be realizable.

4. Conclusion

Applying the Rydberg blockade, we have proposed a scheme for implementing two-qubit Deutsch-Jozsa algorithm. According to the D-J algorithm, we can learn the global property of function f(x). In our scheme, the entangled state of two atoms is sent into quantum black box and undergoes appropriate unitary operations. Finally, the value of function can be completely determined. As far as we know, this result of study is first reported.

Based on the experimental developments of Rydberg blockade in quantum information, we discuss the experimental feasibility of our scheme. Our scheme can be implemented using cold 87Rb atom. Rydberg blockade between two rubidium atoms localized in spatially separated trapping sites has been observed [17

17. E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009). [CrossRef]

]. A controlled-NOT gate between two individually addressed rubidium atoms has been realized [9

9. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]

]. In addition, Rabi oscillation between ground and Rydberg states with dipole-dipole interaction can be effectively controlled [20

20. T. A. Johnson, E. Urban, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions,” Phys. Rev. Lett. 100(11), 113003 (2008). [CrossRef] [PubMed]

], which can help us perform single qubit operation. In our scheme, sequential unitary operations made up of single qubit and two-qubit gates are based on latest experiments of Rydberg blockade. According to the theory of excitation dynamics in a two-atom system driven by external laser field [19

19. C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Many-body theory of excitation dynamics in an ultracold Rydberg gas,” Phys. Rev. A 76(1), 013413 (2007). [CrossRef]

], the interaction Hamiltonian is expressed as H=Δrr|ri|raar|ir|+ΩR2(|raa1|+|rii1|+h.c.). Through solving the equation of evolution of the system, we can calculate the probability of double excitation (i.e. the state |r are simultaneously populated by two atoms.). When the Rydberg-Rydberg interaction is weak (see dashed curve in Fig. 4
Fig. 4 Time evolution of the double-excitation probability Prr. Where Rabi frequencyΩR=2×106s1, the dissipation rate γ=1.5×106s1, and the Rydberg-Rydberg interaction energy Δrr=4.5×106s1 (for dashed curve), Δrr=7.5×106s1 (for solid curve), and Δrr=15×106s1 (for dotted curve).
), population of double Rydberg level |ri|ra is large. The population of the doubly excited state |ri|ra decreases with increase of Rydberg-Rydberg interaction, that is, the double excitation is blocked (see dotted curve in Fig. 4). A complete set of universal gates, which can be comprised of single qubit gates together with a two-qubit controlled-NOT gate, are constructed via Rydberg blockade. Based on the latest experiments and the quantitative calculation of Rydberg blockade, the proposed scheme might be realizable.

Acknowledgments

We thank Swinburne theoretical physics group for useful discussions. Financial support by the National Natural Science Foundation of China under Grant No. 11065007 and the Foundation of Talent of Jinggang of Jiangxi Province, China, Grant No. 2008DQ00400, is acknowledged.

References and links

1.

P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26(5), 1484–1509 (1997). [CrossRef]

2.

L. K. Grover, “Quantum Computers Can Search Rapidly by Using Almost Any Transformation,” Phys. Rev. Lett. 80(19), 4329–4332 (1998). [CrossRef]

3.

D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992). [CrossRef]

4.

I. L. Chuang, I. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, “Experimental realization of a quantum algorithm,” Nature 393(6681), 143–146 (1998). [CrossRef]

5.

J. A. Jones and M. Mosca, “Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer,” J. Chem. Phys. 109(5), 1648–1653 (1998). [CrossRef]

6.

M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91(18), 187903 (2003). [CrossRef] [PubMed]

7.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105(4), 040504 (2010). [CrossRef] [PubMed]

8.

S.-B. Zheng, “Scheme for implementing the Deutsch-Jozsa algorithm in cavity QED,” Phys. Rev. A 70(3), 034301 (2004). [CrossRef]

9.

L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]

10.

T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010). [CrossRef] [PubMed]

11.

M. Saffman and K. Mølmer, “Efficient multiparticle entanglement via asymmetric Rydberg blockade,” Phys. Rev. Lett. 102(24), 240502 (2009). [CrossRef] [PubMed]

12.

H.-Z. Wu, Z.-B. Yang, and S.-B. Zheng, “Implementation of a multiqubit quantum phase gate in a neutral atomic ensemble via the asymmetric Rydberg blockade,” Phys. Rev. A 82(3), 034307 (2010). [CrossRef]

13.

B. Zhao, M. Müller, K. Hammerer, and P. Zoller, “Efficient quantum repeater based on deterministic Rydberg gates,” Phys. Rev. Lett. 81, 052329 (2010).

14.

D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, “Fast quantum gates for neutral atoms,” Phys. Rev. Lett. 85(10), 2208–2211 (2000). [CrossRef] [PubMed]

15.

M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic Rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009). [CrossRef] [PubMed]

16.

Y. Wu, M. G. Payne, E. W. Hagley, and L. Deng, “Preparation of multiparty entangled states using pairwise perfectly efficient single-probe photon four-wave mixing,” Phys. Rev. A 69(6), 063803 (2004). [CrossRef]

17.

E. Urban, T. A. Johnson, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Observation of Rydberg blockade between two atoms,” Nat. Phys. 5(2), 110–114 (2009). [CrossRef]

18.

M. O. Scully, and M. S. Zubairy, Quantum Optics (Cambridge: Cambridge University Press,1997), Chap.5.

19.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Many-body theory of excitation dynamics in an ultracold Rydberg gas,” Phys. Rev. A 76(1), 013413 (2007). [CrossRef]

20.

T. A. Johnson, E. Urban, T. Henage, L. Isenhower, D. D. Yavuz, T. G. Walker, and M. Saffman, “Rabi oscillations between ground and Rydberg states with dipole-dipole atomic interactions,” Phys. Rev. Lett. 100(11), 113003 (2008). [CrossRef] [PubMed]

OCIS Codes
(270.0270) Quantum optics : Quantum optics
(270.5585) Quantum optics : Quantum information and processing

ToC Category:
Quantum Optics

History
Original Manuscript: November 15, 2010
Revised Manuscript: December 18, 2010
Manuscript Accepted: January 9, 2011
Published: January 19, 2011

Citation
Aixi Chen, "Implementation of Deutsch-Jozsa algorithm and determination of value of function via Rydberg blockade," Opt. Express 19, 2037-2045 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-3-2037


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References

  1. P. W. Shor, “Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer,” SIAM J. Comput. 26(5), 1484–1509 (1997). [CrossRef]
  2. L. K. Grover, “Quantum Computers Can Search Rapidly by Using Almost Any Transformation,” Phys. Rev. Lett. 80(19), 4329–4332 (1998). [CrossRef]
  3. D. Deutsch and R. Jozsa, “Rapid solution of problems by quantum computation,” Proc. R. Soc. Lond. A 439(1907), 553–558 (1992). [CrossRef]
  4. I. L. Chuang, I. M. K. Vandersypen, X. Zhou, D. W. Leung, and S. Lloyd, “Experimental realization of a quantum algorithm,” Nature 393(6681), 143–146 (1998). [CrossRef]
  5. J. A. Jones and M. Mosca, “Implementation of a quantum algorithm on a nuclear magnetic resonance quantum computer,” J. Chem. Phys. 109(5), 1648–1653 (1998). [CrossRef]
  6. M. Mohseni, J. S. Lundeen, K. J. Resch, and A. M. Steinberg, “Experimental application of decoherence-free subspaces in an optical quantum-computing algorithm,” Phys. Rev. Lett. 91(18), 187903 (2003). [CrossRef] [PubMed]
  7. F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R. S. Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-temperature implementation of the Deutsch-Jozsa algorithm with a single electronic spin in diamond,” Phys. Rev. Lett. 105(4), 040504 (2010). [CrossRef] [PubMed]
  8. S.-B. Zheng, “Scheme for implementing the Deutsch-Jozsa algorithm in cavity QED,” Phys. Rev. A 70(3), 034301 (2004). [CrossRef]
  9. L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, “Demonstration of a neutral atom controlled-NOT quantum gate,” Phys. Rev. Lett. 104(1), 010503 (2010). [CrossRef] [PubMed]
  10. T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, “Entanglement of two individual neutral atoms using Rydberg blockade,” Phys. Rev. Lett. 104(1), 010502 (2010). [CrossRef] [PubMed]
  11. M. Saffman and K. Mølmer, “Efficient multiparticle entanglement via asymmetric Rydberg blockade,” Phys. Rev. Lett. 102(24), 240502 (2009). [CrossRef] [PubMed]
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