Fast quantum search algorithm for databases of arbitrary size and its implementation in a cavity QED

Abstract We propose a method for implementing the Grover search algorithm directly in a database containing any number of items based on multi-level systems. Compared with the searching procedure in the database with qubits encoding, our modified algorithm needs fewer iteration steps to find the marked item and uses the carriers of the information more economically. Furthermore, we illustrate how to realize our idea in cavity QED using Zeemanʼs level structure of atoms. And the numerical simulation under the influence of the cavity and atom decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.

[1]  R J Schoelkopf,et al.  Quantum computing with an electron spin ensemble. , 2009, Physical review letters.

[2]  Timothy C. Ralph,et al.  Efficient Toffoli gates using qudits , 2007 .

[3]  R J Schoelkopf,et al.  Hybrid quantum processors: molecular ensembles as quantum memory for solid state circuits. , 2006, Physical review letters.

[4]  J. C. Retamal,et al.  Qutrit quantum computer with trapped ions , 2003 .

[5]  G. Long.  Grover algorithm with zero theoretical failure rate , 2001, quant-ph/0106071.

[6]  C. Hamley,et al.  Cavity QED with optically transported atoms , 2003, quant-ph/0309052.

[7]  Lov K. Grover,et al.  Fixed-point quantum search. , 2005, Physical review letters.

[8]  M. Żukowski,et al.  Security of Quantum Key Distribution with entangled Qutrits. , 2002, quant-ph/0207057.

[9]  H. J. Kimble,et al.  Trapping of Single Atoms in Cavity QED , 1999 .

[10]  Mang Feng.  Grover search with pairs of trapped ions , 2001 .

[11]  Christof Zalka.  GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL , 1997, quant-ph/9711070.

[12]  H. J. Kimble,et al.  Photon blockade in an optical cavity with one trapped atom , 2005, Nature.

[13]  Marco Barbieri,et al.  Simplifying quantum logic using higher-dimensional Hilbert spaces , 2009 .

[14]  Lov K. Grover,et al.  Simple Algorithm for Partial Quantum Search , 2006, Quantum Inf. Process..

[15]  Test-state approach to the quantum search problem , 2011, 1102.3628.

[16]  G. Guo,et al.  Efficient scheme for two-atom entanglement and quantum information processing in cavity QED , 2000, Physical review letters.

[17]  Hood,et al.  The atom-cavity microscope: single atoms bound in orbit by single photons , 2000, Science.

[18]  Guang-Can Guo,et al.  Implementing a conditional N-qubit phase gate in a largely detuned optical cavity , 2007 .

[19]  D. D. Awschalom,et al.  Quantum information processing using quantum dot spins and cavity QED , 1999 .

[20]  Zhang Shou,et al.  Generation of an N-qubit phase gate via atom-cavity nonidentical coupling , 2009 .

[21]  Siyuan Han,et al.  n-qubit-controlled phase gate with superconducting quantum-interference devices coupled to a resonator , 2005 .

[22]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[23]  G. Guo,et al.  Quantum logic gate operation and entanglement with superconducting quantum interference devices in a cavity via a Raman transition , 2005 .

[24]  Mang Feng,et al.  Implementation of a nonlocal N-qubit conditional phase gate by single-photon interference , 2007 .

[25]  Y. P. Zhang,et al.  Study of runaway electron behaviour during electron cyclotron resonance heating in the HL-2A Tokamak , 2009 .

[26]  L. H. Pedersen,et al.  Adiabatic elimination in a lambda system , 2006, quant-ph/0610056.