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Phase diagram for the Grover algorithm with static imperfections

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Abstract.

We study effects of static inter-qubit interactions on the stability of the Grover quantum search algorithm. Our numerical and analytical results show existence of regular and chaotic phases depending on the imperfection strength \(\varepsilon\). The critical border \(\varepsilon_c\) between two phases drops polynomially with the number of qubits n q as \(\varepsilon_c \sim n_q^{-3/2}\). In the regular phase \((\varepsilon < \varepsilon_c)\) the algorithm remains robust against imperfections showing the efficiency gain \(\varepsilon_c / \varepsilon\) for \(\varepsilon \gtrsim 2^{-n_q/2}\). In the chaotic phase \((\varepsilon > \varepsilon_c)\) the algorithm is completely destroyed.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique, UMR 5152 du CNRS, Université P. Sabatier, 31062, Toulouse Cedex 4, France

    A. A. Pomeransky & D. L. Shepelyansky

  2. Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia

    O. V. Zhirov

Authors
  1. A. A. Pomeransky
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  2. O. V. Zhirov
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  3. D. L. Shepelyansky
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Corresponding author

Correspondence to D. L. Shepelyansky.

Additional information

Received: 1st July 2004, Published online: 31 August 2004

PACS:

03.67.Lx Quantum Computation - 24.10.Cn Many-body theory - 73.43.Nq Quantum phase transitions

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Pomeransky, A.A., Zhirov, O.V. & Shepelyansky, D.L. Phase diagram for the Grover algorithm with static imperfections. Eur. Phys. J. D 31, 131–135 (2004). https://doi.org/10.1140/epjd/e2004-00113-4

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  • DOI: https://doi.org/10.1140/epjd/e2004-00113-4

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