Phase diagram for the Grover algorithm with static imperfections

2004/03/19 by A. A. Pomeransky, O. V. Zhirov, D. L. Shepelyansky · 1 citation
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum chaos and dynamical systems #quant-ph

paper · pdf · doi:10.1140/epjd/e2004-00113-4

published as Eur. Phys. J. D 31, 131-135 (2004) · 4 pages, 4 figs, research at http://www.quantware.ups-tlse.fr

arxiv created 2004/03/19 · openalex publication_date 2004/08/30 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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 ε. The critical border ε_c between two phases drops polynomially with the number of qubits n_q as ε_c ∼ n_q^-3/2. In the regular phase (ε< ε_c) the algorithm remains robust against imperfections showing the efficiency gain ε_c / ε for ε\gtrsim 2^-n_q/2. In the chaotic phase (ε> ε_c) the algorithm is completely destroyed.

Citations

• Quantitative model for the effective decoherence of a quantum computer with imperfect unitary operations
• Elementary gates for quantum computation

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