Quantum computation of the Anderson transition in presence of imperfections

Abstract

We propose a quantum algorithm for simulation of the Anderson transition in disordered lattices and study numerically its sensitivity to static imperfections in a quantum computer. In the vicinity of the critical point the algorithm gives a quadratic speedup in computation of diffusion rate and localization length, comparing to the known classical algorithms. We show that the Anderson transition can be detected on quantum computers with $7-10$ qubits.

arXiv commentrevtex, 4 pages, 4 figures, research at Quantware MIPS Center http://www.quantware.ups-tlse.fr

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• Quantum simulations of localization effects with dipolar interactions
• A quantitative model for the effective decoherence of a quantum computer with imperfect unitary operations
• Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment
• Entropy of entanglement and multifractal exponents for random states
• Quantum chaos algorithms and dissipative decoherence with quantum trajectories
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• Effects of imperfections for Shor's factorization algorithm
• Classical versus quantum errors in quantum computation of dynamical systems
• Phase diagram for the Grover algorithm with static imperfections
• Dynamical localization, measurements and quantum computing
• Quantum computation of multifractal exponents through the quantum wavelet transform
• Entanglement and localization of wavefunctions
• Critical Dynamics of the Anderson Transition on Small-World Graphs