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AIP conference proceedings

Many-particle localization by constructed disorder and quantum computing

M. I. Dykman

Published Jan 1, 2005• 2 citations
Publisher

Abstract

We demonstrate the onset of strong localization in a one dimensional fermion system, where all particles are almost completely confined to their sites. The on‐site localization is obtained by constructing a bounded one‐parameter sequence of site energies that eliminates resonant hopping between both nearest and remote sites. In an infinite system the time during which all many‐particle states remain on‐site localized scales as a high power of the ratio of the bandwidth of site energies to the hopping integral. The results apply to a system of perpetually coupled qubits and demonstrate that such system can be used for quantum computing.

DOI
10.1063/1.1996881

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We demonstrate the onset of strong localization in a one dimensional fermion system, where all particles are almost completely confined to their sites. The on‐site localization is obtained by constructing a bounded one‐parameter sequence of site energies that eliminates resonant hopping between both nearest and remote sites. In an infinite system the time during which all many‐particle states remain on‐site localized scales as a high power of the ratio of the bandwidth of site energies to the hopping integral. The results apply to a system of perpetually coupled qubits and demonstrate that such system can be used for quantum computing.
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We demonstrate that, in a many-particle system, particles can be strongly confined to their sites. The localization is obtained by constructing a sequence of on-site energies that efficiently suppresses resonant hopping. The time during which a many-particle state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^6$ already for a narrow energy bandwidth. The results show viability of quantum computers with time-independent qubit coupling.
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We show that, in a many‐body system, all particles can be strongly confined to the initially occupied sites for a time that scales as a high power of the ratio of the bandwidth of site energies to the hopping amplitude. Such time‐domain formulation is complementary to the formulation of the many‐body localization of all stationary states with a large localization length. The long localization lifetime is achieved by constructing a periodic sequence of site energies with a large period in a one‐dimensional chain. The scaling of the localization lifetime is independent of the number of particles for a broad range of the coupling strength. The analytical results are confirmed by numerical calculations. image
We demonstrate that, in a quantum computer with perpetually coupled qubits, all excitations can be confined to their sites (qubits) even without refocusing. The on-site localization is obtained by constructing a sequence of qubit energies that efficiently suppresses resonant hopping. The time during which a many-excitation state remains strongly localized in an infinite chain can exceed the reciprocal hopping frequency by $\agt 10^5$ already for a moderate bandwidth of qubit energies. The proposed energy sequence is also convenient for performing quantum operations on the qubits.