## Oxide Systems – An Answer to the Qubit Problem?

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One can produce new oxide-based devices by exploiting their tunability, rich physics, and coupling between the various degrees of freedom (such as charge, lattice, spin, etc.). We propose that oxide-based double quantum dots with only one electron (tunneling between the dots) can be regarded as a qubit with little decoherence; these dots can possibly meet future challenges of miniaturization.

The logical qubit is formed from the two possible electron occupation states with |0>Q ≡ |01> and |1>Q ≡ |10>. The advantages of an oxide double-quantum-dot system are as follows: (a) as in semiconductor double quantum dots, here too fast electrical control of the exchange interaction is possible; (b) compared to semiconductors, the extent of the electronic wave function in oxides (which is about a lattice constant) is much smaller and thus the size of the oxide quantum dot can be much smaller, leading to them being much better suited for miniaturization; and (c) the decoherence due to optical phonons (the main source of noise) in oxide dots is significantly smaller than the decoherence due to nuclear spins in semiconductor dots. The dot with the eg electron can be treated as an up spin while the dot without the eg electron can be regarded as a down spin. The tunneling of the eg electron between the dots and the attraction between the electron and the hole on adjacent dots can be modeled as an anisotropic Heisenberg interaction between two spins with the total z component of the spins being zero.

We study two anisotropically interacting spins coupled to optical phonons; we restrict our analysis to the regime of strong coupling to the environment, to the antiadiabatic region, and to the subspace with zero value for SzT (the z component of the total spin). In the case where each spin is coupled to a different phonon bath, we assume that the system and the environment are initially uncorrelated (and form a simply separable state) in the polaronic frame of reference. By analyzing the polaron dynamics through a non-Markovian quantum master equation, we find that the system manifests a small amount of decoherence that decreases both with increasing nonadiabaticity ω/J⊥ and with enhancing strength of coupling g. We also show that, if each of the sites has a different potential, then coherence is preserved when the potential differences between sites is as far away as possible from any of the environmental eigenenergies.

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