Qubits with electrons on liquid helium

Abstract

We study dissipation effects for electrons on the surface of liquid helium, which may serve as the qubits of a quantum computer. Each electron is localized in a 3D potential well formed by the image potential in helium and the potential from a submicron electrode submerged into helium. We estimate parameters of the confining potential and characterize the electron energy spectrum. Decay of the excited electron state is due to two-ripplon scattering and to scattering by phonons in helium. We identify mechanisms of coupling to phonons. An estimate of contributions from different scattering mechanisms shows that the decay rate should be $\ensuremath{\lesssim}{10}^{4}{\mathrm{s}}^{\ensuremath{-}1}.$ We analyze dephasing of the electron states due to quasielastic ripplon scattering off an electron. The dephasing rate is $\ensuremath{\lesssim}{10}^{2}{\mathrm{s}}^{\ensuremath{-}1}$ for $T=10\mathrm{mK}$ and depends on temperature as ${T}^{3}.$ Decay and decoherence of the electron states result also from classical and quantum electrode noise. We relate the corresponding relaxation rates to the power spectrum of the fluctuating electric field on the electron. The dependence of the rates on the electrode parameters is obtained.