Feasibility study of quantum computing using trapped electrons

Feasibility study on ground-state cooling and single-phonon readout of trapped electrons using hybrid quantum systems

“…An Oscillatory motion of an electron can couple to the readout mode and it allows for the coupling of phonon mode to the propagating mode with the rate ∼ 33 kHz, as discussed in the previous Section. One can immediately see that this cooling rate well surpasses the thermal population of the phonon n th < 20 at the cryogenic temperature multiplied by a conservatively assessed phonon-bath coupling of ∼ 10 Hz [13]. Thanks to this, the phonon mode equilibrates well with the thermal bath, which yields the mean phonon number of 6 at 300 mK environment.…”

“…At 300 mK environment with motional frequency of 1 GHz, mean phonon occupation number n can be roughly estimated by assuming the Bose-Einstein distribution to be n ≃ 6. Moreover, it is revealed that the heating rate for trapped electrons amounts 140 quanta per second [13], which may compete the resistive-cooling rate. Other ways than just using dilution refrigerator to cool the trapped electrons are highly demanded, and in this Section, we discuss two cooling methods: one using a cavity mode and another one using a transmon qubit and its measurement.…”

“…Through the beam-splitter interaction synthesized above, the electron is sympathetically cooled [17] by a cooling rate of Γ e ↓ = 4g 2 0 n d /Γ i , where Γ i > g 0 n d is assumed. Then the average phonon number of the electron is estimated by ne = n th Γ e th ′ /(Γ e ↓ + Γ e th ′ ), where n th = 12 is the mean phonon number of the electron at 300 mK with the phonon frequency of 500 MHz and Γ e th ′ = Γ e th + Γ i with Γ e th being the coupling rate of electron's motion to the thermal bath, which we shall conservatively assume it to be 10 Hz [13].…”

“…For such a purpose, trapped-electron system [9][10][11][12][13] is a good candidate. An electron is a spin-1/2 system, literally being a pure two-level system or an intrinsic qubit without any other internal states into which the quantum information leaks.…”

“…Electrons in a Paul trap have just been realized recently [12], and high-fidelity quantum operations [13], spin-state detection [16] and coupling to superconducting electronics for the quantum-state conversion [10] are discussed. A few more things should be addressed in order to fully utilize above advantages.…”