The first gate confines a hole quantum dot encoding the spin qubit, the second one a helper dot enabling readout. We use a p-type double-gate transistor made using industry-standard silicon technology. Here we report the implementation of gate-coupled RF reflectometry for the dispersive readout of a fully functional hole spin qubit device. In this thesis, we conduct experiments on p-type silicon-nanowire devices to take advantage of the above mentioned properties.In order to pave the way for large-scale quantum processors, the development of scalable qubit readout schemes involving a minimal device overhead is a compelling step. Hole spins carry some attractive properties: for instance, strong spin-orbit coupling enables fast coherent spin rotations using a radio-frequency electric field also, we expect long coherence times due to the absence of contact hyperfine interaction. However, hole spin qubits in silicon remain a barely explored hosting platform as compared to their electron counterpart. Owing to ever increasing gate fidelities and to a potential transferability to industrial CMOS technology, silicon spin qubits have become a compelling option in the strive for quantum computation. The signal and carrier components from Eq. We assume that the signal ͑ and noise ͒ has been amplified sufficiently, so that the noise added by the detection is negligible. If ⌫ 0 0, the scheme corresponds to the amplitude modulation ͑ AM ͒. n ( t ) is the noise term in the time domain. m is the modulation frequency, 0 is the carrier frequency ( m Ӷ 0 ), and v 0 the amplitude of the incoming voltage wave. We start the analysis for the signal-to-noise ratio by defining a model for the reflected signal amplitude from the impedance transformer: v 0 ͓ ⌫ 0 ϩ ⌬⌫ cos ͑ m t ͔͒ cos ͑ 0 t ͒ ϩ n ͑ t ͒, ͑ 6 ͒ where the reflection coefficient ⌫ is modulated sinusoidally with ⌬⌫ cos( m t ) at the working point ⌫ 0. The total ͑ loaded ͒ quality factor Q L that sets the bandwidth is then 1/ Q L ϭ 1/ Q ϩ 1/ Q. We may define unloaded quality factor Q SET ϭ R SET / ͱ L / C and external quality factor Q e ϭ ͱ L / C / Z 0. In the undercoupled case, the SET and the LC circuit limit the system resonance bandwidth, while the external generator impedance Z 0 is the limiting factor in the overcoupled case. The coupling is a measure of which component limits the LC resonance bandwidth. If R eff Ͻ Z 0, the SET is overcoupled, and if R eff Ͼ Z 0, the SET is undercoupled to the feedline. In the S -matrix formalism it is easier to describe more realistic resonator circuits including the parasitic terms of available passive components. Appendix A defines a more general formalism expressing ⌫ ( R SET ) by S matrices. 3 illustrate the ideal frequency response described by Eqs. Increasing R SET moves this point to the left. ⌫ at the LC resonance ( Z ϭ R eff ) is represented as a point on the real axis ( x axis ͒ in the Smith chart. 3 ͒, one can visualize how R SET changes the reflected wave. By looking at the Smith chart representation 18 of ⌫ ͑ Fig. Z 0 is the characteristic impedance of a transmission line.
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