Design and implementation of parity error detection in donor qubits in silicon

Abstract

In this thesis we assess the design and optimisation of critical device requirements for the realisation of three qubit parity error detection in donor spin qubits in silicon. Three key results are presented: (i) the capacitative modelling and design of triple donor dot architectures needed to realise a parity device, highlighting the need for multi-donor quantum dots (ii) optimisation of the geometry of the donor charge sensor and noise levels required for reproducible high fidelity spin readout, and (iii) understanding how the configurations of the additional donor nuclear spins in these multi-donor dots impact the electron spin resonance (ESR) spectra observed and how this will affect the operation of the parity measurement. Using electrostatic simulations of the different device geometries we show that either a 1P-2P-1P or 1P-3P-1P configuration of donors in each of the individual quantum dots is needed to achieve the required (1,1)↔(2,0) equivalent interdot charge transitions with the available gate space. Using such a higher donor number ancilla qubit, we then compared the sequence of logical gates required to perform the parity measurement using single qubit rotations and different 2-qubit gates. This analysis highlighted the need for isotopically pure silicon-28 to maintain coherence within the time frame of the measurement and stable, high fidelity single shot spin read-out. We then conducted a series of experiments of how to achieve stable, high fidelity single shot spin read out in our triple dot devices. It is known that read-out fidelity is improved by increasing the signal to noise of the charge sensor and by reducing the electron temperature. As such we investigated two triple dot device designs to investigate the interplay between these two requirements. The first design had the donor dots tunnel coupled to the single electron transistor (SET) charge sensor and the second had the donor dots capacitively coupled to an independent reservoir 50nm away from the SET charge sensor. We showed that under high bias of the SET (1mV) where we achieve a good signal to noise (1nA) of the charge sensor, electron-electron interactions within the tunnel coupled SET lead to heating of the qubits (680mK) compared with the independent reservoir qubits (170mK). Ultimately we showed that this heating limits spin read-out fidelities at high power where the signal to noise of the charge sensor is greatest. We simulated the spin readout fidelity for both designs and found the independent reservoir parity design can achieve above 99% fidelities over a greater range of SET resistances (up to 10MΩ) and tunnel rates (up to 100kHz), whereas the tunnel coupled design is limited to ≈100kΩ SET resistances with tunnel rates below 100Hz. i To further investigate the reproducibility of our SET charge sensors we then investigated the optimal tunnel barrier dimensions in a series of STM-patterned devices to achieve high fidelity single shot spin read-out. We found a simple width dependent exponential model describes the optimal tunnel barrier lengths for different lead widths. For tunnel barriers with 6±0.5nm lead widths, tunnel gap lengths of 11±0.5nm were found to give reliable SET resistances of 100KΩ optimal for providing good S/N. We then measured the charge noise in several SET devices and found that charge noise is correlated with high (> 350W) powers on the SUSI cell giving rise to an increase in pressure in the growth chamber (> 1×10−10mbar). We investigated the impact of charge noise on the ability to perform high fidelity spin readout and determined a noise threshold limit (0.03meV2) to achieve fidelities above 99%. In the final chapter we integrated an antenna on a triple dot device aiming for a 1,3,1 donor dot configuration. Using a detailed analysis of STM image height profiles, charging energies from gate-gate maps, capacitance triangulation and T1 measurements we determined that the final donor number was 0,3,2 indicating that no donor had incorporated in the lefthand dot. Despite this we were able to perform single shot spin read-out of the middle (≈92%) and right dots (92%) and confirmed the donor number of the right dot to be a 2P donor molecule using ESR resonance spectrum. We measured different hyperfine couplings of A1 = 189MHz and A2 = 83MHz to each of the donors within the dot, which under different slightly electric fields of 3.2MV/m and 3.8MV/m gave rise to a Stark shift of 41±31MHz/(MV/m). Using the ESR spectra, Stark shift measurements and tight binding simulations of the donor hyperfine Hamiltonian we are able to locate the exact configuration of the phosphorus atoms within the 2P donor molecule with the second donor being [0.5 1.5 0]a0 from the first donor. From these results we identified that a (3,2) donor configuration for the ancilla/data qubit does provide an equivalent (1,1) ↔ (2,0) interdot charge transitions with the available gate space. We then present a detailed outlook, with specific device recommendations as to how to achieve the parity measurement in donor qubits going forward.