Ab initio modelling of quantum dot qubits: Coupling, gate dynamics and robustness versus charge noise

TL;DR

The paper tackles predicting two-qubit gate performance for silicon quantum-dot qubits in realistic devices by developing a real-space, ab initio grid model that directly computes exchange coupling $J$ and the dynamics of a ${\sqrt{\text{SWAP}}}$ gate. It introduces both 3D and efficient quasi-2D treatments, enabling accurate yet computationally tractable predictions of gate fidelity and qubit leakage in the presence of static and dynamic charge noise. The study shows how to characterize $J(V_g)$ from first principles, demonstrates near-ideal gate operation in clean environments, and demonstrates robustness through a fully compensating nine-pulse sequence that mitigates charge-noise and magnetic-detuning errors, albeit with longer gate times. The results provide a practical pathway to screen device layouts and tailor control pulses for high-fidelity two-qubit operations in semiconductor quantum processors.

Abstract

Electron spins in semiconductor devices are highly promising building blocks for quantum processors (QPs). Commercial semiconductor foundries can create QPs using the same processes employed for conventional chips, once the QP design is suitably specified. There is a vast accessible design space; to identify the most promising options for fabrication, one requires predictive modelling of interacting electrons in real geometries and complex non-ideal environments. In this work we explore a modelling method based on real-space grids, an ab initio approach without assumptions relating to device topology and therefore with wide applicability. Given an electrode geometry, we determine the exchange coupling between quantum dot qubits, and model the full evolution of a $\sqrt{\text{SWAP}}$ gate to predict qubit loss and infidelity rates for various voltage profiles. We determine full, 3D solutions and introduce a method which can obtain near-identical predictions using far more efficient 2D computations. Moreover we explore the impact of unwanted charge defects (static and dynamic) in the environment, and test robust pulse sequences. As an example we exhibit a sequence correcting both systematic errors and (unknown) charge defects, observing an order of magnitude boost in fidelity. The technique can thus identify the most promising device designs for fabrication, as well as bespoke control sequences for each such device.

Figures (17)

• Figure 1: Schematic of the iterative design process of a quantum dot device. Starting from an idea of an integrated circuit layout we would like to know the performance of the chip without sending it through the lengthy fabrication process. Using an extruder we generate a 3D version of the chip for which we specified the different materials. This in turn allows us to extract realistic quantum dot potentials. The grid-based modelling tool presented in this paper then gives us access to the device's key performance metrics. For instance, we could discard designs that show a small exchange coupling between neighbouring dots. On top of the static properties, we can also study the qubits' dynamics and e.g. compute two-qubit gate fidelities, how they are impacted by the presence of charge noise and how we can mitigate this effect. Finally, this process will inform new layouts and through similar iterations will lead to more promising devices that can be sent for fabrication.
• Figure 2: Plots showing the potential well constituting the double dot (left and centre) and states of the confined electrons (right). The 3D visualisation and the upper contour plot show the 'barrier up' case, while the lower contour plot shows the 'barrier down' potential. The right-most plots show probability densities on a logarithmic scale. The upper-right plot shows the ground state probability density for the 'barrier up' scenario (due to symmetry the distribution is identical for either particle). We then explore the subspace corresponding to "a given electron is definitely on the left of the structure" and plot the probability distribution for the other electron; this reveals a small but non-zero probability that the second particle is also on the left, i.e. a (2,0) charge state which would not constitute a legitimate qubit configuration. The total probability of (2,0) and (0,2) is 0.04%.
• Figure 3: Observed variation of the exchange coupling $J$ with the barrier gate voltage $V_g$. The blue and purples lines correspond to a strictly 2D dot modelled with 16, 32 and 64 basis states per particle, per dimension. One notes from the inset that curves for 32 and 64 are near-identical (the 64 line is shown dashed for visibility), while the lower basis size of 16 deviates in the low $J$ limit. The green curve corresponds to the far more computationally demanding 3D model; the basis size is 32 in the $x$-direction (the axis along which the two dots lie) and 16 in the orthogonal directions. One sees that the 2D model underestimates the $J$ coupling strength appreciably.
• Figure 4: Panel (a) shows the variation in potential within the 3D double dot in the $z$-direction (the $x$,$y$ location corresponds to a dot minimum). The potential is linear, ramping at 4 meV per nanometre. Panel (b) shows the probability density for an analytic Airy function solution to a 1D problem with potential from (a), but taking the step to be infinite. One sees that this analytic form is a near-perfect match to the probability density that is obtained from our ab initio calculation to the full 3D quantum dot potential.
• Figure 5: Performance of our resource-efficient quasi-3D model, which uses a 2D space and an adjusted Coulomb interaction. The black dots correspond to the true 3D model, and are the same data as in the green line of Fig. \ref{['fig:exchange_couplingA']}. The triangles denote the predictions made from the quasi-3D model. One sees that the match is near-perfect; in fact the quasi-3D model slightly underestimates $J$ by deviation of between $0.6\%$ and $0.8\%$.