Python notebooks reproducing the numerical results and figures of the manuscript "Qubit encodings in the p-orbital-valley spectrum for enhanced coherence and tunable two-qubit interaction" by John H. Caporaletti and J. P. Kestner (University of Maryland Baltimore County). The manuscript proposes the pOv qubit, an encoding in the two-level subspace spanned by the lowest p-orbital state in the excited valley and the excited p-orbital in the ground valley of an anisotropic silicon quantum dot, coupled by disorder-induced valley-orbit coupling (VOC). This archive contains three self-contained notebooks: VOC_std_calc.ipynb — evaluates the VOC statistics of Appendix VI A using the discretized effective-mass theory of alloy disorder: the vertical envelope function is obtained from a finite-difference solve of the heterostructure confinement potential, and the standard deviations of the disorder-induced generator coefficients, together with the mean valley splitting and mean VOC magnitude, follow from the lattice sum over independent cells. The correlation matrix of the VOC generators is also reported. fig6_Qeff_hist.ipynb — reproduces Fig. 6. For each of
104 alloy-disorder realizations it finds the pair of dot orientations that switches off the two-qubit coupling Omega_zz while maximizing the effective two-qubit quality factor Q_eff, and histograms the result. fig7_inf_scatter_plot.ipynb — reproduces Fig. 7. It synthesizes the R_ZZ(
π/2) entangling gate for each disorder realization and evaluates its infidelity against a Monte-Carlo ensemble of quasistatic two-level-fluctuator dipole configurations, comparing a single-segment analytic pulse with a three-segment composite pulse obtained from a two-stage optimization (L-BFGS-B on the deterministic infidelity with analytic gradients, then SLSQP minimizing total gate time subject to a deterministic-infidelity budget). All notebooks use the device parameters of Table I, run top to bottom with no input files, and require only NumPy, SciPy, and Matplotlib (developed under Python 3.12). All random draws are seeded, so the published figures reproduce exactly.
We propose encoding a qubit in a two-level subspace spanned by the lowest
p-orbital state in the excited valley of an anisotropic quantum dot and the excited
p-orbital in the ground valley, which we dub the
pOv qubit. There is an avoided crossing between these states due to valley-orbit coupling (VOC) induced by alloy disorder, enabling complete single-qubit control using baseband electrical control of the dot anisotropy. We find that `sweet spots' exist at specific dot orientations where the instantaneous eigenstates are first-order insensitive to charge noise. Using a phenomenological two-level fluctuator (TLF) dipole noise model, we estimate an average dephasing time of
T2∗≈10μs and a quality factor of
Q∼104. Alternatively, encoding in the
p-orbital states in the ground valley near the isotropic dot point, we show that one can induce a similar sweet spot via an out-of-plane magnetic field. Finally, we find that two-qubit gates for the
pOv qubit are mediated by the quadrupole-quadrupole Coulomb interaction and can be electrically tuned from zero to
∼1 GHz by adjusting the relative orientation of the anisotropic dots, providing a novel pathway towards scalable quantum computation.
While bulk silicon has long been understood to exhibit relatively weak spin-orbit coupling (SOC), confinement of electrons to quantum dots (QDs) at a silicon heterointerface results in significantly larger SOC. This is a concern for electron spin qubit performance, as intravalley and intervalley SOC can significantly perturb the operation of electron spin qubits. While these interactions can be harnessed to drive coherent rotations in a singlet-triplet qubit, coupling to low-lying excited valley states can lead to undesirable spin relaxation when valley splitting is on resonance with the Zeeman energy. In this work, we measure the angular dependence of the interfacial spin-orbit interaction as a function of the direction and magnitude of an applied external magnetic field in SiMOS and Si/SiGe heterostructures, two common material platforms for silicon spin qubits. We construct a physical model that accurately infers intra- and inter-valley SOC physics from fits to the data, allowing for a direct comparison between these two material systems. For the devices measured we find that, while the
g-factor differences are comparable, the SiMOS QDs exhibit an order of magnitude larger spin-valley coupling than for Si/SiGe. Moreover, we find that the angular dependence of the spin-valley coupling is similar for both devices, with similar magnetic field orientations minimizing the spin-valley coupling. Our work points towards operational schemes for optimizing spin-valley coupling to avoid or exploit this mechanism for qubit operation.