We consider possible encodings of a qubit within the space spanned by the $p$-orbital manifold of an anisotropic silicon quantum dot, including the effects of alloy disorder. We find two types of avoided crossing in this manifold: one due to alloy disorder and one due to an out-of-plane magnetic field. Defining a qubit at such an avoided crossing offers prolonged coherence time and complete single-qubit control using baseband electrical control of the dot anisotropy. Using a phenomenological two-level fluctuator dipole noise model, we estimate an average dephasing time of $T_2^{*}\approx 10\mu \text{s}$ and a quality factor of $Q\sim {10}^4$. At the avoided crossing due to magnetic field, the qubit is a minor adaptation of the previously proposed $pO$ qubit, spanned by the ground and excited $p$ orbitals in the ground valley. However, at the avoided crossing due to alloy disorder, the qubit is qualitatively different, spanning the ground $p$ orbital in the excited valley and the excited $p$ orbital in the ground valley, and we dub it the $pOv$ qubit. While the charge noise robustness is similar for $pO$ and $pOv$ qubits, we find that $pOv$ qubits have desirable interaction properties. Namely, in contrast to the always-on transverse Coulomb coupling of $pO$ qubits, we show that transverse coupling between $pOv$ qubits is negligible, leaving only a longitudinal two-qubit interaction that can be tuned by modulating the orientation of adjacent elliptical dots.

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• Charge dynamics
• Quantum computation
• Quantum engineering
• Spintronics
• Valley degrees of freedom
• Valleytronics
• Quantum dots
• Qubits