<p>Recently, gate-defined Josephson junctions based on magic-angle twisted bilayer graphene (MATBG) have been fabricated. In such a junction, local electrostatic gating can create two superconducting regions connected by an interaction-driven valley-polarized state as the weak link. Due to the spontaneous time-reversal and inversion symmetry breaking, novel phenomena such as the Josephson diode effect have been observed with zero external magnetic fields. Importantly, when the so-called nonreciprocity efficiency (which measures the sign and strength of the Josephson diode effect) changes sign, the energy-phase relation of the junction is approximately <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>F</mi> <mo stretchy="false">(</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <mo>cos</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mi>ϕ</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$F(\phi ) \propto \cos (2\phi )$</EquationSource> </InlineEquation> where <i>F</i> is the free energy and <i>ϕ</i> is the phase difference of the two superconductors. In this work, we show that such a MATBG-based Josephson junction, when shunted by a capacitor, can be used to realize the long-sought-after 0-<i>π</i> qubits which are protected from local perturbation-induced decoherence. Interestingly, by changing the junction parameters to the regime where a large nonreciprocity efficiency is obtainable, transmon-like qubits with large anharmonicity can also be realized. The gate-defined Josephson junctions can be employed as platforms for realizing qubits that are protected from local perturbations.</p>