First-Order Magnetic Field Insensitive Qudits in Trapped ¹⁷³Yb⁺

Qudit encoding could help alleviate the challenges of scaling and quantum error correction that remain at the forefront of quantum computing. A key challenge, however, is finding several long-lived magnetic-field-insensitive states to define a qudit with coherence times sufficient for computation. The large nuclear spin of  ¹⁷³Yb⁺ makes this isotope ideal for defining qudits, with six first-order magnetic-field-insensitive m_F = 0 states in the long lived [O(days)] ²F^o_7/2 manifold. We propose taking advantage of these states to define a long lived, first-order magnetic field insensitive qudit. We present progress towards state preparation and measurement (SPAM) of these qudit states, including SPAM of the m_F = 0 qubit defined in the ²S_1/2 ground state of ¹⁷³Yb⁺.