Demonstrating Experimentally the Encoding and Dynamics of an Error-Correctable Logical Qubit on a Hyperfine-Coupled Nuclear Spin Qudit

The realization of effective quantum error correction protocols remains a central challenge in the development of scalable quantum computers. Employing high-dimensional quantum systems (qudits) can offer more hardware-efficient protocols than qubit-based approaches. Using electron-nuclear double resonance, we implement a logical qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to an S=1/2 electron spin qubit; the encoding protects against the dominant decoherence mechanism in such systems, i.e., fluctuations of the quantizing magnetic field. We explore the dynamics of the encoded state both under a controlled application of the fluctuation and under natural decoherence processes. Our results confirm the potential of these proposals for practical, implementable, fault-tolerant quantum memories.