  The realization of effective quantum error correction protocols remains a
central challenge in the development of scalable quantum computers. Protocols
employing redundancy over multiple physical qubits to encode a single
error-protected logical qubit are theoretically effective, but imply a large
resource overhead. Alternative, more hardware-efficient, approaches seek to
deploy higher-dimensional quantum systems known as qudits. Recently, proposals
have emerged for exploiting high-spin magnetic nuclei coupled to condensed
matter electron spin qubits to implement fault-tolerant memories.
  Here, we explore experimentally the simplest of these proposals, a logical
qubit encoded on the four states of a I=3/2 nuclear spin hyperfine-coupled to a
S=1/2 electron spin qubit; the encoding protects against the dominant
decoherence mechanism in such systems, fluctuations of the quantizing magnetic
field. We implement the encoding using electron-nuclear double resonance within
a subspace of the spin levels in an ensemble of highly coherent manganese
defects in zinc oxide. 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.
