  High-dimensional quantum systems are a valuable resource for quantum
information processing. They can be used to encode error-correctable logical
qubits, for instance in continuous-variable states of oscillators such as
microwave cavities or the motional modes of trapped ions. Powerful encodings
include 'Schr\"odinger cat' states, superpositions of widely displaced coherent
states, which also embody the challenge of quantum effects at the large scale.
Alternatively, recent proposals suggest encoding logical qubits in high-spin
atomic nuclei, which can host hardware-efficient versions of
continuous-variable codes on a finite-dimensional system. Here we demonstrate
the creation and manipulation of Schr\"odinger cat states using the spin-7/2
nucleus of a single antimony ($^{123}$Sb) atom, embedded and operated within a
silicon nanoelectronic device. We use a coherent multi-frequency control scheme
to produce spin rotations that preserve the SU(2) symmetry of the qudit, and
constitute logical Pauli operations for logical qubits encoded in the
Schr\"odinger cat states. The Wigner function of the cat states exhibits parity
oscillations with a contrast up to 0.982(5), and state fidelities up to
0.913(2). These results demonstrate high-fidelity preparation of nonclassical
resource states and logical control in a single atomic-scale object, opening up
applications in quantum information processing and quantum error correction
within a scalable, manufacturable semiconductor platform.
