  Quantum computation requires qubits that satisfy often-conflicting criteria,
including scalable control and long-lasting coherence. One approach to creating
a suitable qubit is to operate in an encoded subspace of several physical
qubits. Though such encoded qubits may be particularly susceptible to leakage
out of their computational subspace, they can be insensitive to certain noise
processes and can also allow logical control with a single type of entangling
interaction while maintaining favorable features of the underlying physical
system. Here we demonstrate a qubit encoded in a subsystem of three coupled
electron spins confined in gated, isotopically enhanced silicon quantum dots.
Using a modified "blind" randomized benchmarking protocol that determines both
computational and leakage errors, we show that unitary operations have an
average total error of 0.35%, with 0.17% of that coming from leakage driven by
interactions with substrate nuclear spins. This demonstration utilizes only the
voltage-controlled exchange interaction for qubit manipulation and highlights
the operational benefits of encoded subsystems, heralding the realization of
high-quality encoded multi-qubit operations.
