  A successful quantum error correction protocol would allow quantum computers
to run algorithms without suffering from the effects of noise. However, fully
fault-tolerant quantum error correction is too resource intensive for existing
quantum computers. In this context we develop a quantum error detection code
for implementations on existing trapped-ion computers. By encoding $k$ logical
qubits into $k+2$ physical qubits, this code presents fault-tolerant state
initialisation and syndrome measurement circuits that can detect any
single-qubit error. It provides a universal set of local and global logical
rotations that have physical support on only two qubits. A high-fidelity --
though non fault-tolerant -- compilation of this universal gate set is possible
thanks to the two-qubit physical rotations present in trapped-ion computers
with all-to-all connectivity. Given the particular structure of the logical
operators, we nickname it the Iceberg code. We demonstrate the protection of
circuits of 8 logical qubits with up to 256 layers, saturate the logical
quantum volume of $2^8$, and show the positive effect of increasing the
frequency of syndrome measurements within the circuit. These results illustrate
the practical usefulness of the Iceberg code to protect expressive circuits on
existing trapped-ion quantum computers.
