  Current quantum technology is approaching the system sizes and fidelities
required for quantum error correction. It is therefore important to determine
exactly what is needed for proof-of-principle experiments, which will be the
first major step towards fault-tolerant quantum computation. Here we propose a
surface code based experiment that is the smallest, both in terms of code size
and circuit depth, that would allow errors to be detected and corrected for
both the $X$ and $Z$ basis of a qubit. This requires $17$ physical qubits
initially prepared in a product state, on which $16$ two-qubit entangling gates
are applied before a final measurement of all qubits. A platform agnostic error
model is applied to give some idea of the noise levels required for success. It
is found that a true demonstration of quantum error correction will require
fidelities for the preparation and measurement of qubits and the entangling
gates to be above $99\%$.
