  An entangled state is said to be $m$-uniform if the reduced density matrix of
any $m$ qubits is maximally mixed. This is intimately linked to pure quantum
error correction codes (QECCs), which allow not only to correct errors, but
also to identify their precise nature and location. Here, we show how to create
$m$-uniform states using local gates or interactions and elucidate several QECC
applications. We first show that $D$-dimensional cluster states are $m$-uniform
with $m=2D$. This zero-correlation length cluster state does not have finite
size corrections to its $m=2D$ uniformity, which is exact both for infinite and
for large enough but finite lattices. Yet at some finite value of the lattice
extension in each of the $D$ dimensions, which we bound, the uniformity is
degraded due to finite support operators which wind around the system. We also
outline how to achieve larger $m$ values using quasi-$D$ dimensional cluster
states. This opens the possibility to use cluster states to benchmark errors on
quantum computers. We demonstrate this ability on a superconducting quantum
computer, focusing on the 1D cluster state which, we show, allows to detect and
identify 1-qubit errors, distinguishing $X$, $Y$ and $Z$ errors.
