  Performing large calculations with a quantum computer will likely require a
fault-tolerant architecture based on quantum error-correcting codes. The
challenge is to design practical quantum error-correcting codes that perform
well against realistic noise using modest resources. Here we show that a
variant of the surface code -- the XZZX code -- offers remarkable performance
for fault-tolerant quantum computation. The error threshold of this code
matches what can be achieved with random codes (hashing) for every single-qubit
Pauli noise channel; it is the first explicit code shown to have this universal
property. We present numerical evidence that the threshold even exceeds this
hashing bound for an experimentally relevant range of noise parameters.
Focusing on the common situation where qubit dephasing is the dominant noise,
we show that this code has a practical, high-performance decoder and surpasses
all previously known thresholds in the realistic setting where syndrome
measurements are unreliable. We go on to demonstrate the favourable
sub-threshold resource scaling that can be obtained by specialising a code to
exploit structure in the noise. We show that it is possible to maintain all of
these advantages when we perform fault-tolerant quantum computation.
