  Current quantum technologies are at the cusp of becoming useful, but still
face formidable obstacles such as noise. Noise severely limits the ability to
scale quantum devices to the point that they would offer an advantage over
classical devices. To understand the sources of noise it is necessary to fully
characterise the quantum processes occurring across many time steps; only this
would reveal any time-correlated noise called non-Markovian. Previous efforts
have attempted such a characterisation but obtained only a limited
reconstruction of such multi-time processes. In this work, we fully
characterise a multi-time quantum process on superconducting hardware using
in-house and cloud-based quantum processors. We achieve this by employing
sequential measure-and-prepare operations combined with post-processing.
Employing a recently developed formalism for multi-time processes, we detect
general multi-time correlated noise. We also detect quantum correlated noise
which demonstrates that part of the noise originates from quantum sources, such
as physically nearby qubits on the chip. Our findings and techniques are
expected to advance error-mitigation techniques in current quantum hardware, a
necessary component to scale up the technology and achieve its true potential.
