  We show how phase and amplitude estimation algorithms can be parallelized.
This can reduce the gate depth of the quantum circuits to that of a single
Grover operator with a small overhead. Further, we show that for quantum
amplitude estimation, the parallelization can lead to vast improvements in
resilience against quantum errors. The resilience is not caused by the lower
gate depth, but by the structure of the algorithm. Even in cases with errors
that make it impossible to read out the exact or approximate solutions from
conventional amplitude estimation, our parallel approach provided the correct
solution with high probability. The results on error resilience hold for the
standard version and for low depth versions of quantum amplitude estimation.
Methods presented are subject of a patent application [Quantum computing
device: Patent application EP 21207022.1].
