  Quantum computing promises enabling solving large problem instances, e.g.
large linear equation systems with HHL algorithm, once the hardware stack
matures. For the foreseeable future quantum computing will remain in the
so-called NISQ era, in which the algorithms need to account for the flaws of
the hardware such as noise. In this work, we perform an empirical study to test
scaling properties and directly related noise resilience of the the most
resources-intense component of the HHL algorithm, namely QPE and its
NISQ-adaptation Iterative QPE. We explore the effectiveness of noise mitigation
techniques for these algorithms and investigate whether we can keep the gate
number low by enforcing sparsity constraints on the input or using circuit
optimization techniques provided by Qiskit package. Our results indicate that
currently available noise mitigation techniques, such as Qiskit readout and
Mthree readout packages, are insufficient for enabling results recovery even in
the small instances tested here. Moreover, our results indicate that the
scaling of these algorithms with increase in precision seems to be the most
substantial obstacle. These insights allowed us to deduce an approximate
bottleneck for algorithms that consider a similar time evolution as QPE. Such
observations provide evidence of weaknesses of such algorithms on NISQ devices
and help us formulate meaningful future research directions.
