  Computational physics is an important tool for analysing, verifying, and --
at times -- replacing physical experiments. Nevertheless, simulating quantum
systems and analysing quantum data has so far resisted an efficient classical
treatment in full generality. While programmable quantum systems have been
developed to address this challenge, the resources required for classically
intractable problems still lie beyond our reach. In this work, we consider a
new target for quantum simulation algorithms; analysing the data arising from
physics experiments -- specifically, muon spectroscopy experiments. These
experiments can be used to probe the quantum interactions present in condensed
matter systems. However, fully analysing their results can require classical
computational resources scaling exponentially with the simulated system size,
which can limit our understanding of the studied system. We show that this task
may be a natural fit for the coming generations of quantum computers. We use
classical emulations of our quantum algorithm on systems of up to 29 qubits to
analyse real experimental data, and to estimate both the near-term and error
corrected resources required for our proposal. We find that our algorithm
exhibits good noise resilience, stemming from our desire to extract global
parameters from a fitted curve, rather than targeting any individual data
point. In some respects, our resource estimates go further than some prior work
in quantum simulation, by estimating the resources required to solve a complete
task, rather than just to run a given circuit. Taking the overhead of
observable measurement and calculating multiple datapoints into account, we
find that significant challenges still remain if our algorithm is to become
practical for analysing muon spectroscopy data.
