  In blind quantum computing, a user with a simple client device can perform a
quantum computation on a remote quantum server such that the server cannot gain
knowledge about the computation. Here, we numerically investigate hardware
requirements for verifiable blind quantum computing using an ion trap as server
and a distant measurement-only client. While the client has no direct access to
quantum-computing resources, it can remotely execute quantum programs on the
server by measuring photons emitted by the trapped ion. We introduce a
numerical model for trapped-ion quantum devices in NetSquid, a discrete-event
simulator for quantum networks. Using this, we determine the minimal hardware
requirements on a per-parameter basis to perform the verifiable blind quantum
computing protocol. We benchmark these for a five-qubit linear graph state,
with which any single-qubit rotation can be performed, where client and server
are separated by 50 km. Current state-of-the-art ion traps satisfy the minimal
requirements on a per-parameter basis, but all current imperfections combined
make it impossible to perform the blind computation securely over 50 km using
existing technology. Using a genetic algorithm, we determine the set of
hardware parameters that minimises the total improvements required, finding
directions along which to improve hardware to reach our threshold error
probability that would enable experimental demonstration. In this way, we lay a
path for the near-term experimental progress required to realise the
implementation of verifiable blind quantum computing over a 50 km distance.
