Abstract
Quantum computers have the potential to revolutionise the way that nuclear simulations
are performed. The exponential nature of quantum bits (qubits), due to the exponen-
tially scaling Hilbert space associated with qubit systems, could give quantum computers
the capability to perform computations of large model spaces that classical computational
methods are unable to compute. Current quantum computers are not fault-tolerant, with
low numbers of qubits and high error rates and are prone to noise within the system. This
makes complex quantum algorithms near-impossible to perform on current quantum hard-
ware. This challenge can be partially overcome with the use of variational algorithms,
which employ the use of a classical computer and a quantum computer in tangent, reduc-
ing the computational load on the quantum computer. This allows for small problems to
be computed accurately using current quantum hardware. In this body of work several
new variational algorithms, the Variance-VQE and the Variance-VarQITE algorithms, will
be introduced and applied to various nuclear models, such as the Lipkin-Meshkov-Glick
model and the shell model. These algorithms are able to find both the ground state and
the full excitation spectra of each model when performed using both simulated methods
and real quantum hardware. These algorithms could present a solution to perform small
nuclear physical calculations on quantum hardware until quantum algorithms that depend
on fault-tolerant quantum computers can be realised.