  Quantum computing opens up new possibilities for the simulation of many-body
nuclear systems. As the number of particles in a many-body system increases,
the size of the space if the associated Hamiltonian increases exponentially.
This presents a challenge when performing calculations on large systems when
using classical computing methods. By using a quantum computer, one may be able
to overcome this difficulty thanks to the exponential way the Hilbert space of
a quantum computer grows with the number of quantum bits (qubits). Our aim is
to develop quantum computing algorithms which can reproduce and predict nuclear
structure such as level schemes and level densities. As a sample Hamiltonian,
we use the Lipkin-Meshkov-Glick model. We use an efficient encoding of the
Hamiltonian onto many-qubit systems, and have developed an algorithm allowing
the full excitation spectrum of a nucleus to be determined with a variational
algorithm capable of implementation on today's quantum computers with a limited
number of qubits. Our algorithm uses the variance of the Hamiltonian, $\langle
H^2\rangle - \langle H\rangle ^2$, as a cost function for the widely-used
variational quantum eigensolver (VQE). In this work we present a variance based
method of finding the excited state spectrum of a small nuclear system using a
quantum computer, using a reduced-qubit encoding method.
