  We consider simulating the BCS Hamiltonian, a model of low temperature
superconductivity, on a quantum computer. In particular we consider conducting
the simulation on the qubus quantum computer, which uses a continuous variable
ancilla to generate interactions between qubits. We demonstrate an O(N^3)
improvement over previous work conducted on an NMR computer [PRL 89 057904
(2002) & PRL 97 050504 (2006)] for the nearest neighbour and completely general
cases. We then go on to show methods to minimise the number of operations
needed per time step using the qubus in three cases; a completely general case,
a case of exponentially decaying interactions and the case of fixed range
interactions. We make these results controlled on an ancilla qubit so that we
can apply the phase estimation algorithm, and hence show that when N \geq 5,
our qubus simulation requires significantly less operations that a similar
simulation conducted on an NMR computer.
