Ancilla-based quantum simulation

We describe in detail how a qubus quantum computer using a continuous variable ancilla to control the qubits can provide significant efficiency savings for quantum simulation. We illustrate this by using as an example the simulation of the Bardeen, Cooper and Schrieffer (BCS) Hamiltonian, a model of low-temperature superconductivity. We demonstrate an O(Ns) improvement over previous studies conducted on an NMR computer [1, 2] for nearest- neighbour and completely general cases. We make these results controlled on an ancilla qubit so that we can apply the phase estimation algorithm, and hence show that when N ≥ 5, our qubus simulation requires significantly fewer operations than a similar simulation conducted on an NMR computer.