Ancilla-based quantum simulation

Abstract

Abstract. 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 ≥ 5, our qubus simulation requires significantly less operations that a similar simulation conducted on an NMR computer.

Quantum simulation

“…This question has been thoroughly studied, and several methods have been developed (see, e.g., (Berry et al, 2007;Bravyi et al, 2008;Bremner et al, 2005;Brown et al, 2011;Dodd et al, 2002;Dür et al, 2008;Hastings, 2006;Wang and Zanardi, 2002;Wocjan et al, 2002a,b,c)), but it still remains a difficult problem. Moreover, note that ancilla qubits are required, which adds to the resource requirements (see Section V. B).…”