Ancilla-based quantum simulation

TL;DR

This paper presents an efficient method for simulating the BCS Hamiltonian, relevant to superconductivity, on a qubus quantum computer, achieving significant improvements over previous NMR-based approaches.

Contribution

It introduces a qubus-based simulation technique with reduced operation complexity and demonstrates its advantages for larger system sizes compared to prior methods.

Findings

O(N^3) improvement over previous NMR simulations

Reduced operations per time step using qubus in various interaction cases

Significantly fewer operations for N ≥ 5 compared to NMR methods

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