# Noise enhanced performance of adiabatic quantum computing by lifting degeneracies 

R.D. Wilson, ∗ A.M. Zagoskin, and S. Savel’ev 

Department of Physics, Loughborough University, 

Loughborough, Leicestershire LE11 3TU, UK 

## Abstract 

We investigate the symmetry breaking role of noise in adiabatic quantum computing using the example of the CNOT gate. In particular, we analyse situations where the choice of initial Hamil- tonian produces symmetries in the Hamiltonian and degeneracies in the spectrum. We show that, in these situations, the conventional stipulation that the initial and problem Hamiltonians do not commute is unnecessary as noise will inherently play the role of a universal symmetry breaking perturbation and split any level crossings that may impede or obstruct the computation. The effects of an artificial noise source with a tailored time-dependent amplitude are also explored and it is found that such a scheme could offer a considerable performance enhancement. These results are found using a novel, generalised version of the Pechukas-Yukawa model of eigenvalue dynamics. 

