content_image/336691.jpg
<img src='content_image/336691.jpg'>

, where α is a constant determining the rate of decay at λ ( t ) ≳ 0. This would ensure that δh ( λ )$_{ij}$ will not be significantly larger than H$_{0}$$_{ij}$ at λ ( t ) ≳ 0, where the bias term is small and the levels are densely packed. The results of simulations performed using a time-dependent amplitude of the form of (7) are shown in Fig. 4. On average, a given success probability can be achieved at a much faster computation speed, with an improvement of over 10 2 in some cases. In this idealised situation it is also clear to see that the fidelity of the final solution state would be unaffected (i.e. F = 1) by this artifical noise signal as ϵ ( λ = 0) = 0. 

## VII. CONCLUSIONS 

We generalise the Pechukas-Yukawa equations to the stochastic case by including an additional noise term in the Hamiltonian. This was used in conjunction with a simple, yet generic, noise model, based on random matrices and a coloured stochastic process, to investigate the effects of noise on the adiabatic algorithm for the CNOT gate. We found 

