I. INTRODUCTION Recently there has been a lot of interest in alternative paradigms to the standard approach to quantum computing (i.e. the quantum circuit model). Adiabatic quantum computing (AQC) is a promising example which is particularly suited to solving optimisation problems [1]. AQC involves slow adiabatic evolution from a configuration with an easily reachable ground state to one where the ground state encodes the solution to the hard computational problem in hand. This scheme is believed to have a number of advantages over the “stan- dard” approach, namely, the precise time-dependent control of individual qubits is no longer required, and it benefits from an inherent robustness against some of the effects of decoher- ence by remaining in the instantaneous ground state at all times [2–4]. Crucially, AQC has been shown to be polynomially equivalent, under certain conditions, to the standard gate model of quantum computing [6, 7]. The effects of noise on AQC are generally considered to be detrimental but manageable [2–4]. It was nevertheless stated that its effect can increase the success probability of AQC in some situations by; providing an alternative evolution trajectory [2], or by thermal relaxation back to the ground state [5]. Here, we investigate a more general effect of noise on AQC.Namely, how noise inherently breaks any hidden symmetries in the Hamiltonian and, thus, splits any level crossings in the energy spectrum which could impede or even prevent the computation. AQC can be described by the following Hamiltonian; where the ground state of the final Hamiltonian, H$_{0}$ , encodes the desired solution, ZH$_{b}$ is a large bias term (with Z ≫ 1) and the initial configuration, H ( λ = 1) = H$_{0}$ + ZH$_{b}$ , has an easily reachable, non-degenerate ground state. In order for there to be a high probability of the system remaining in the ground state as the bias is switched off, the rate of change of the control parameter λ ( t ) must be sufficiently slow to suppress excitation via Landau- Zener-St¨ uckelberg tunneling [8–10]. In AQC, the initial and final Hamiltonians are usually chosen such that no symmetries exist in H ( λ ( t )) by ensuring that they do not commute. This is done to ensure that there are no degeneracies in the energy spectrum during the evolution. However, this restriction on the choice of initial Hamiltonian may prove practically impossible to realise for generic problems. In [11] the example of the adiabatic equivalent of the CNOT gate is discussed as H ( λ ( t )) = H$_{0}$ + λ ( t ) ZH$_{b}$, (1) 2