Eigenstate preparation by phase decoherence

A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: at each step we apply the instantaneous Hamiltonian for a random time. The resulting decoherence approximates a projective measurement onto the desired eigenstate, achieving a version of the quantum Zeno effect. The average cost of our method is O(L²/Delta) for constant error probability, where L is the length of the path of eigenstates and Delta is the minimum spectral gap of the Hamiltonian. For many cases of interest, L does not depend on Delta so the scaling of the cost with the gap is better than the one obtained in rigorous proofs of the adiabatic theorem. We give an example where this situation occurs.