Quantum adiabatic algorithms using unitary interpolation

We present two efficient quantum adiabatic algorithms for Bernstein-Vazirani problem and Simon's problem. We show that the time complexities of the algorithms for Bernstein-Vazirani problem and Simon's problem are O(1) and O(n), respectively, which are the same complexities as the corresponding algorithms in quantum circuit model. In these two algorithms, the adiabatic Hamiltonians are realized by unitary interpolation instead of standard linear interpolation. Comparing with the adiabatic algorithms using linear interpolation, the energy gaps of our algorithms keep constant. Therefore, the complexities are much easier to analyze using this method.