Majorization in Quantum Adiabatic Algorithms
نویسندگان
چکیده
We study the Majorization arrow in a big class of quantum adiabatic algorithms. In a quantum adiabatic algorithm, the ground state of the Hamiltonian is a guide state around which the actual state evolves. We prove that for any algorithm of this class, step-by-step majorization of the guide state holds perfectly. We also show that step-by-step majorization of the actual state appears if the running time becomes longer and longer. This supports the empirical viewpoint that step-by-step majorization seems to appear universally in quantum adiabatic algorithms. On the other hand, the performance of these algorithms discussed in this paper can all be estimated, which is exponential in the problem size. This can be looked as a strong evidence that step-by-step majorization is not a sufficient condition for efficiency.
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