Finite temperature quantum algorithm and majorization
Debabrata Ghoshal, Richard B. Gomez, Marco O. Lanzagorta, Jeffrey K. Uhlmann · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
It is often believed that quantum entanglement plays an important role in the speed-up of quantum algorithms. In addition, a few research groups have found that Majorization behavior may also play an important role in some quantum algorithms. In some of our previous work we showed that for a simple spin 1/2 system, consisting of two or three qubits, the value of a Groverian entanglement (a rather useful measure of entanglement) varies inversely with the temperature. In practical terms this means that more iterations of the Grover's algorithm may be needed when a quantum computer is working at finite temperature. That is, the performance of a quantum algorithm suffers due to temperature-dependent changes on the density matrix of the system. Most recently, we have been interested in the behavior of Majorization for the same types of quantum system, and we are trying to determine the relationship between Groverian entanglement and Majorization at finite temperature. As Majorization entails the probability distribution arising out of the evolving quantum state from the probabilities of the final outcomes, our study will reveal how Majorization affects the evolution of Grover's algorithm at finite temperature.