Quantum search at low temperature in the single avoided crossing model

We begin with an n-qubit quantum search algorithm and formulate it in terms of quantum walk and adiabatic quantum computation. We then represent and transform the n-qubit search algorithm into a two-level system and hence the single avoided crossing model. We perform and present the analytical calculations and numerical simulations of the dynamics of quantum walk search algorithm and AQC search algorithm in a thermal bath. We use the master equations formulation to represent the open quantum system. We nd out that while generally the performance of algorithms worsen with increase in temperature and the system size, there are interesting features in quantum walk search where there is an optimal low temperature for the best performance for other specied parameters. Similarly for AQC search, the performance generally worsens with increase in temperature, but for specied parameter ranges, the system is more robust against temperature eects.