Quantum search at low temperature in the single
avoided crossing model

Abstract

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.