Probing semiconductor quantum well qubits and associated Shannon entropy using semi‑relativistic quantum mechanics

Abstract

Electron states in GaAs, GaN and AlN quantum wells are studied by solving a semi-relativistic wave equation within the effective mass approximation. The quantum states are in turn used to probe the properties of two-level qubits formed in the different quantum wells at various temperatures. Results indicated that the period of oscillation between the quantum states increases with increasing width of the quantum wells, with AlN having the longest period and shortest for GaAs. Transition rates were also studied, since their product with the period of oscillation yield important information concerning the feasibility of carrying out a quantum computation. This product is equivalent to the ratio of the period of oscillation between states to the lifetime of an electron in an excited state. From the results, GaAs quantum wells may be preferable as they have the lowest ratio compared with the other quantum wells of other materials. AlN has the highest ratio of the three semiconductors considered here. Shannon entropy in the different quantum wells was studied also. It was found that the entropy in GaAs quantum wells varies rapidly through the passage of time, while those of GaN and AlN vary relatively slowly.