Thermal CNOT gate based on Silicon quantum dots using Tsallis statistics

Abstract We consider a CNOT gate based on Silicon semiconductor quantum dots in thermal non-equilibrium conditions (TNEC). By applying Tsallis statistics, we analyze the time evolution of fidelity between the dot state and Bell state in TNEC, considering the effects of control magnetic fields on the left and right dots, exchange interaction, and microwave frequencies in the presence of environmental exposure. We present a thermal model for the time-dependent behavior of exchange interaction in silicon and compare our findings with experimental data. Our model incorporates physical dimensions and highlights the trade-off between achieving high fidelity near absolute zero temperatures and generating strong, high-frequency point magnetic fields to stabilize the CNOT gate. We determine that <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>q</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>1</mml:mn> </mml:math> is the optimal geometric region for extending gate lifetime. Utilizing quantum materials to generate strong point fields and topological manipulation of the qubit could be a viable approach to achieve such a gate. We aim to manipulate states to achieve high fidelity using control magnetic fields to create a functional CNOT gate in thermal noise, simultaneously ensuring strong entanglement between the dots.