Designing single-shot readout protocols on spin-valley qubit systems via stochastic simulations

2D material based quantum dots can host three different kind of qubits, namely spin-, valley- and Kramers (spin-valley) qubits. One of the key requirements for practical and effective qubits is the T1 relaxation time, which is typically measured through single-shot projective techniques like Elzerman readout. In a multi-state system, the possible combinations of load and read levels give rise to many viable readout protocols [1]. As the load and read levels vary, the stochastic dynamics of the system results in time constants which are different than the intrinsic two-state time constants obtained from Fermi's Golden Rule (FGR) or simple combinations of FGR time constants through Matthiessen's rule. Here we develop a general formalism for a 'N' level system and apply it specifically to a four-level system like a 2D material based quantum dot with spin-valley locking [2]. We develop analytical predictions for measured relaxation times (as a function of the intrinsic two-state time constants) under all the six different possible load and read level protocols. We validate these analytical predictions with detailed Markov chain Monte Carlo simulations to mimic the stochastic nature of experiments. Finally, we validate our results with experiments measuring T1 relaxation times in BLG and propose a flowchart to extract the intrinsic FGR based time constants from a series of experiments for a 2D material based quantum dot.