Effects of valley splitting on resonant-tunneling readout of spin qubits

Abstract

The effect of valley splitting on the readout of qubit states is theoretically investigated in a three-quantum-dot (QD) system. A single unit of the three-QD system consists of qubit-QDs and a channel-QD that is connected to a conventional transistor. The nonlinear source--drain current characteristics under resonant-tunneling effects are used to distinguish different qubit states. Using nonequilibrium Green functions, the current formula for the three-QD system is derived when each QD has two valley energy levels. Two valley states in each QD are considered to be affected by variations in the fabrication process. We found that when valley splitting is smaller than Zeeman splitting, the current nonlinearity can improve the readout, provided that the nonuniformity of the valley energy levels is small. Conversely, when the valley splitting is larger than the Zeeman splitting, the nonuniformity degraded the readout. In both cases, we showed that there are regions where the measurement time $t_{\rm meas}$ is much less than the decoherence time $t_{\rm dec}$ such that $t_{\rm dec}/t_{\rm meas}>100$. This suggests that less than 1\% measurement error is anticipated, which opens up the possibility for implementing surface codes even in the presence of valley splitting.