Resonant probing of charge noise through singlet-triplet silicon spin qubit valley states

Although semiconductor spin qubits are a promising platform for quantum computing, they are hampered by charge noise. Probing in-situ charge noise quickly could allow for closed-loop control circumventing the difficulties associated with open-loop control methods. Charge noise also causes fluctuation of the valley splitting in silicon. Here we propose a method for probing charge noise with a silicon singlet-triplet spin-qubit by coupling it to a conventional resonator. Charge-noise-induced fluctuations in the voltage cause fluctuations in the valley splitting. If the system is initialized with one excited valley, then the resonator can measure fluctuations in the difference of valley splitting between dots. Since the difference in valley splitting can be relatively small, ~1GHz, this method allows us to probe resonantly, giving a large sensitivity to fluctuations. Additionally, it only requires equipment already used for radio-frequency readout. Signal-to-noise ratio analysis including the equilibration time of the system shows that fast measurement times are possible depending on system parameters such that closed-loop control could be implemented.