Power Spectra of Non-Stationary Noises
For the Modelling of Qubit Decoherence
E.A. Tacettin (TU Delft - Applied Sciences)
V.V. Dobrovitski – Mentor (TU Delft - QID/Dobrovitski Group)
M.F. Russ – Graduation committee member (TU Delft - QCD/Rimbach-Russ)
L.M.K. Vandersypen – Graduation committee member (TU Delft - QCD/Vandersypen Lab)
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Abstract
Long operation of quantum computers, on the scale of days, weeks, or months, is essential for the realisation of large-scale quantum algorithms. However, qubits interact with their environment, leading to decoherence and the loss of quantum information. These environmental interactions are collectively referred to as noise, and are commonly modelled as stochastic processes. A key assumption in many such models is stationarity, meaning that the statistical properties of the noise do not depend on the absolute time at which the noise is measured.
Recent experiments on semiconductor quantum dots have shown that this assumption may not hold over long timescales. Such non-stationarity may arise when the system has not had sufficient time to equilibrate before measurement, or when fluctuations initialise the system far from equilibrium. In this thesis, we investigate how non-stationarity affects the power spectral density, which describes how the noise power is distributed across frequencies.
We introduce non-stationarity by conditioning the initial state of the noise process away from equilibrium. We first study the conditioned Ornstein-Uhlenbeck process, showing that non-stationarity modifies the amplitude of the ideal power spectral density while preserving its Lorentzian shape. We then study a conditioned ensemble of two-level fluctuators, a common model for charge noise in semiconductor qubits. Surprisingly, we find that non-stationarity can change the low-frequency spectrum from the usual $1/f$ behaviour to a $1/f^2$ dependence. Similar effects have been reported in recent experiments, and our model suggests one possible mechanism by which they may arise.
Finally, we investigate several spectral estimation methods to examine how finite observation times and non-stationarity affect PSD estimation. Overall, this thesis shows that non-stationarity can significantly affect measured noise spectra, and should be considered when interpreting long-timescale noise measurements in qubit devices.