Figure 3: Effect of QP tunnelling on the qubit degree of freedom.
From: Millisecond charge-parity fluctuations and induced decoherence in a superconducting transmon qubit

(a) Pulse sequence measuring the autocorrelation function of charge parity. Two charge-parity sequences, ending with measurements P1 and P2, respectively, are separated by a variable delay, followed by a qubit measurement M. We indicate by τ the time between the end of P1 and the start of M. Postselection on P1=+1 (ref. 28) prepares the state |0e〉. Similarly, a measurement M=+1 ensures that the final qubit state is |0〉. P2 will coincide with P1 only if the parity is unchanged. Inserting π rotations after P1 and/or before M allows measuring the parity autocorrelation for different combinations of qubit states. A preliminary measurement (not shown) initializes the qubit in |0〉 by postselection. Note that every measurement is projective on the qubit state. When the initial qubit state is known and the measurement is preceded by the parity-controlled qubit flip (Fig. 2), the result also denotes the charge parity. (b) Diagram of the four energy levels with the modelled transition rates (not to scale). (c) Charge-parity autocorrelation Rkk′(τ) for qubit in state |0〉 (dots), |1〉 (squares), or having relaxed from |1〉 to |0〉 (diamonds) during τ (Tr=20 mK). The average of the conditioned P2 is corrected for detection infidelity (see Methods). Fitting the solution of the rate equations, conditioned on initial and final qubit states, gives the inverse rates:
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