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I read from some papers that the charge noise is one of the factors that cause decoherence of qubits. May I know what charge noise is and how exactly the charge fluctuation affects the qubit frequency? I also saw a term charge dispersion and have no idea what it is. Thank you so much!

Daniele Cuomo
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Hans
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1 Answers1

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For a complete answer (and much more!), see Charge insensitive qubit design derived from the Cooper pair box

What is charge noise ?

The energy of the capacitor in the transmon is $4 E_C (n-n_g)^2$ with $n$ the number of excess Cooper pairs ($Q = 2en$) and $n_g$, an offset in the number of Cooper pairs due to the environment of the junction (trapped charges in the substrate for example). In the Cooper-pair box (from which the transmon inherits), the energy levels are controlled using a gate voltage ($V_g$ in fig.1 in ref), which has the effect to change the charge $n_g$ (offset amounts to the charge in the capacitor). Note however that even if you were to remove the voltage source, there would always be “charge noise”, which can be seen as a noisy $V_g$ due to the environment.

Link with charge dispersion extracted from ref:

“The charge dispersion describes the variation of the energy levels with respect to environmental offset charge and gate voltage, and determines the sensitivity of the CPB to charge noise: the smaller the charge dispersion, the less the qubit frequency will change in response to gate charge fluctuations. The magnitudes of charge dispersion [is] determined by the ratio of the Josephson energy to the charging energy $E_J /E_C$.”

In the context of transmon:

“The transmon exploits a remarkable fact: the charge dispersion reduces exponentially in $E_J /E_C$, while the anharmonicity only decreases algebraically with a slow power law in $E_J /E_C$. Consequently, by operating the transmon at a much larger $E_J /E_C$ ratio than the CPB, one can greatly reduce charge noise sensitivity in the qubit while only sacrificing a small amount of anharmonicity.”

francois-marie
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