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Capacitively Coupled Charge Qubits: Difference between revisions
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Capacitively Coupled Charge Qubits (view source)
Revision as of 19:26, 25 October 2014
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==Sweet Spots==
A major issue with charge qubits is that they are very susceptible to '''charge noise''', which occurs when charge fluctuations outside the system induce undesired shifts in the parameters of the Hamiltonian. The goal of a sweet spot is to find a point in the parameter space where the energy levels are as invariant to the shifts as possible.
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The most dominant noise source is due to the shifts in the detuning. It is believed that the only point at which the first order dependence on the detunings disappears is at <math>\epsilon_1 = \epsilon_2 = 0</math>. This has been confirmed analytically in the limit of small <math>g</math>, and no exceptions have been observed numerically.
<gallery widths=400px mode="nolines">
Image:00-10 gap.png |Gap between 00 and 10 states
</gallery>
===Second Order Detuning Noise===
===Tunnel Coupling and Capacitive Coupling Noise===
Assuming that we sit at the sweet spot <math>\epsilon_1 = \epsilon_2 = 0</math>, the energies are relatively simple, so we can easily see the effect of noise on the other parameters.
{| border="1" cellpadding="2"
!width="50"|State
!width="225"|Energy
!width="225"|Effect of <math>\delta\Delta_1</math>
!width="225"|Effect of <math>\delta g</math>
|-
|<math>|00\rangle</math> || <math>-\sqrt{(\Delta_1+\Delta_2)^2 + g^2}</math> || <math>-\frac{(\Delta_1+\Delta_2)}{\sqrt{(\Delta_1+\Delta_2)^2 + g^2}}\delta\Delta_1</math> || <math>-\frac{g}{\sqrt{(\Delta_1+\Delta_2)^2 + g^2}}\delta g</math>
|-
|<math>|01\rangle</math> || <math>-\sqrt{(\Delta_1-\Delta_2)^2 + g^2}</math> || <math>-\frac{(\Delta_1-\Delta_2)}{\sqrt{(\Delta_1-\Delta_2)^2 + g^2}}\delta\Delta_1</math> || <math>-\frac{g}{\sqrt{(\Delta_1-\Delta_2)^2 + g^2}}\delta g</math>
|-
|<math>|10\rangle</math> || <math>\sqrt{(\Delta_1-\Delta_2)^2 + g^2}</math> || <math>\frac{(\Delta_1-\Delta_2)}{\sqrt{(\Delta_1-\Delta_2)^2 + g^2}}\delta\Delta_1</math> || <math>\frac{g}{\sqrt{(\Delta_1-\Delta_2)^2 + g^2}}\delta g</math>
|-
|<math>|11\rangle</math> || <math>\sqrt{(\Delta_1+\Delta_2)^2 + g^2}</math> || <math>\frac{(\Delta_1+\Delta_2)}{\sqrt{(\Delta_1+\Delta_2)^2 + g^2}}\delta\Delta_1</math> || <math>\frac{g}{\sqrt{(\Delta_1+\Delta_2)^2 + g^2}}\delta g</math>
|}
==Rotations==
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