Charge shelving and bias spectroscopy for the readout of a charge qubit on the basis of superposition states

Charge-based qubits have been proposed as fundamental elements for quantum computers. One commonly proposed readout device is the single-electron transistor (SET). SETs can distinguish between localized charge states, but lack the sensitivity to directly distinguish superposition states, which have greatly enhanced coherence times compared with position states. We propose introducing a third dot, and exploiting energy dependent tunneling from the qubit into this dot (bias spectroscopy) for pseudo-spin to charge conversion and superposition basis readout. We introduce an adiabatic fast passage-style charge pumping technique which enables efficient and robust readout via charge shelving, avoiding problems due to finite SET measurement time.

Figure 1

(Top) configuration showing phosphorus donors and gate structure. There is one electron and an SET for readout. The qubit is defined by donors marked $\mid l⟩$ and $\mid r⟩$, monitoring the third donor, $\mid p⟩$ (probe) provides the readout. State energies $\left(E\right)$ are controlled via gates $S_l$, $S_r$, and $S_p$, and the coherent tunneling rates, ${\Omega }_{lr}$ and ${\Omega }_{rp}$ are controlled by barrier gates $B_{lr}$ and $B_{rp}$ respectively. (Bottom) triple well diagram with $E_l=E_r$, the symmetric $\mid S⟩$ and antisymmetric $\mid AS⟩$ states are equally separated from $E_l$. $E_p$ has been tuned to $E_{AS}$ so resonant tunneling between $\mid AS⟩$ and $\mid p⟩$ occurs.

Figure 2

(a) ${\rho }_{ll}$ (black solid line), ${\rho }_{rr}$ (black broken line), and ${\rho }_{pp}$ (gray solid line) as a function of time (in units of $\pi ∕{\Omega }_{lr}$) for ${\Delta }_{pl}={\Omega }_{lr}=2$. Density plots showing ${\rho }_{ll}$ (b), ${\rho }_{rr}$ (c), and ${\rho }_{pp}$ (d), as a function of time and ${\Delta }_{pl}$ (in units of ${\Omega }_{lr}$) for $E_l=E_r=0$, ${\Omega }_{rp}={\Omega }_{lr}∕20$ and $\Gamma ={\Omega }_{lr}∕100$ for a qubit in state $\mid l⟩$ at time $t=0$. Note the dominant oscillatory behavior in ${\rho }_{ll}\left(t\right)$ and ${\rho }_{rr}\left(t\right)$ and the AT doublet-like feature in ${\rho }_{pp}$.

Figure 3

AFP readout (a) ${\Omega }_{rp}$ as a function of time (in units of $\pi ∕{\Omega }_{lr}$) showing modulation of the coherent tunneling rate. (b) State energies (in units of ${\Omega }_{lr}$) as a function of time. The dashed, black lines represent the energies unperturbed by ${\Omega }_{rp}$, whilst the solid blue lines represent state energies with ${\Omega }_{rp}\left(t\right)$ applied. At $t=0$ the states are (highest to lowest energy) $\mid p⟩$, $\mid AS⟩$ and $\mid S⟩$. (c),(d) ${\rho }_{ll}$ (black solid line), ${\rho }_{rr}$ (black broken line) and ${\rho }_{pp}$ (gray solid line) as a function of time for $\rho \left(0\right)=\mid AS⟩$ (c) $\rho \left(0\right)=\mid S⟩$ (d). In all cases ${\Omega }_{rp}^{\max }=0.4{\Omega }_{lr}$.