Charge-Fluctuation-Induced Dephasing of Exchange-Coupled Spin Qubits

Exchange-coupled spin qubits in semiconductor nanostructures are shown to be vulnerable to dephasing caused by charge noise invariably present in the semiconductor environment. This decoherence of exchange gate by environmental charge fluctuations arises from the fundamental Coulombic nature of the Heisenberg coupling and presents a serious challenge to the scalability of the widely studied exchange gate solid state spin quantum computer architectures. We estimate dephasing times for coupled spin qubits in a wide range (from 1 ns up to $>1\mu \mathrm{s}$) depending on the exchange coupling strength and its sensitivity to charge fluctuations.

Figure 1

Charge fluctuations invariably present in the semiconductor environment affect a double quantum dot mainly by causing variations of barrier potential height (A) and producing a random bias potential between the two dots (B).

Figure 2

Panel (a) presents exchange splitting as a function of interdot distance (directly related to the interdot barrier height) for various dot sizes (directly related to the single dot confinement energy $E_0$) with the quartic double dot potential, while panel (b) presents $dJ/d{V}_B$ (derivative of $J$ over the interdot barrier potential) as a function of interdot distance. Panel (b) gives a quantitative estimate of the sensitivity of exchange coupling to background charge fluctuations.

Figure 3

Phase diffusion of a biased double dot charge qubit with a cutoff frequency of 1 Hz. Dephasing of a two-spin qubit can be determined from this figure as well, since it is linearly proportional to the charge qubit phase diffusion, as illustrated by Eq. (4). The lower horizontal line indicates that $\Delta {\varphi }_c\sim 1$ corresponds to $t\sim T_1/10$; the middle (upper) horizontal line indicates that $\Delta {\varphi }_c\sim {10}^4$ (${10}^6$) corresponds to $t\sim 10T_1$ ($100T_1$). In other words, if $dJ/dV\sim 0.001$, $\Delta {\varphi }_s\sim 1$ would correspond to a time of $100T_1$, where charge relaxation time $T_1$ is on the order of 10 ns, so that spin dephasing time $\sim 1\mu \mathrm{s}$.