Fast Hybrid Silicon Double-Quantum-Dot Qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers $S^2=3/4$ ($S=1/2$) and $S_z=-1/2$, with the two different states being singlet and triplet in the doubly occupied dot. Gate operations can be implemented electrically and the qubit is highly tunable, enabling fast implementation of one- and two-qubit gates in a simpler geometry and with fewer operations than in other proposed quantum dot qubit architectures with fast operations. Moreover, the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.

Figure 1

The logical qubit states of the hybrid qubit are $|0{⟩}_L=|S⟩|\downarrow ⟩$ and $|1{⟩}_L=\sqrt{\frac{1}{3}}|T_0⟩|\downarrow ⟩-\sqrt{\frac{2}{3}}|T_{-}⟩|\uparrow ⟩$, where $|S⟩$, $|T_{-}⟩$, and $|T_0⟩$ are two-particle singlet (S) and triplet (T) states in the left dot, and $|\uparrow ⟩$ and $|\downarrow ⟩$ respectively denote a spin-up and spin-down electron in the right dot. Fast qubit gate operations are performed by applying gate voltages that change the energy splittings between the singlet and triplet states in the left dot and that change the tunnel couplings $t_S$ and $t_T$ between the two dots. (a): Introducing tunneling between the dots induces transitions between $|0{⟩}_L$ and $|1{⟩}_L$. Starting from $|0{⟩}_L$, in which the electrons in the left dot are in a singlet, if an electron tunnels from the left dot to the right dot, and then the other electron tunnels back to the left dot, the spins in the left dot will end up in a triplet. The actual process conserves the total $S^2$ and $S_z$ and yields transitions between $|0{⟩}_L$ and $|1{⟩}_L$ (see 28). (b) and (c): Schematic illustrating independent tuning of the coupling between the electron in the singly occupied dot and the singlet and triplet states in the doubly occupied dot via the barrier height and relative energies in the two dots, as described in the text. (d): Effective connectivity of two hybrid qubits composed of four dots in a linear geometry. Each connection is a tunable two-electron interaction. There are eight effective connections, compared to five effective connections in a linear array of six dots for the qubits considered in Ref. 13, shown in (e). For (d), a two-qubit gate equivalent to CNOT up to local (one-qubit) unitary operations can be implemented in 16 steps, compared to 18 for (e) [35] (see 28). (f): Connectivity for which a 14-operation two-qubit gate equivalent to CNOT up to local unitary operations has been found (see 28).

Figure 2

Experimental measurements demonstrating readout mechanism (different tunnel rates for the different qubit states) and also a long singlet-triplet relaxation time in a $\mathrm{Si}/\mathrm{SiGe}$ quantum dot. (a) Scanning electron micrograph of a top-gated $\mathrm{Si}/\mathrm{SiGe}$ dot with the same gate structure as the one used in the experiment, which is described in 17. (b) Measurement of the tunnel rates into the dot at 1 T, when the dot ground state is a singlet S (${\gamma }_{\mathrm{load}}^S$, gray line) and at 3 T, when the dot ground state is the triplet $T_{-}$ (${\gamma }_{\mathrm{load}}^{T_{-}}$, black line). The measured charge sensor current $I_{\mathrm{QPC}}$ decreases when the charge in the dot increases, and an exponential fit to $I_{\mathrm{QPC}}$ versus time after the voltage on gate PL is changed yields tunnel rates ${\gamma }_{\mathrm{load}}^S=81\mathrm{Hz}$ and ${\gamma }_{\mathrm{load}}^{T_{-}}=521\mathrm{Hz}$. (c) Analogous measurement of the tunnel rates out of the dot, yielding ${\gamma }_{\mathrm{unload}}^S=182\mathrm{Hz}$ and ${\gamma }_{\mathrm{unload}}^{T_{-}}=645\mathrm{Hz}$. (d) Measurement of the triplet $T_{-}$ to singlet $S$ relaxation time $T_1$, using the method of 36. The gate voltages on the dot are changed quickly, so both the triplet and singlet states can load, and the unloading rate is measured as a function of the duration of the loading pulse, or dwell time, $\Delta t$. As $\Delta t$ is increased and triplets decay to singlets, the unloading rate decreases. Fitting the unloading rate versus dwell time to an exponential form (shown as the solid line) yields $T_1=141\pm 12\mathrm{ms}$.