Figure 1

(a) Bloch sphere representation of the singlet-triplet qubit, which is formed by the singlet $S$ and $m_s=0$ triplet $T_0$ electron spin states of two singly occupied quantum dots. (b) Electrostatic interaction between proximal double quantum dots (DQDs) alters the rate of coherent evolution in one DQD depending on the charge configuration of the other DQD.Reuse & Permissions

Figure 2

(a) Micrograph of a device similar to the one measured. Gate voltages $V_T^L$ and $V_T^R$ ($V_C^L$ and $V_C^R$) control the charge state of the target (control) DQD. Quantum point contacts (QPCs) with conductances $g_T$ and $g_C$ sense charge states of target and control DQDs. The DQDs are capacitively coupled by an electrostatic interaction $E_{\mathrm{cpl}}$. (b) [(c)] QPC conductance measured as a function of gate voltages $V_T^L$ and $V_T^R$ [$V_C^L$ and $V_C^R$] dot shows distinct conductance levels $g_T$ [$g_C$] for each electron configuration $(N_L,N_R{)}_T$ [$(N_L,N_R{)}_C$]. Detuning axes ${ϵ}_T$ and ${ϵ}_C$ for target and control DQD are indicated. (d) Voltage detuning ${ϵ}_T$ of the target DQD as a function of the voltage detuning ${ϵ}_C$ of the control DQD. The shift of the target detuning axis ${ϵ}_{\mathrm{cpl}}$ that occurs when the occupancy of the control DQD changes is indicated on the left axis. The right axis shows the corresponding energy shift $E_{\mathrm{cpl}}^0$. The difference in conductance of the $(1,1{)}_T$ and $(2,0{)}_T$ occupancy between (b) and (d) is due to a difference in operating point of the QPC.Reuse & Permissions

Figure 3

(a) Energy diagram near the $(1,1{)}_T\mathrm{\text{−}}(2,0{)}_T$ transition of the target DQD. Energy levels of the hybrid singlet state as a function of target detuning ${ϵ}_T$ for $(1,1{)}_C$ [dark gray (blue) curve] and $(0,2{)}_C$ [light gray (red) curve] occupation of the control DQD. Detuning of the target qubit at which separation of the electrons in separate quantum dots ${ϵ}_T^S$, interaction of the two DQDs ${ϵ}_T^I$, measurement ${ϵ}_T^M$, and singlet preparation ${ϵ}_T^P$ take place during coherent manipulation are indicated. The yellow area indicates detuning range considered in (b). (b) Singlet-triplet energy splittings and corresponding target qubit precession frequency $f_T$ for control DQD occupation $(1,1{)}_C$ [dark gray (blue) curve] and $(0,2{)}_C$ [light gray (red) curve]. Difference in exchange energies, $E_{\mathrm{cpl}}({ϵ}_T)$ (black curve) determine the duration for conditional operation. Exchange energies obtained from fits to the data of Fig. 5, coupling energy from the model in Ref. 11.Reuse & Permissions

Figure 4

(a) Pulse sequence used in coherent manipulation of the target qubit. Target detuning ${ϵ}_T^P$ for singlet preparation, ${ϵ}_T^S$ for adiabatic loading of the singlet-triplet superposition state, ${ϵ}_T^I$ for exchange and coupling interaction, and ${ϵ}_T^M$ for measurement are indicated. (b) Target qubit evolution in Bloch sphere representation during adiabatic loading, coherent exchange precession, and adiabatic unloading. Moving an electron in the control DQD towards the target qubit shifts the target qubit detuning from ${ϵ}_T$ to ${ϵ}_T-{ϵ}_{\mathrm{cpl}}$, causing slower precession. (c) Singlet probability of the target qubit $P_T^S$ as a function of interaction time ${\tau }_I$ and control DQD detuning ${ϵ}_C$, with ${ϵ}_T^I=-3.2\mathrm{mV}$. A shift in period occurs around ${ϵ}_C=0\mathrm{mV}$, where control DQD occupancy changes. Dashed rectangles indicate the detuning ranges used in (e). Cut at ${\tau }_I=30\mathrm{ns}$ is shown in (d) (right axis). (d) Left axis: Precession frequency of the target qubit $f_T$ as function of detuning, from (c). Right axis: Singlet probability for interaction time ${\tau }_I=30\mathrm{ns}$, vertical cut from (c). (e) Precession of the target qubit as a function of interaction time ${\tau }_I$ at control DQD detuning ${ϵ}_C=-2.5\mathrm{mV}$ [blue dots, control DQD in $(1,1{)}_C$] and ${ϵ}_C=2.2\mathrm{mV}$ [red triangles, control DQD in $(0,2{)}_C$]. Nonzero phase of the damped cosine fits at ${\tau }_I=$ is due to the rise time of the coupling voltage pulse.Reuse & Permissions

Figure 5

(a) Singlet probability of the target qubit $P_T^S$ as a function of interaction time ${\tau }_I$. After 30 ns (indicated with the dashed line) a $4\pi$ rotation of the target qubit has been performed when the control DQD is in the $(1,1{)}_C$ charge state (blue dots and fit to the data), while a $3\pi$ rotation is performed when the control DQD is in the $(0,2{)}_C$ charge state (red triangles and fit to the data). This corresponds to a phase flip of the target qubit conditional on the occupancy of the control DQD. (b) Precession frequency $f_T$ as a function of target qubit detuning ${ϵ}_T$ with the control DQD in the $(1,1{)}_C$ (blue circles, detuning ${ϵ}_C=-8.1\mathrm{mV}$) and $(0,2{)}_C$ (red triangles, detuning ${ϵ}_C=5.4\mathrm{mV}$) charge state. Coupling frequency is the difference frequency between both data sets. Black curve is a fit to the coupling frequency data with the tunnel coupling as only free parameter. The two data points in the box correspond to the oscillations in (a). The right axis shows the interaction time required for a phase flip.Reuse & Permissions