Microwave response of electrically driven spins in a three-qubit quantum processor

Abstract

In electric dipole spin resonance (EDSR), a single spin is electrically driven in the field gradient produced by a micromagnet. While EDSR has enabled high fidelity gate operations in many devices, there are reports of unexpected non-linearities in the Rabi frequency as a function of microwave drive amplitude. We carefully measure the response of Loss-DiVincenzo (LD) single spin qubits to resonant drives as well as simultaneous resonant and off-resonant drives, as would be encountered in a realistic quantum processor. With the microwave amplitude carefully calibrated, we find that the Rabi frequency scales linearly with drive amplitude, even when all three spins are driven simultaneously. We also determine that heating-induced resonance frequency shifts from off-resonant drives are comparable to typical temporal drifts. Our results indicate that the previously observed nonlinear response is not a general feature of LD spin qubits.

Figures (7)

• Figure 1: Device architecture and quantum control sequence. (a) Top: False-color scanning electron microscope image of the TQD before the deposition of the Co micromagnet. Bottom: Cartoon depicting the resulting electrostatic confinement potential $V(x)$. (b--c) Charge stability diagrams acquired by measuring the charge sensor conductance $g_s$ as a function of gate voltages $V_{\rm Pi}$ and $V_{\rm Pj}$. The initialization, quantum control and readout sequence is indicated by the roman numerals (see text). (d) Spin-up probability $P_\uparrow$ plotted as a function of microwave drive time $\tau_R$ for each of the three qubits. Data are offset by 1.0 for clarity.
• Figure 2: Linearity of single spin Rabi oscillations with drive amplitude. (a) Rabi's equation predicts a linear dependence of the Rabi frequency $f_{\rm R}$ on the microwave drive amplitude $A_{\rm MW}$. The non-linear behavior observed by Undseth et al. is shown for comparison undseth2023nonlinear. Experimental limitations, such as the saturation of amplifiers at high powers, could also lead to slight deviations from linearity. (b) Measured $f_\text{R}$ as a function of $A_{\rm MW}$ for each qubit, showing the expected linear dependence. Solid lines are linear fits to the data.
• Figure 3: Sensitivity of qubit resonance frequencies to off-resonant drives. (a) Qubit resonance frequencies are determined using a Ramsey pulse sequence. To assess the sensitivity of a qubit to off-resonant drives that will be present in multi-qubit implementations, the Ramsey sequence is preceded by a pre-pulse of duration $\tau_\text{p}$. The resulting qubit frequency shift $\Delta f_{\rm Q}$ is plotted as a function of $\tau_\text{p}$. (b) Ramsey pulse sequence with an off-resonant pulse applied during the entire free-evolution interval $\tau_\text{wait}$. $\Delta f_{\rm Q}$ is plotted as a function of $A_\text{\rm MW}$. Data are offset by 0.5 for clarity.
• Figure 4: Linearity of three simultaneously driven single spin Rabi oscillations with drive power. (a) The three qubit drive tones are multiplexed into a single $IQ$ channel that modulates a vector microwave source driving the MS gate. We vary the drive amplitude $A_{\rm Qi}$ of a single qubit while holding the drive amplitude of the other two qubits fixed. (b -- d) Extracted $f_{\rm R}$ plotted as a function of $A_{\rm Qi}$. As the power delivered to one qubit is increased, we see a slight decrease in the Rabi frequency of the other two qubits. Solid lines are the measured power output by the microwave source scaled by the single qubit linear fits, which suggests that the curvature comes from microwave power saturation rather than qubit crosstalk.
• Figure 5: Block diagram depicting microwave signal generation and delivery to the device. An arbitrary waveform generator drives the $IQ$ ports of a vector microwave source, modulating the local oscillator $LO$. The modulated signal is high-pass filtered (HPF), isolated (ISO), and routed through several stages of cryogenic attenuation before it reaches the device. The output can optionally (dashed line) be connected to a spectrum analyzer to calibrate the output amplitude.