Probing two-qubit capacitive interactions beyond bilinear regime using dual Hamiltonian parameter estimations

Semiconductor quantum dots (QDs) are a promising platform for scalable quantum information processing. Recent advancements in III-V and IV semiconductors have demonstrated high-fidelity single- and two-qubit gates, simultaneous qubit operations, multi-qubit entanglement, high-temperature operation, and long-range coupling. However, low-frequency noise (quasi-static nuclear fluctuations and slow charge noise) significantly limits coherence times. This noise affects spin coherence time and exchange or capacitive coupling-based two-qubit control. Real-time Hamiltonian parameter estimation and measurement-based feedback are techniques for error mitigation. Previous studies applied this to GaAs, suppressing quasi-static nuclear spin fluctuations for single spins and singlet-triplet (ST₀) qubits. This study extends this technique to a two-qubit system in GaAs, demonstrating simultaneous drive of a pair of ST₀ qubits, actively decoupling quasi-static nuclear noise using Bayesian inference. The goal is to achieve high-quality Rabi oscillations and measure electrostatic coupling of two ST₀ qubits beyond the bilinear form, assessing the potential for high-fidelity and fast conditional phase gates using capacitive interactions.

The paper reviews the significant progress in semiconductor quantum dot spin qubits, highlighting achievements such as high-fidelity single and two-qubit gates in silicon, simultaneous qubit operations in GaAs with long coherence times, multi-qubit entanglement, high-temperature operations, and long-range coupling using superconducting cavities. It also discusses the significant challenge of low-frequency noise, specifically quasi-static nuclear fluctuations and slow charge noise, which limit coherence times and affect two-qubit control mechanisms. Existing techniques like real-time Hamiltonian estimation and measurement-based feedback for noise mitigation are reviewed, along with their previous applications in single-qubit systems. The limitations of the bilinear form assumption for capacitive coupling in previous studies are also highlighted, setting the stage for the present research that aims to investigate the two-qubit interaction beyond this assumption.

The experiment uses a quadruple QD device on a GaAs/AlGaAs heterostructure, hosting a pair of ST₀ qubits. High-frequency voltage pulses and DC voltages are applied to gates V₁-V₆. Dual RF reflectometry is performed using RF single-electron transistors. The device operates in a dilution refrigerator at ~7 mK with an external magnetic field. Simultaneous Hamiltonian parameter estimation is performed using a Bayesian inference-based real-time Hamiltonian estimation circuit. The qubits are initialized and measured via fast energy-selective tunneling (EST)-based single-shot readout and adaptive initialization. The Bayesian inference updates the estimation of the field gradient (ΔB_zi) for each qubit based on the measurement results. The time resolution of the estimation is ~1.8 ms. The estimated ΔB_zi values are used for active frequency feedback during qubit control. Rabi oscillations are measured for individual and simultaneous qubit operations. Simultaneous Ramsey interference is performed to extract T₂*. Capacitive coupling is measured using a state-dependent exchange oscillation technique. A control qubit is used to induce a state-conditional frequency shift in the target qubit. The capacitive coupling strength (J_RL) is extracted from the frequency shift. T₂* and spin-echo coherence time (T_echo) are measured to quantify the quality of the conditional phase-flip operation. The super-linearity of J_RL is investigated by varying J_L and J_R and fitting to (J_LJ_R)^α. The quality factor of the conditional phase-flip operation is calculated as Q = T₂*/T_echo. The device fabrication involves wet etching and e-beam lithography, with measurements conducted in a dilution refrigerator using an arbitrary waveform generator.

The study demonstrates simultaneous, high-quality Rabi oscillations of two ST₀ qubits in GaAs with active suppression of quasi-static nuclear noise using a real-time Bayesian inference circuit. The Rabi decay times (T_Rabi) are approximately 1.7 μs for individual qubit operation and slightly shorter (1.6 μs) for simultaneous operation. The observed strong two-qubit capacitive interaction (J_RL) significantly exceeds the previously assumed bilinear form (J_RL ≈ J_LJ_R) and reaches values greater than 190 MHz. The experimental data supports a super-linear scaling of J_RL, with α = 2.14 in the fitting of J_RL to (J_LJ_R)^α, which is consistent with theoretical predictions. A high ratio (>16) is observed between coherence time and conditional phase-flip time, indicating the potential for high-fidelity and fast entanglement generation using capacitive interactions. This high quality factor of the conditional phase flip operation suggests that the fidelity of a conditional phase-flip operation could reach as high as 94%. The study also demonstrates a significant increase in achievable Bell state fidelity compared to previous work, projecting a maximum attainable fidelity of ~95%.

The findings address the research question by demonstrating the feasibility of generating high-fidelity and fast entanglement in a two-qubit system using capacitive interaction, even in the presence of significant environmental noise. The observed super-linear scaling of the capacitive coupling strength offers a pathway to enhance the fidelity and speed of two-qubit operations, compared to previous methods that assumed a bilinear form. The high ratio of coherence time to conditional phase-flip time suggests that this approach is highly promising for building scalable quantum computers, because high-fidelity entangling gates are crucial for fault-tolerant quantum computation. The results confirm recent theoretical calculations and suggest further improvements are possible with faster signal sources and optimized pulse sequences. The limitations of the current setup (e.g., FPGA resources, waveform generator speed) are discussed as areas for future research.

This work demonstrated simultaneous Hamiltonian estimation and active quasi-static noise suppression for two ST₀ qubits in a GaAs quadruple QD array. The strong, super-linear capacitive coupling observed supports the potential for high-fidelity and fast entanglement generation using simple capacitive interactions, surpassing previous assumptions about bilinear scaling. The high quality factor of the conditional phase flip operation signifies a significant step toward practical quantum computation. Future work will focus on implementing a full two-qubit gate and entanglement demonstration with improved hardware and optimized pulse sequences.

The current experimental setup has limitations in terms of FPGA resources and the waveform generator's sampling rate. The limited FPGA resources result in increased latency during simultaneous Bayesian estimation and frequency feedback, affecting the Rabi decay time and oscillation visibility. The limited sampling rate (2.4 GSa/s) prevents performing full two-qubit gate operations and entanglement demonstration, thus requiring faster signal sources for future investigations. The adiabatic switching of the interaction in the current pulse sequence might lead to decoherence in the control qubit during the measurement of the two-qubit interaction.