Single-shot latched readout of a quantum dot qubit using barrier gate pulsing

1. Problem Statement

Single-shot readout is essential for quantum error correction and control protocols in semiconductor spin qubits. Latched readout is a technique used to enhance this process by mapping short-lived qubit states to metastable charge states, thereby extending the measurement window. However, traditional latched readout faces significant challenges:

• Tunnel Rate Constraints: It requires the simultaneous fulfillment of two conflicting conditions:
  1. Fast Tunneling (Condition 1): The tunnel rate from the qubit dot to the reservoir ($\Gamma_L$) must be much faster than the spin relaxation rate ($T_1^{-1}$) to ensure rapid latching.
  2. Slow Tunneling (Condition 2): The tunnel rate out of the metastable latched state ($\Gamma_R$) must be much slower than the measurement bandwidth ($\Delta f_{BW}$) to allow sufficient time for detection.
• Single-Reservoir Limitation: In devices coupled to a single reservoir, satisfying these conditions simultaneously is difficult. Increasing inter-dot tunnel couplings ($\Delta_1, \Delta_2$) to enable fast, coherent qubit manipulation often increases $\Gamma_R$ (via cotunneling) too much, violating Condition 2. Conversely, reducing $\Gamma_R$ to satisfy Condition 2 often slows down initialization, violating Condition 1.
• Reset Time: Even if latching is successful, the reset time (returning the qubit to the ground state) can be prohibitively long (hundreds of milliseconds) without active intervention, limiting the duty cycle of experiments.

2. Methodology

The authors propose a dynamic barrier gate pulsing scheme to decouple the requirements for manipulation, latching, and reset, allowing them to be met sequentially rather than simultaneously.

• Device Architecture: The experiment utilizes a Silicon/Silicon-Germanium (Si/SiGe) Quantum Dot Hybrid Qubit (QDHQ) with a double-dot structure (gates P1 and P2) and a charge sensor (gate CS). The system is coupled to a single electron reservoir via barrier gate B1.
• Dynamic Control Strategy: Instead of keeping tunnel rates static, the authors apply specific voltage pulses to barrier gate B1 (and compensate on P1) to dynamically alter the tunnel rates at different stages of the experiment:
  1. Initialization & Manipulation: A baseband pulse on B1 opens the tunnel barrier to the reservoir, allowing fast initialization and enabling the qubit to be manipulated (Larmor pulse) with large inter-dot couplings ($\Delta_1, \Delta_2$) for coherence.
  2. Latching: After manipulation, the qubit is moved to the readout window. If the qubit is in state $|1\rangle$, it tunnels into a metastable (4,2) charge state.
  3. Readout Window Optimization: Immediately after latching initiates, the B1 pulse is terminated (pinched off). This drastically reduces $\Gamma_R$ (the rate out of the latched state) by forcing transport through a higher-order cotunneling process, satisfying Condition 2 for a long-lived latched state.
  4. Active Reset: To overcome the slow natural reset, a sequence of pulses is applied to B1 to temporarily increase the tunnel rate, rapidly returning the qubit to the ground state (4,1).
• Crosstalk Compensation: The authors implement a compensation protocol where pulses on B1 are counter-balanced by pulses on P1 to maintain the qubit's operating point (detuning) despite the crosstalk inherent in the gate architecture.

3. Key Contributions

• Single-Reservoir Latching: Demonstrated a method to achieve high-fidelity latched readout using only a single electron reservoir, overcoming the traditional requirement for dual reservoirs or complex static tuning.
• Sequential Condition Fulfillment: Introduced a time-multiplexed approach where fast tunneling is used for initialization/manipulation and slow tunneling is enforced for readout, resolving the trade-off between coherent control speed and readout stability.
• Active Reset Mechanism: Developed a pulse sequence that accelerates the qubit reset time by orders of magnitude, making high-repetition-rate experiments feasible.
• Coherent Control with Single-Shot Readout: Successfully demonstrated coherent Larmor oscillations of a QDHQ using this new readout scheme, proving that the dynamic pulsing does not degrade qubit coherence.

4. Results

• Readout Fidelity: The method achieved a Signal-to-Noise Ratio (SNR) of 10.2 for single-shot readout. The charge sensitivity was measured at $3.10 \times 10^{-3} e/\sqrt{\text{Hz}}$.
• State Separation: Probability density plots showed two well-separated Gaussian peaks corresponding to logical states $|0\rangle$ and $|1\rangle$, confirming successful state discrimination.
• Reset Speedup:
  • Without reset pulses, the initialization probability after 2 ms was only 80%.
  • With the active reset pulse sequence, the initialization probability rose to 98% at 2 ms, representing a 15$\times$ speedup in the reset process.
• Coherent Oscillations: The authors observed clear Larmor oscillations as a function of pulse amplitude and wait time. Fast Fourier Transform (FFT) analysis yielded:
  • Inter-dot tunnel coupling $\Delta_1 \approx 750$ MHz.
  • Singlet-triplet splitting $E_{ST} \approx 4.0$ GHz.
  • These values align with theoretical expectations and magneto-spectroscopy data.

5. Significance

This work addresses a critical bottleneck in scaling semiconductor spin qubits. By enabling single-shot latched readout with a single reservoir, the technique simplifies device architecture and control complexity, which is vital for scaling to large qubit arrays.

• Scalability: It removes the need for multiple reservoirs per qubit, a major hurdle in dense qubit layouts.
• Efficiency: The active reset mechanism significantly reduces the dead time between experimental cycles, enabling faster data acquisition and more efficient error correction cycles.
• Generalizability: While demonstrated on a QDHQ, the barrier gate pulsing strategy is broadly applicable to other spin-based qubits (e.g., singlet-triplet, exchange-only, and single-spin qubits) that rely on spin-to-charge conversion in double-dot systems.

In summary, the paper presents a robust, dynamic control scheme that decouples the conflicting requirements of qubit manipulation and readout, paving the way for more efficient and scalable quantum computing architectures in silicon.