[Paper Review] Real-time feedback protocols for optimizing fault-tolerant two-qubit gate fidelities in a silicon spin system

Nard Dumoulin Stuyck, Amanda E. Seedhouse+11 more|arXiv (Cornell University)|Sep 21, 2023

Advancements in Semiconductor Devices and Circuit DesignEngineering3 citations

TL;DR

This paper presents FPGA-optimized real-time feedback protocols to stabilize single- and two-qubit parameters in silicon spin qubits, achieving high-fidelity two-qubit gates (>99%) over multi-hour timescales. By applying Haar wavelet analysis to feedback data, the study identifies distinct noise sources—discrete jumps, slow drifts, and 1/f noise—enabling systematic noise characterization crucial for fault-tolerant quantum computing.

ABSTRACT

Recently, several groups have demonstrated two-qubit gate fidelities in semiconductor spin qubit systems above 99%. Achieving this regime of fault-tolerant compatible high fidelities is nontrivial and requires exquisite stability and precise control over the different qubit parameters over an extended period of time. This can be done by efficiently calibrating qubit control parameters against different sources of micro- and macroscopic noise. Here, we present several single- and two-qubit parameter feedback protocols, optimised for and implemented in state-of-the-art fast FPGA hardware. Furthermore, we use wavelet-based analysis on the collected feedback data to gain insight into the different sources of noise in the system. Scalable feedback is an outstanding challenge and the presented implementation and analysis gives insight into the benefits and drawbacks of qubit parameter feedback, as feedback related overhead increases. This work demonstrates a pathway towards robust qubit parameter feedback and systematic noise analysis, crucial for mitigation strategies towards systematic high-fidelity qubit operation compatible with quantum error correction protocols.

Motivation & Objective

• Address the challenge of maintaining high-fidelity two-qubit gates in silicon spin qubits over extended timescales despite environmental noise.
• Develop fast, real-time feedback protocols optimized for FPGA hardware to stabilize qubit control parameters.
• Use feedback data to characterize complex noise dynamics beyond standard Fourier analysis.
• Enable systematic noise source identification to guide improvements in qubit fabrication and control.
• Demonstrate scalability and robustness of feedback protocols for integration into fault-tolerant quantum computing architectures.

Proposed method

• Implement real-time feedback protocols on fast FPGA hardware to dynamically correct single- and two-qubit control parameters in silicon quantum dots.
• Use wavelet-based analysis (specifically Haar wavelet transform) to extract time-frequency characteristics of feedback data, capturing non-stationary noise signals.
• Compare wavelet results with standard Fourier power spectral density (PSD) to highlight advantages in resolving transient and time-varying noise features.
• Analyze feedback data for discrete jumps, slow drifts, and 1/f noise by examining amplitude and sign patterns in the wavelet transform at different scale parameters (1/λ).
• Correlate wavelet features with physical noise mechanisms such as two-level fluctuators and dielectric traps.
• Use feedback data to detect and classify noise types, including unidirectional and multi-directional drifts, and high-frequency jumps.

Experimental results

Research questions

• RQ1 How can real-time FPGA-based feedback protocols stabilize single- and two-qubit parameters in silicon spin qubits over multi-hour timescales?
• RQ2 What advantages does wavelet analysis offer over traditional Fourier analysis in characterizing non-stationary noise in quantum feedback data?
• RQ3 What distinct noise signatures (e.g., jumps, drifts, 1/f noise) can be identified in qubit feedback data using wavelet transforms?
• RQ4 How do different noise components—such as two-level fluctuators and dielectric traps—affect qubit fidelity and parameter stability?
• RQ5 To what extent can feedback data inform improvements in qubit fabrication and control strategies?

Key findings

• The FPGA-optimized feedback protocols successfully maintained high-fidelity two-qubit gates (>99%) over multi-hour timescales in a silicon spin qubit system.
• Wavelet analysis revealed three dominant noise components: discrete jumps with ~0.05 mV amplitude, slow low-amplitude drifts, and high-frequency 1/f-like noise.
• The wavelet transform identified unidirectional drifts as features with constant sign at small 1/λ (e.g., positive at 1/λ < 10⁻⁴ s⁻¹), while multi-directional drifts showed alternating positive and negative amplitudes.
• A bump in the Fourier PSD at ω ≈ 3×10⁻² Hz indicated the presence of a strongly coupled two-level fluctuator or ensemble of fluctuators, confirmed by wavelet dynamics.
• Wavelet analysis detected 1/f noise through features at high 1/λ with near-zero normalized amplitude, distinguishing it from larger-amplitude fluctuations.
• The wavelet transform provided superior time-domain resolution of noise dynamics compared to Fourier PSD, especially for non-stationary and transient signals.