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

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.