Noise-correlation spectrum for a pair of spin qubits in silicon

Semiconductor qubits are appealing for building quantum processors as they may be densely integrated due to small footprint. However, a high density raises the issue of noise correlated across different qubits, which is of practical concern for scalability and fault tolerance. Here, we analyse and quantify in detail the degree of noise correlation in a pair of neighbouring silicon spin qubits ~100 nm apart. We evaluate all a-priori independent auto- and cross- power spectral densities of noise as a function of frequency. We reveal strong inter-qubit noise correlation with a correlation strength as large as ~0.7 at ~1 Hz (70% of the maximum in-phase correlation), even in the regime where the spin-spin exchange interaction contributes negligibly. We furthermore find that fluctuations of single-spin precession rates are strongly correlated with exchange noise, giving away their electrical origin. Noise cross-correlations have thus enabled us to pinpoint the most influential noise in the present device among compelling mechanisms including nuclear spins. Our work presents a powerful tool set to assess and identify the noise acting on multiple qubits and highlights the importance of long-range electric noise in densely packed silicon spin qubits.