Summary
In a five-qubit silicon spin-qubit array, researchers used pairwise calibration to counter microwave-induced a.c.-Stark shifts. Randomized benchmarking measured primitive single-qubit gate fidelity above 99.99% during simultaneous control of up to three qubits, and about 99.9% across all five.
A five-qubit silicon spin-qubit array retained primitive single-qubit gate fidelity above 99.99% while operating up to three qubits at once, according to a Nature Physics study published on 15 October 2026. The researchers traced a major source of fidelity loss during parallel operation to microwave-induced a.c.-Stark shifts and used pairwise calibrations to compensate for them. When all five qubits were driven simultaneously, four exceeded 99.9% fidelity and the fifth reached approximately 99.9%.
The experiment addresses a scaling challenge: a processor needs to run gates on multiple qubits in parallel, rather than keep most qubits idle while operating them one by one. The device used a shared microwave-control line, which reduces the need for separate wiring but exposes neighbouring qubits to off-resonant microwave signals.
Why parallel microwave control loses fidelity
The experiment used five quantum dots in an isotopically enriched silicon/silicon-germanium device. Each dot hosts a spin qubit. Microwave pulses manipulate the spins through electric-dipole spin resonance, while a magnetic-field gradient gives neighbouring qubits distinct resonance frequencies—about 150 MHz apart in this device—so they can be addressed individually.
A microwave tone intended for one qubit can still affect another on the shared line. Even when that second qubit is not resonantly driven, the off-resonant field shifts its resonance frequency through the a.c.-Stark effect. The shift accumulates as a phase error, reducing gate fidelity during simultaneous operation. The study identified these shifts as the dominant source of the parallel-operation degradation it measured.
The researchers used randomized benchmarking to estimate the fidelity of primitive X and Y gates, each a π/2 rotation. With tailored Kaiser-window pulses, all five qubits individually exceeded 99.99% fidelity, with some approaching 99.999%. The windowed pulse shape helps suppress direct microwave crosstalk from spectral leakage.
Pairwise calibration preserves gate performance
To correct the phase errors, the team measured how driving one qubit changed the phase of another, then compensated by adjusting microwave phases in the gate sequences. They also calibrated pulse amplitudes for simultaneous operation to reduce over- or under-rotation errors. For operations involving more qubits, pairwise phase measurements could be summed to estimate the combined shift on each qubit. The researchers found that this approach performed as well as a full calibration in which the other four qubits were driven during each measurement.
With these adjustments, simultaneous operation of two and then three qubits achieved primitive gate fidelities above 99.99% for each qubit. In five-qubit randomized benchmarking, the team tested gate durations of 250 ns and 500 ns. Four qubits exceeded 99.9% fidelity in both cases; the fifth was approximately 99.9%. The researchers attribute the trade-off between gate durations to microwave-induced decoherence at higher drive power and greater exposure to low-frequency noise during longer gates.
The 99.9% figure is a widely targeted benchmark for fault-tolerant operation, although the relevant threshold depends on the error model. It describes these single-qubit operations, not the performance of a complete processor. The paper notes that this device’s controlled-Z two-qubit gates were limited to below 97% by spin–valley mixing, and that full circuit performance also depends on two-qubit operations, state preparation, measurement and idling.