Enrichment Lengthens Coherence but Barely Changes Circuit Success: A Model of Silicon Spin Qubits

Abstract

Abstract - Silicon spin qubits can be built in existing chip factories, but three physical mechanisms limit them: charge noise, hyperfine coupling to residual 29Si nuclear spins, and phonon-driven relaxation. Many groups enrich silicon to remove the 29Si, so I ask whether that is what limits a quantum circuit. I build a closed-form model of the three mechanisms and use it to predict the success probability of a width-8 mirror circuit (56 two-qubit gates). No spin-qubit hardware was available, so every silicon number is a model prediction, not a measurement. Enriching from 4.7% 29Si to 800 ppm lengthens the hyperfine-limited coherence time 7.6-fold, and to 50 ppm 31-fold, yet changes the predicted success probability by less than one percentage point. Charge noise on the two-qubit gate dominates the error, while magnetic field, temperature and relaxation time have no effect. The predicted success probability, 0.73, is lower than the 0.83 measured on a Rigetti superconducting device. The two-qubit error is calibrated to published results and not predicted, and crosstalk and leakage are left out, so this comparison is a rough guide only.