Dipolar Coupling Errors in Nuclear Spin Qubits

Nuclear spins have been studied since the beginning of quantum information science since they form the prototypical qubit with long coherence times and high-fidelity operation. To perform practical fault-tolerant quantum computations, however, not only do we require precision manufacturing techniques to produce millions of qubits, but these techniques need to consistently yield low-error qubits. A deep understanding and control of the interactions between the qubits and their environment are needed as we scale so that devices can be engineered to avoid high error rates. In this work, we experimentally and theoretically characterize two often-overlooked error mechanisms affecting nuclear spin qubits in silicon caused by local interactions. The first is the direct magnetic interactions between nuclear spins, causing dipolar coupling errors, and the second is the interactions between the nuclear spins and their associated electron spin, causing "hotspots" of anisotropic hyperfine coupling errors. By modeling the properties of the combined electron-nuclear spin system as a function of magnetic field, contact hyperfine strength, and electron tunnel rate, we show how these errors can be reliably mitigated, giving rise to readout fidelities of $\gtrsim 99.9\%$ .