Quantum Error Correction with Atomic Spin Qubits in Silicon

The realisation of fault-tolerant quantum computing is predicated on effective quantum error correction to protect fragile quantum information during computations. Atom qubits in silicon have recently demonstrated high-fidelity single (>99.9%) and two-qubit (>99.3%) gates [1]. Combined with their potential for rapid scalability, they are emerging as leading candidates for encoding large-scale logic operations. As these systems scale in size, there is great opportunity to demonstrate efficient error correction arising from the long coherence times intrinsic to nuclear spin qubits. In our four-qubit silicon processor, we implement a phase-flip correction code to protect a three-qubit logical state encoded across three nuclear spins against phase errors. We report corrected fidelities well above the ideal physical qubit for multi-qubit injected phase errors over a significant error probability range. Importantly, this advantage is maintained when allowing phase errors to accumulate naturally through decoherence processes in any of the nuclear qubits while under realistic operating conditions. This remarkable improvement in error correction capability stems in-part from the native multi-qubit Toffoli gate of our electron-nuclear hyperfine coupled connectivity, with the enhanced spin qubit performance paving the road towards fault-tolerant quantum computation in silicon.

[1] I. Thorvaldson et al., accepted Nat. Nano., arXiv:2404.08741 (2024)