Towards fault-tolerant quantum error correction with spin qubits in diamond

Quantum error correction (QEC) is essential for reliable large-scale quantum information processing. Pioneering experiments have demonstrated QEC codes that could only correct specific types of errors using various physical platforms [1,2]. However, full experimental demonstration of a fault-tolerant QEC code that can correct any type of single-qubit error remains an open challenge. Here, I will present our results towards the implementation of a fault-tolerant QEC code using a solid-state spin register in diamond. Recently, we have demonstrated that such a register can hold up to 10 qubits with high-fidelity universal control, coherence times up to one minute, and genuine multipartite entanglement [3,4]. Building upon these results, I will show how we can use multiple non-destructive parity measurements to encode logical states in C13 nuclear-spin qubits in diamond. These parity measurements might be further used to detect and correct arbitrary single-qubit errors on the encoded states, and are therefore an important step towards fault-tolerant quantum information processing.

[1] Kelly et al., Nature, 519, 7541, 2015
[2] Cramer et al., Nat. Commun., 7, 11526, 2016
[3] Bradley et al., Phys. Rev. X, 9, 031045, 2019
[4] Abobeih et al., Nature, 576, 411, 2019