The dawn of error correction with spin qubits

Takao Aoki, Go Takahashi, Tadashi Kajiya +4 more

Hai Lu, Isidora Araya Day, Anton Akhmerov +2 more

We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the "Ising molecule qubit," is experimentally feasible and provides a path for compact noise-biased qubits.

Haoran Lu, Isidora Araya Day, Anton Akhmerov +2 more

We propose an architecture for bit-flip error correction of Andreev spins that is protected by Kramers' degeneracy. Specifically, we show that a coupling network of linear inductors and Andreev spin qubits results in a static Hamiltonian composed of the stabilizers of a bit-flip code. The electrodynamics of the many-body spin states also respect these stabilizers, and we show how reflectometry off a single coupled resonator can thereby accomplish their projective measurement. We further show how circuit-mediated spin couplings enable error correction operations and a complete set of single- and two-module logical quantum gates. The concept, which we dub the ``Ising molecule qubit,'' is experimentally feasible and provides a path for compact noise-biased qubits.

Jesús Yaljá Montiel-Pérez, Jordi Fabián González-Contreras, Erik Zamora +1 more

Mauricio Gutiérrez, Juan S. Rojas-Arias, David Obando +1 more

We investigate the performance of two quantum error-correcting codes, the surface code and the Bacon-Shor code, for implementation with spin qubits in silicon. In each case, we construct a logical qubit using a planar array of quantum dots, exploring two encoding schemes: one based solely on single-electron Zeeman qubits (Loss-DiVincenzo qubits), and a hybrid approach combining Zeeman and singlet-triplet qubits. For both codes, we evaluate key performance metrics, including logical state preparation fidelity and cycle-level error correction performance, using state-of-the-art experimental parameters. Our results show that the hybrid encoding consistently outperforms the pure Zeeman-qubit implementation. By identifying the dominant error mechanisms that limit quantum error correction performance, our study highlights concrete targets for improving spin qubit hardware and provides a path toward scalable fault-tolerant architectures. In particular, we find that the logical error rate is not limited by memory errors, but rather by gate errors, especially 1- and 2-qubit gate errors.

Adam Siegel, Simon Benjamin

Fast and high fidelity shuttling of spin qubits has been demonstrated in semiconductor quantum dot devices. Several architectures based on shuttling have been proposed; it has been suggested that singlet-triplet (dual-spin) qubits could be optimal for the highest shuttling fidelities. Here we present a fault-tolerant framework for quantum error correction based on such dual-spin qubits, establishing them as a natural realisation of erasure qubits within semiconductor architectures. We introduce a hardware-efficient leakage-detection protocol that automatically projects leaked qubits back onto the computational subspace, without the need for measurement feedback or increased classical control overheads. When combined with the XZZX surface code and leakage-aware decoding, we demonstrate a twofold increase in the error correction threshold and achieve orders-of-magnitude reductions in logical error rates. This establishes the singlet-triplet encoding as a practical route toward high-fidelity shuttling and erasure-based, fault-tolerant quantum computation in semiconductor devices.