Erasure conversion for singlet-triplet spin qubits enables high-performance shuttling-based quantum error correction

TL;DR

This work develops a fault-tolerant erasure-based quantum error correction scheme using singlet-triplet qubits in semiconductor devices, leveraging leakage detection to project leaked states back to the computational subspace without feedback. By designing two stabiliser circuits—one exchange-only and one driven-gate—to convert X-type noise into erasure (or bias it via XZZX encoding)—the approach yields higher error thresholds and dramatically lower logical error rates when combined with leakage-aware decoding. Simulations across CSS and XZZX surface codes show a threshold increase from ~0.45–0.49% (LD/CSS) to ~1.3% (XZZX+ST), with shuttling-induced errors further suppressing logical errors in the biased, erasure-enabled regime. The results position singlet-triplet encoding as a practical path toward high-fidelity, erasure-based fault-tolerant quantum computation in silicon spin-qubit devices.

Abstract

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.

Figures (9)

• Figure 1: QEC with dual-spin qubits, using the surface code as an example. Left: data and ancilla qubits are encoded in singlet-triplet pairs i.e. dual-spins living in the odd-parity subspace. These qubits have a degree of natural protection against phase noise but suffer from leakage errors (orange pair). Stabilisers are not designed to catch such errors thus leakage detection strategies (or erasure checks) must be designed. Right: leakage is checked by unitarily transferring the information from an old to a new data pair before measuring the old one out, which reduces the entropy of the system. This protocol both accurately detects leakage and projects the new pair back to the computational subspace without the need for a measurement feedback.
• Figure 2: Circuit implementation of the CZ and CNOT gates between two ST qubits.
• Figure 3: Leakage detection circuit and projection back onto the computational subspace. When the initial state $\ket{\psi}$ is in the computational subspace, its measurement yields a singlet and the output state $\ket{\psi'}$ is equal to $X\ket{\psi}$. The X flip is not problematic as it is deterministic and can be stored in memory. When the input state is leaked however, the measurement outcome becomes $\ket{T_\pm}$ and the output $\ket{\psi'}$ is in an (unknown) state back in the computational subspace.
• Figure 4: Stabiliser circuits for the ST qubits. Each pair of lines represents one ST qubit. The measurement is assumed to distinguish between $\ket{S}$, $\ket{T_0}$ and $\ket{T_\pm}$ as explained in \ref{['sec:physical_implementation']}. Left: X stabiliser using exchange gates only. The Z stabiliser is obtained by removing the H gates. Right: XZZX stabiliser, using exchange and driven gates. This stabiliser is bias-preserving.
• Figure 5: Decoding is performed via MWPM, whose weights are adjusted according to the additional information extracted from the leakage detection circuit. Left: standard CSS surface code. Leakage detections correspond to the measurement of a $\ket{T_\pm}$ state (yellow stars). The exclusive use of exchange gates allows one to confirm leakage by pairing such detection events in space or time (see main text). Isolated detections (faded) are most likely the result of measurement errors. In case of leakage, both neighbouring X and Z stabilisers (in bright colours) are connected with weight 0. Right: XZZX surface code. We consider both $\ket{T_\pm}$ and $\ket{T_0}$ as detection events (resp. yellow and orange stars). The latter is used to detect Pauli X errors only (therefore only the weight between the SW and NE stabilisers is set to 0). Detections here cannot be paired due to the use of CNOTs, which are not spin-conserving, thus there is a higher risk of false leakage detection.