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arXiv:2608.14214

Exchange-only qubit stabilized by a single-spin qubit

Irina Heinz, Mira Sharma, Joris Kattemölle

quant-phcond-mat.mes-hallSubmitted Aug 14, 2026• Announced Aug 17, 2026• 0 citations
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Abstract

Hybrid approaches that combine different spin qubit encodings offer promising advantages. In particular, the additional degrees of freedom available in exchange-only qubits and their extensions enable enhanced spin lifetimes and facilitate error detection through the use of auxiliary spins. We show that integrating Loss-DiVincenzo with exchange-only qubits provides a practical route to realizing these benefits while remaining compatible with spin-shuttling architectures. We further demonstrate how the singlet-only exchange-only qubit can be employed for error detection, and we present a fault-tolerant $π$-rotation about each of the three control axes of the (singlet-only) exchange-only qubit. By enabling error detection at the lowest encoding level, our approach effectively converts charge and nuclear noise into erasures, thereby suppressing error propagation and potentially enhancing the performance of quantum error-correction schemes. More broadly, our work establishes a new perspective on the singlet-only exchange-only qubit as a logical encoding, opening the door to fault-tolerant gate constructions and spin-tailored quantum error-correction protocols for semiconductor-based quantum computing.

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Hybrid approaches that combine different spin qubit encodings offer promising advantages. In particular, the additional degrees of freedom available in exchange-only qubits and their extensions enable enhanced spin lifetimes and facilitate error detection through the use of auxiliary spins. We show that integrating Loss-DiVincenzo with exchange-only qubits provides a practical route to realizing these benefits while remaining compatible with spin-shuttling architectures. We further demonstrate how the singlet-only exchange-only qubit can be employed for error detection, and we present a fault-tolerant πππ-rotation about each of the three control axes of the (singlet-only) exchange-only qubit. By enabling error detection at the lowest encoding level, our approach effectively converts charge and nuclear noise into erasures, thereby suppressing error propagation and potentially enhancing the performance of quantum error-correction schemes. More broadly, our work establishes a new perspective on the singlet-only exchange-only qubit as a logical encoding, opening the door to fault-tolerant gate constructions and spin-tailored quantum error-correction protocols for semiconductor-based quantum computing.
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.
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.
Quantum error correction (QEC) is indispensable for scalable quantum computing, but implementing it with minimal hardware overhead remains a central challenge. Large spin systems with collective degrees of freedom offer a promising route to reducing the control complexity of qubit architectures while retaining a large Hilbert space for fault-tolerant encoding. However, existing proposals for logical gates and QEC in spin ensembles generally rely on inefficient higher-order interactions. Here we introduce spin-N-Cat codes, which encode logical qubits in superpositions of spin-coherent states and generalize bosonic Cat codes to the modular subspaces of permutationally symmetric spin ensembles. The code corrects collective and individual dephasing, excitation, and decay errors. We also present an efficient physical realization in central-spin systems, such as a quantum dot, where encoding, decoding, and a universal, fault-tolerant, and bias-preserving gate set are implemented using only first-order interactions. Numerical simulations demonstrate high logical fidelity under dephasing and excitation-decay noise, independent of noise bias, and that full QEC cycles are feasible with realistic microscopic parameters. For the large collective spins available in quantum dots, this translates into a substantial extension of coherence time. Our results establish spin-N-Cat codes as a scalable, hardware-efficient approach to QEC in spin-based quantum architectures.
Single-spin qubits in semiconductor quantum dots proposed by Loss and DiVincenzo (LD qubits) hold promise for universal quantum computation with demonstrations of a high single-qubit gate fidelity above 99.9 % and two-qubit gates in conjunction with a long coherence time. However, initialization and readout of a qubit is orders of magnitude slower than control, which is detrimental for implementing measurement-based protocols such as error-correcting codes. In contrast, a singlet-triplet (ST) qubit, encoded in a two-spin subspace, has the virtue of fast readout with high fidelity and tunable coupling to the electric field. Here, we present a hybrid system which benefits from the different advantages of these two distinct spin-qubit implementations. A quantum interface between the two codes is realized by electrically tunable inter-qubit exchange coupling. We demonstrate a controlled-phase (CPHASE) gate that acts within 5.5 ns, much faster than the measured dephasing time of 211 ns. The presented hybrid architecture will be useful to settle remaining key problems with building scalable spin-based quantum computers.
Measurement-based quantum computing (MBQC) promises an alternative approach to quantum computation that has natural compatibility with error-correction codes at the cost of a polynomial increase in physical qubits. MBQC implementations have previously focused on photonic systems where two-qubit gates are difficult. On the other hand, semiconductor spin qubit systems offer fast two-qubit gates via the exchange interaction. To explore the benefits of MBQC on spin systems, two hybrid measurement-exchange schemes for full qubit control with semiconductor double-quantum-dot spin qubits are considered. Protocol 1 fully realizes the cluster-state approach to MBQC but requires singlet-triplet qubits in a magnetic field gradient. Protocol 2 implements a direct measurement-based replacement for more traditional gate-based encoded operations, without need for magnetic field gradients. Both protocols demonstrate full single- and two-qubit control through a combination of interqubit and intraqubit exchange and measurement onto the singlet-triplet basis. We show that both schemes suppress individual qubit spin-state leakage errors and offer fast gate times, up to known phase and Pauli corrections.
We propose multi-spin molecules as a viable architecture for fault-tolerant quantum computing. To this aim, we introduce a correction protocol handling both diagonal and off-diagonal errors, typically associated with dephasing and relaxation. The scheme is based on a hybrid encoding which combines dephasing-tolerant units suppressing the leading pure dephasing error into a multi-spin molecule implementing a multi-qubit code for residual off-diagonal errors. Our proposal leverages peculiar properties of molecular spins, i.e. the strong hierarchy between different errors and the possibility to engineer multi-spin molecules at the synthetic level. Moreover, it addresses the important issue of the loss of coherences in anharmonic systems subject to off-diagonal errors, which hampers their correction at the single spin level. Thanks to the huge suppression of dephasing by the first-level code, we numerically demonstrate the potential performance of this strategy even with a limited number of spins per logical unit.