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Nature Physics

Fault-tolerant architecture for quantum computation using electrically controlled semiconductor spins

Jacob M. Taylor, Hans‐Andreas Engel, Wolfgang Dür, Amir Yacoby, Charles M. Marcus, P. Zoller, Mikhail D. Lukin

Published Dec 1, 2005• 431 citations
Publisher
DOI
10.1038/nphys174

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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.
Scalable fault-tolerant quantum computer architectures require quantum gates that operate within a small fraction of the qubit decoherence time and with high accuracy over a bandwidth set by the decoherence rate. Electron spin quantum bits in Si are promising because of long decoherence times (∼0.5 ms), but electrical gating schemes still seem problematic. Oxide–semiconductor heterostructures have the potential for precise electrical control of gate operations in the semiconductor, using optical rectification in the ferroelectric oxide. Accurate (∼80 dB), local (∼10 nm), dynamic (>THz) and programmable optical control over electric polarization in the ferroelectric can be achieved using existing technology. Optical techniques may also be useful in rapid initialization of the quantum computer, and for providing a source of initialized qubits to use for quantum error correction. Advantages of optical methods will be discussed within a framework proposed for a quantum information processor using ferroelectrically coupled electron spins and Ge quantum dots in Si.
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.