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An iterative transversal CNOT decoder
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abstract
Modern platforms for potential qubit candidates, such as trapped ions or neutral atoms, allow long range connectivity between distant physical qubits through shuttling. This opens up an avenue for transversal logical CNOT gates between distant logical qubits, whereby physical CNOT gates are performed between each corresponding physical qubit on the control and target logical qubits. However, the transversal CNOT can propagate errors from one logical qubit to another, leading to correlated errors between logical qubits. We have developed a multi-pass iterative decoder that decodes each logical qubit separately to deal with this correlated error. We show that under circuit-level noise and only $\mathcal{O}(1)$ code cycles, a threshold can still persist, and the logical error rate will not be significantly degraded, matching the sub-threshold logical error rate scaling of $p^{\lfloor\frac{d}{2}\rfloor}$ for a distance $d$ rotated surface code.
Forward citations
Cited by 7 Pith papers
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Decoding across transversal Clifford gates in the surface code
A new logical-observable matching decoder lets surface codes run fast transversal Clifford gates while correcting all errors below half the code distance, and windowed variants trade efficiency against reset speed.
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Scalable decoding protocols for fast transversal logic in the surface code
The paper presents windowed decoding protocols that restore modularity and locality to decoding of fast transversal logic, enabling constant-time logical gates with scalable error correction.
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Transversal Logical Clifford gates on rotated surface codes with reconfigurable neutral atom arrays
The authors complete a transversal Clifford gate set on rotated surface codes by embedding a fold-transversal S gate inside a syndrome extraction round, with detector construction and numerical support.
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Do Not Let CNOTs Overwhelm the Decoder: Scheduling Transversal Gates for Fast FTQC
A decoder-aware scheduler packs transversal CNOT gates into surface-code quantum programs as densely as decoder capacity allows, using hybrid decoder selection, template-based DEM stitching, and sub-window parallel decoding.
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Fast correlated decoding of transversal logical algorithms
Decoding only back-propagated reliable logical Pauli products turns transversal-circuit decoding into a matchable graph, so fast minimum-weight perfect matching works with memory-like thresholds.
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Learning to decode logical circuits
A modular neural decoder, MCCD, learns to decode surface-code logical circuits with single-qubit and entangling gates, keeping accuracy while running faster than MWPM, MLE, and BP-OSD in simulated benchmarks.
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Pauli webs spun by transversal $|Y\rangle$ state initialisation
A diagrammatic verification, using Pauli webs, that the CCLP fold-transversal S gate maps the logical X correlator to the logical Y correlator.
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