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A Constant Rate Quantum Computer on a Line

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arxiv 2502.16132 v1 pith:LPLMQPUM submitted 2025-02-22 quant-ph

Craig Gidney , Thiago Bergamaschi This is my paper · ORCID
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keywords codescomputerconstructionlineprovequantumratestabilizer
verification ladder T0 review T1 audit T2 compute T3 formal

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We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5% and quasi-polylog time overhead, out of a line of qubits with nearest-neighbor connectivity, and prove it has a threshold. The construction is based on modifications to the tower of Hamming codes of Yamasaki and Koashi (Nature Physics, 2024), with operators measured using a variant of Shor's measurement gadget.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Blocklet concatenation: Low-overhead fault-tolerant protocols for fusion-based quantum computation

    quant-ph 2025-06 conditional novelty 8.0 of 10

    Blocklet concatenation yields fusion-based quantum computing protocols with constant-sized resource states, erasure thresholds up to 19.1%, and footprint per logical qubit scaling better than surface codes.

  2. Duality constrains optimal thresholds in quantum error correction

    quant-ph 2026-07 conditional novelty 7.0 of 10

    Zero-rate em-symmetric CSS codes are self-dual under generalized Kramers-Wannier duality, pinning their optimal code-capacity threshold (at leading order in a replica limit) to the zero-rate hashing bound p≈0.110.

  3. Growing Sparse Quantum Codes from a Seed

    quant-ph 2025-07 conditional novelty 6.0 of 10

    Conjoining only bit-flip and phase-flip repetition codes can generate any CSS code, and an iterative algorithm grows sparse subsystem codes with kd^2=O(n) worst-case scaling.

  4. Quantum circuit lower bounds in the magic hierarchy

    quant-ph 2025-04 conditional novelty 6.0 of 10

    A Clifford circuit followed by a shallow two-qubit circuit cannot prepare several explicit entangled states, including some topological ground states and quantum codes.

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