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A Constant Rate Quantum Computer on a Line
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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.
Forward citations
Cited by 2 Pith papers
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Growing Sparse Quantum Codes from a Seed
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.
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