A Hybrid Atom-Array Architecture for Universal Quantum Computation: The FCC Sheet Code with 3D Color-Code Magic-State Factory
Year: 2026
Type: preprint
Abstract: A fault-tolerant quantum computer needs a memory code and a source of magic states. On a neutral-atom array the two can use different codes. This paper connects a [[15,1,3]] color-code factory, which has a transversal T gate, to the FCC sheet code, a [[3L³, 6L, L]] CSS memory at K = 4 connectivity. The connection is a transfer: a logical state is moved from a color-code block into one sheet-code logical by one-bit teleportation. We build the transfer circuit with a flagged joint Z̄ₐZ̄ᵦ measurement and simulate it at L = 4 under circuit-level depolarizing noise. The noise-free truth table holds for all four basis states. The circuit distance is 4 in the Z sector and 3 in the X sector. At p = 10⁻³ the transfer fails at 0.17% (Z) and 1.7% (X); the sheet memory alone fails at 0.07% and below 0.27% over the same rounds. When all noise on the color-code block is turned off, the X-sector excess disappears. The cost of the transfer is therefore the distance-3 factory block failing while it waits, not the interface. Two further results support the architecture. The lattice rotation R: (x, y, z) ↦ (y, z, x) maps each of the three sheets onto the next. We verify at L = 4, 6, 8 that R is a CSS isomorphism and that it permutes the 2L logicals of a sheet. The sheets are copies of one code with a pairing fixed by the lattice, and the standard transversal CNOT between copies of a CSS code applies to any two sheets. One CNOT layer on R-paired qubits gives 2L logical CNOTs. Under noise, decoding the two sheets separately fails on the target sheet, with an apparent threshold near 0.3%, because the CNOT copies the control sheet's residual errors onto the target. A feed-forward decoder that propagates the decoded control errors through R restores suppression with L, with a crossing near 0.8% against the memory's 1.1%; with exact knowledge of the control errors the memory value is recovered. We also count the atoms used by the cross-sheet triangle-ribbon merge of the companion surgery paper: 3L/2 against 2L for a surface-code routing channel. We state what is not new. Each sheet is L rotated toric codes, so the memory is the toric code's. A transversal CNOT between copies of a CSS code is available to any stacked code, including surface-code patches on atom arrays. The sheet code adds a lattice-fixed pairing and the ribbon merge, not a throughput advantage; the pairing is not spatially local, since the distance between R-paired qubits grows as about 0.47L.
Author: Kulkarni, Raghavendra
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7164998858