Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
Year: 2026
Type: preprint
Abstract: We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1453181110, Track 4: Advanced CI Coordination Ecosystem: Monitoring and Measurement Services, G3317073709, G3562386289, Track 1: ACCESS Resource Allocations Marketplace and Platform Services (RAMPS), G4010157413, G4352653118, ACO: An Open CI Ecosystem to Advance Scientific Discovery (OpenCI), G470481161, Track 3: COre National Ecosystem for CyberinfrasTructure (CONECT), G5367127336, G5464919783, Category I: Bridging the Gap Between AI/ML Computing Demands and Today's Capabilities, Graduate Research Fellowship Program (GRFP), G7474180956, G776438391, Track 2: Customized Multi-tier Assistance, Training, and Computational Help (MATCH) for End User ACCESS to CI
OpenAlex ID: W7212281517