From Syndromes to Computation: A General Framework for Logical Operations in Quantum Error-Correcting Codes
quant-ph
Submitted: 2026-10-13
Updated: 2026-10-13
Comments: 29+19 pages
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Sources
- Algebra of Bivariate-Bicycle Surface Codes
- Entangling logical qubits without physical operations
- Quantum Lego Power-up: Designing Transversal Gates with Tensor Networks
- Non-Clifford and parallelizable fault-tolerant logical gates on constant and almost-constant rate homological quantum LDPC codes via higher symmetries
- Transversal non-Clifford gates for quantum LDPC codes on sheaves
- Quantum LDPC Codes with Transversal Non-Clifford Gates via Products of Algebraic Codes
- Beyond transversality: structure of Clifford circuits for CSS codes
- A Classification of Transversal Clifford Gates for Qubit Stabilizer Codes
- Hardware-tailored logical Clifford circuits for stabilizer codes
- Finding diagonal logical gates in CSS codes and circuits
- Quantum Rainbow Codes: Achieving Linear Rate, Growing Distance and Transversal Non-Clifford Gates with Generalised Colour Codes
- Copy-cup Gates in Tensor Products of Group Algebra Codes
- Asymptotically Good Quantum Codes with Transversal Non-Clifford Gates
- Quantum Codes with Transversal $CCZ$ Gates and Sublinear $Z$-Stabilizers
- A topological theory for qLDPC: non-Clifford gates and magic state fountain on homological product codes with constant rate and beyond the $N^{1/3}$ distance barrier
- Transversal non-Clifford gates on almost-good quantum LDPC and quantum locally testable codes
- Theory and Architecture of Syndrome-Resolved Logical Gates
- Qubit CSS codes with Universal Transversal Gates
- Quantum Logic Codes: Complete Transversal Logical Clifford Instruction Sets for High-Rate Stabilizer Quantum Error Correcting Codes
Related papers
- Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
- Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
- Polynomial-time classical and quantum simulation of quantum impurity models
- Incoherent Imaging with Spatially Structured Quantum Probes
- A quasiparticle-protected superconducting qubit
- Theory of quantum-enhanced interferometry with general Markovian light sources