5 papers
Theory of approximate quantum error correction and the error-set model
Dor Elimelech, Victor V. Albert, Alexander Barg
We develop a theory of approximate quantum error correction (QEC) based on the error-set model, complemented by general methods for code construction. Exact QEC has a powerful erro…
Breaking the bicycle frame: Coset-based quantum LDPC codes
Arda Aydin, Itzhak Tamo, Alexander Barg
Generalizing the construction of two-block group algebra (2BGA) codes, we introduce a family of two-block quantum LDPC codes constructed using the action of a group on the cosets o…
Asymptotically good bosonic Fock state codes
Dor Elimelech, Arda Aydin, Alexander Barg
We study the error-correction properties of multi-mode Fock-state codes under amplitude-damping (AD) noise, focusing on the asymptotic regime in which the total excitation of the c…
Quantum error correction beyond : spin, bosonic, and permutation-invariant codes from convex geometry
Arda Aydin, Victor V. Albert, Alexander Barg
We develop a framework for constructing quantum error-correcting codes and logical gates for three types of spaces -- composite permutation-invariant spaces of many qubits or qudit…
Targeted Clifford logical gates for hypergraph product codes
Adway Patra, Alexander Barg
Starting with an explicit framework for designing logical Clifford circuits for CSS codes, we construct logical gates for Hypergraph Product Codes. We first derive symplectic matri…