Institute for Quantum Information Seminar
Research in quantum error correction has been heavily dominated by just two classes of codes: concatenated and surface codes. Both code families can only encode a limited number of qubits per block and thus require huge redundancy for any useful quantum computation. I will discuss recently discovered quantum hypergraph-product codes (QHPCs) which generalize the surface codes but can encode many more qubits per block. Just like the surface codes, QHPCs have convenient planar representations, with each encoded qubit corresponding to a pair of topologically non-trivial patterned strings. The allowed patterns correspond to codewords of two classical binary codes which form the QHPC. Further, each of the quantum measurements needed for error correction can involve just a few qubits, these measurements can be done in parallel, and almost all errors affecting a finite fraction of qubits can be corrected.