ConstantOverhead Quantum Error Correction with Thin Planar Connectivity
Abstract
Quantum low density parity check (LDPC) codes may provide a path to build lowoverhead faulttolerant quantum computers. However, as general LDPC codes lack geometric constraints, naïve layouts couple many distant qubits with crossing connections which could be hard to build in hardware and could result in performancedegrading crosstalk. We propose a 2D layout for quantum LDPC codes by decomposing their Tanner graphs into a small number of planar layers. Each layer contains longrange connections which do not cross. For any CalderbankShorSteane code with a degreeδ Tanner graph, we design stabilizer measurement circuits with depth at most (2 δ +2 ) using at most ⌈δ /2 ⌉ layers. We observe a circuitnoise threshold of 0.28% for a positiverate code family using 49 physical qubits per logical qubit. For a physical error rate of 10^{4}, this family reaches a logical error rate of 10^{15} using fourteen times fewer physical qubits than the surface code.
 Publication:

Physical Review Letters
 Pub Date:
 July 2022
 DOI:
 10.1103/PhysRevLett.129.050504
 arXiv:
 arXiv:2109.14609
 Bibcode:
 2022PhRvL.129e0504T
 Keywords:

 Quantum Physics;
 Computer Science  Information Theory
 EPrint:
 7 pages, 4 figures