We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, …
We introduce quantum pin codes: a class of quantum CSS codes. Quantum pin codes are a vast generalization of quantum color codes and Reed-Muller codes. A lot of the structure and properties of color codes carries over to pin codes. Pin codes have …
We explore a distance-3 homological CSS quantum code, namely the small stellated dodecahedron code, for dense storage of quantum information and we compare its performance with the distance-3 surface code. The data and ancilla qubits of the small …
We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of for the -hyperbolic surface code in a phenomenological noise model (as compared with for the toric …
We show how to obtain concrete constructions of homological quantum codes based on tilings of 2D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in two-dimensional quantum codes whose tradeoff of encoding …