TY - JOUR
T1 - Hyperbolic and semi-hyperbolic surface codes for quantum storage
AU - Breuckmann, Nikolas P.
AU - Vuillot, Christophe
AU - Campbell, Earl
AU - Krishna, Anirudh
AU - Terhal, Barbara M.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3%for the {4, 5}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9% for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the {4, 5}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.
AB - We show how a hyperbolic surface code could be used for overhead-efficient quantum storage. We give numerical evidence for a noise threshold of 1.3%for the {4, 5}-hyperbolic surface code in a phenomenological noise model (as compared with 2.9% for the toric code). In this code family, parity checks are of weight 4 and 5, while each qubit participates in four different parity checks. We introduce a family of semi-hyperbolic codes that interpolate between the toric code and the {4, 5}-hyperbolic surface code in terms of encoding rate and threshold. We show how these hyperbolic codes outperform the toric code in terms of qubit overhead for a target logical error probability. We show how Dehn twists and lattice code surgery can be used to read and write individual qubits to this quantum storage medium.
KW - quantum codes
KW - quantum error correction
KW - quantum fault-tolerance
UR - http://www.scopus.com/inward/record.url?scp=85047967362&partnerID=8YFLogxK
U2 - 10.1088/2058-9565/aa7d3b
DO - 10.1088/2058-9565/aa7d3b
M3 - Article
AN - SCOPUS:85047967362
SN - 2058-9565
VL - 2
JO - Quantum Science and Technology
JF - Quantum Science and Technology
IS - 3
M1 - 035007
ER -