2,587 research outputs found

    Constructions and Noise Threshold of Hyperbolic Surface Codes

    Full text link
    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 rate versus protection is more favorable than for the surface code. These surface codes would require variable length connections between qubits, as determined by the hyperbolic geometry. We provide numerical estimates of the value of the noise threshold and logical error probability of these codes against independent X or Z noise, assuming noise-free error correction

    The Small Stellated Dodecahedron Code and Friends

    Get PDF
    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 stellated dodecahedron code can be located on the edges resp. vertices of a small stellated dodecahedron, making this code suitable for 3D connectivity. This code encodes 8 logical qubits into 30 physical qubits (plus 22 ancilla qubits for parity check measurements) as compared to 1 logical qubit into 9 physical qubits (plus 8 ancilla qubits) for the surface code. We develop fault-tolerant parity check circuits and a decoder for this code, allowing us to numerically assess the circuit-based pseudo-threshold.Comment: 19 pages, 14 figures, comments welcome! v2 includes updates which conforms with the journal versio

    Single-Shot Decoding of Linear Rate LDPC Quantum Codes With High Performance

    Get PDF
    We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, distance scaling as nϵ for ϵ>0 and efficient decoding schemes. The code family is based on tessellations of closed, four-dimensional, hyperbolic manifolds, as first suggested by Guth and Lubotzky. The main contribution of this work is the construction of suitable manifolds via finite presentations of Coxeter groups, their linear representations over Galois fields and topological coverings. We establish a lower bound on the encoding rate k/n of 13/72=0.180… and we show that the bound is tight for the examples that we construct. Numerical simulations give evidence that parallelizable decoding schemes of low computational complexity suffice to obtain high performance. These decoding schemes can deal with syndrome noise, so that parity check measurements do not have to be repeated to decode. Our data is consistent with a threshold of around 4% in the phenomenological noise model with syndrome noise in the single-shot regime

    Quantum Low-Density Parity-Check Codes

    Get PDF
    Quantum error correction is an indispensable ingredient for scalable quantum computing. In this Perspective we discuss a particular class of quantum codes called “quantum low-density parity-check (LDPC) codes.” The codes we discuss are alternatives to the surface code, which is currently the leading candidate to implement quantum fault tolerance. We introduce the zoo of quantum LDPC codes and discuss their potential for making quantum computers robust with regard to noise. In particular, we explain recent advances in the theory of quantum LDPC codes related to certain product constructions and discuss open problems in the field
    • …
    corecore