Related papers: Generalized toric codes on twisted tori for quantu…
Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter. We explore geometry to enhance the performance of topological quantum codes by rotating the four dimensional…
Given their potential for fault-tolerant operations, topological quantum states are currently the focus of intense activity. Of particular interest are topological quantum error correction codes, such as the surface and planar stabilizer…
We present a three-dimensional generalization of a renormalization group decoding algorithm for topological codes with Abelian anyonic excitations that we previously introduced for two dimensions. This 3D implementation extends our previous…
We suggest several techniques to improve the toric codes and the finite-rate generalized toric codes (quantum hypergraph-product codes) recently introduced by Tillich and Z\'emor. For the usual toric codes, we introduce the rotated lattices…
Qudit toric codes are a natural higher-dimensional generalization of the well-studied qubit toric code. However standard methods for error correction of the qubit toric code are not applicable to them. Novel decoders are needed. In this…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Three-dimensional (3D) topological codes offer the advantage of supporting fault-tolerant implementations of non-Clifford gates, yet their performance against realistic noise remains largely unexplored. In this work, we focus on the…
Although it is well known that all quantum states can be produced by single qubit measurements on the cluster states, it is not a simple task to explicitly find which measurement patterns on the cluster states can generate different quantum…
We propose a unifying paradigm for analyzing and constructing topological quantum error correcting codes as dynamical circuits of geometrically local channels and measurements. To this end, we relate such circuits to discrete fixed-point…
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
Topological quantum error correction codes are currently among the most promising candidates for efficiently dealing with the decoherence effects inherently present in quantum devices. Numerically, their theoretical error threshold can be…
Since the long range entanglement is a universal characteristic of topological quantum states belonging to the same class, a suitable mathematical representation of the long range entanglement has to be also universal. In this Letter, we…
To date, a great deal of attention has focused on characterizing the performance of quantum error correcting codes via their thresholds, the maximum correctable physical error rate for a given noise model and decoding strategy. Practical…
Quasi-twisted (QT) codes generalize several important families of linear codes, including cyclic, constacyclic, and quasi-cyclic codes. Despite their potential, to the best of our knowledge, there exists no efficient decoding algorithm for…
This work explores a deformation of the Kitaev toric code that induces a phase transition out of the topologically ordered phase. By placing the model on a cylinder, the bulk global 1-form symmetries separate into distinct boundary…
We study the robustness of a generalized Kitaev's toric code with Z_N degrees of freedom in the presence of local perturbations. For N=2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis…
Toric varieties and their associated toric codes, as well as determination of their parameters with intersection theory, are presented in the two dimensional case. Linear Secret Sharing Schemes with strong multiplication are constructed…
We examine the performance of the single-mode GKP code and its concatenation with the toric code for a noise model of Gaussian shifts, or displacement errors. We show how one can optimize the tracking of errors in repeated noisy error…
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…