Related papers: Projecting 3D color codes onto 3D toric codes
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…
We prove several theorems characterizing the existence of homological error correction codes both classically and quantumly. Not every classical code is homological, but we find a family of classical homological codes saturating the Hamming…
We study the resources needed to construct topological 2D stabilizer codes as a way to estimate in part their efficiency and this leads us to perform a comparative study of surface codes and color codes. This study clarifies the…
Recent work on fault-tolerant quantum computation making use of topological error correction shows great potential, with the 2d surface code possessing a threshold error rate approaching 1% (NJoP 9:199, 2007), (arXiv:0905.0531). However,…
We study the protection of information in nearly critical topological quantum codes, constructed by perturbing topological stabilizer codes towards continuous quantum phase transitions. Our focus is on the transverse-field toric code…
We show that belief propagation combined with ordered statistics post-processing is a general decoder for quantum low density parity check codes constructed from the hypergraph product. To this end, we run numerical simulations of the…
Time-of-flight cameras provide depth information, which is complementary to the photometric appearance of the scene in ordinary images. It is desirable to merge the depth and colour information, in order to obtain a coherent scene…
Quantum error correction is essential for bridging the gap between the error rates of physical devices and the extremely low logical error rates required for quantum algorithms. Recent error-correction demonstrations on superconducting…
We investigate topological descriptors for 3D surface analysis, i.e. the classification of surfaces according to their geometric fine structure. On a dataset of high-resolution 3D surface reconstructions we compute persistence diagrams for…
In texture-plus-depth representation of a 3D scene, depth maps from different camera viewpoints are typically lossily compressed via the classical transform coding / coefficient quantization paradigm. In this paper we propose to reduce…
The color code model is a crucial instance of a Calderbank--Shor--Steane (CSS)-type topological quantum error-correcting code, which notably supports transversal implementation of the full Clifford group. Its robustness against local noise…
We study topological order in a toric code in three spatial dimensions, or a 3+1D Z_2 gauge theory, at finite temperature. We compute exactly the topological entropy of the system, and show that it drops, for any infinitesimal temperature,…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
The surface code scheme for quantum computation features a 2d array of nearest-neighbor coupled qubits yet claims a threshold error rate approaching 1% (NJoP 9:199, 2007). This result was obtained for the toric code, from which the surface…
A theory for constructing quantum error correcting codes from Toric surfaces by the Calderbank-Shor-Steane method is presented. In particular we study the method on toric Hirzebruch surfaces. The results are obtained by constructing a…
We establish and explore a new connection between quantum information theory and classical statistical mechanics by studying the problem of qubit losses in 2D topological color codes. We introduce a protocol to cope with qubit losses, which…
Color transfer is an image editing process that adjusts the colors of a picture to match a target picture's color theme. A natural color transfer not only matches the color styles but also prevents after-transfer artifacts due to image…
Quantum error correction (QEC) is crucial for realizing scalable quantum technologies, and topological quantum error correction (TQEC) has emerged as the most experimentally advanced paradigm of QEC. Existing homological and topological…