相关论文: On Subsystem Codes Beating the Hamming or Singleto…
The weighted-Hamming metric generalizes the Hamming metric by assigning different weights to blocks of coordinates. It is well-suited for applications such as coding over independent parallel channels, each of which has a different level of…
Controlling operational errors and decoherence is one of the major challenges facing the field of quantum computation and other attempts to create specified many-particle entangled states. The field of quantum error correction has developed…
Inspired by holographic codes and tensor-network decoders, we introduce tensor-network stabilizer codes which come with a natural tensor-network decoder. These codes can correspond to any geometry, but, as a special case, we generalize…
In this paper motivated from subspace coding we introduce subspace-metric codes and subset-metric codes. These are coordinate-position independent pseudometrics and suitable for the folded codes. The half-Singleton upper bounds for linear…
Scalable realisation of quantum computing is reliant on the development of fault tolerant devices. Analysis of quantum error correction protocols typically considers incoherent noise models or noise-free syndrome measurements. While this is…
The syndrome decoding problem has been proposed as a computational hardness assumption for code based cryptosystem that are safe against quantum computing. The problem has been reduced to finding the codeword with the smallest non-zero…
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…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
The parameters of a nondegenerate quantum code must obey the Hamming bound. An important open problem in quantum coding theory is whether or not the parameters of a degenerate quantum code can violate this bound for nondegenerate quantum…
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
We prove by construction that the Bravyi-Poulin-Terhal bound on the spatial density of stabilizer codes does not generalize to stabilizer circuits. To do so, we construct a fault tolerant quantum computer with a coding rate above 5% and…
Executing a logical quantum circuit fault-tolerantly incurs a large spacetime overhead. Recent work has proposed and investigated phantom codes, defined by the property that every in-block logical $\mathrm{CNOT}$ circuit can be implemented…
The Gottesman-Kitaev-Preskill (GKP) error correcting code encodes a finite dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we…
We describe a general method for turning quantum circuits into sparse quantum subsystem codes. The idea is to turn each circuit element into a set of low-weight gauge generators that enforce the input-output relations of that circuit…
Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least $ 3 $ (thus one-error-correcting) for a fixed redundancy $ r $,…
We consider an approach to fault tolerant quantum computing based on a simple error detecting code operating as the substrate for a conventional surface code. We develop a customised decoder to process the information about the likely…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
We demonstrate propagation rules of subsystem code constructions by extending, shortening and combining given subsystem codes. Given an $[[n,k,r,d]]_q$ subsystem code, we drive new subsystem codes with parameters $[[n+1,k,r,\geq d]]_q$,…