Related papers: Quantum Error Correcting Codes Using Qudit Graph S…
Entangled qubit can increase the capacity of quantum error correcting codes based on stabilizer codes. In addition, by using entanglement quantum stabilizer codes can be construct from classical linear codes that do not satisfy the…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
With the advent of physical qubits exhibiting strong noise bias, it becomes increasingly relevant to identify which quantum gates can be efficiently implemented on error-correcting codes designed to address a single dominant error type.…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a…
We show that the Quantum State Distinguishability (QSD), which is a QSZK-complete problem, and the Quantum Circuit Distinguishability (QCD), which is a QIP-complete problem, can be solved by the verifier who can perform only single-qubit…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
In this work, we develop an efficient decoding method for graph codes, a class of stabilizer quantum error-correcting codes constructed from graph states. While optimal decoding is generally NP-hard, we propose a faster decoder exploiting…
Graph states are a family of stabilizer states which can be tailored towards various applications in photonic quantum computing and quantum communication. In this paper, we present a modular design based on quantum dot emitters coupled to a…
The hypergraph product (HGP) construction of quantum error-correcting codes (QECC) offers a general and explicit method for building a QECC from two classical codes, thereby paving the way for the discovery of good quantum low-density…
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…
In the absence of fault tolerant quantum error correction for analog, Hamiltonian quantum computation, error suppression via energy penalties is an effective alternative. We construct families of distance-$2$ stabilizer subsystem codes we…
Quantum error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols.…
For every stabiliser $N$-qudit absolutely maximally entangled state, we present a method for determining the stabiliser generators and logical operators of a corresponding quantum error correction code. These codes encode $k$ qudits into…
We construct explicitly two infinite families of genuine nonadditive 1-error correcting quantum codes and prove that their coding subspaces are 50% larger than those of the optimal stabilizer codes of the same parameters via the linear…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
We propose to construct large quantum graph codes by means of superconducting circuits working at the ultrastrong coupling regime. In this physical scenario, we are able to create a cluster state between any pair of qubits within a fraction…
Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…
This is a short review on an interdisciplinary field of quantum information science and statistical mechanics. We first give a pedagogical introduction to the stabilizer formalism, which is an efficient way to describe an important class of…