Related papers: Analysis of quantum error correction with symmetri…
Graph states, which include for example Bell states, GHZ states and cluster states, form a well-known class of quantum states with applications ranging from quantum networks to error-correction. Deciding whether two graph states are…
Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of the qubits can…
A universal set of quantum gates is constructed for the recently developed jump-error correcting quantum codes. These quantum codes are capable of correcting errors arising from the spontaneous decay of distinguishable qubits into…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
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…
Several entanglement measures are used to define equivalence classes in the set of hypergraph states of three qubits. Our classifications reveal that (i) under local unitary transformations, hypergraph states of three qubits are split into…
Graph states provide a powerful framework for describing multipartite entanglement in quantum information science. In their standard formulation, graph states are generated by controlled-$Z$ interactions and naturally encode symmetric…
We investigate the performance of a quantum error-correcting code when pushed beyond its intended capacity to protect information against errors, presenting formulae for the probability of failure when the errors affect more qudits than…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
In this paper an extended scalability condition is proposed to achieve the ground-state stability for a class of multipartite quantum systems which may involve two-body interactions, and an explicit procedure to construct the dissipation…
The possibility of using the two-fold topological degeneracy of spin-1/2 chiral spin liquid states on the torus to construct quantum error correcting codes is investigated. It is shown that codes constructed using these states on finite…
By using highly entangled states, quantum metrology guarantees precision impossible with classical measurements. Unfortunately such states can be very susceptible to noise, and it is a great challenge of the field to maintain quantum…
Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum (NISQ) devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum…
Hypergraph states as real equally weighted pure states are important resources for quantum codes of non-local stabilizer. Using local Pauli equivalence and permutational symmetry, we reduce the 32768 four qubit real equally weighted pure…
In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…
Homomorphic quantum error correction aims to protect quantum data against both unauthorized access and environmental noise during server-based processing. We investigate the algebraic compatibility between quantum homomorphic encryption and…
Given an $m-$qubit $\Phi_0$ and an $(n,m)-$quantum code $\mathcal{C}$, let $\Phi$ be the $n-$qubit that results from the $\mathcal{C}-$encoding of $\Phi_0$. Suppose that the state $\Phi$ is affected by an isotropic error (decoherence),…
The discovery of holographic codes established a surprising connection between quantum error correction and the anti-de Sitter-conformal field theory correspondence. Recent technological progress in artificial quantum systems renders the…
We present an approach to one-way quantum computation (1WQC) that can compensate for single-qubit errors, by encoding the logical information residing on physical qubits into five-qubit error-correcting code states. A logical two-qubit…
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…