Related papers: Entanglement-Assisted Quantum Error-Correcting Cod…
We show how entanglement-assisted codes can be constructed from arbitrary quantum codes by associating them with quantum codes for erasure channels. If a subset of physical qubits is correctable for an erasure error, then it naturally forms…
We prove that the known formulae for computing the optimal number of maximally entangled pairs required for entanglement-assisted quantum error-correcting codes (EAQECCs) over the binary field hold for codes over arbitrary finite fields as…
Entanglement-assisted quantum error-correcting codes (EAQECCs) make use of preexisting entanglement between the sender and receiver to boost the rate of transmission. It is possible to construct an EAQECC from any classical linear code,…
This is the chapter \emph{Topological Codes} of the book \emph{Quantum Error Correction}, edited by Daniel A. Lidar and Todd A. Brun, Cambridge University Press, New York, 2013.…
We present a universal framework for quantum error-correcting codes, i.e., the one that applies for the most general quantum error-correcting codes. This framework is established on the group algebra, an algebraic notation for the nice…
We provide several formulas that determine the optimal number of entangled bits (ebits) that a general entanglement-assisted quantum code requires. Our first theorem gives a formula that applies to an arbitrary entanglement-assisted block…
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…
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…
A quantum error-correcting code is defined to be a unitary mapping (encoding) of k qubits (2-state quantum systems) into a subspace of the quantum state space of n qubits such that if any t of the qubits undergo arbitrary decoherence, not…
Proposals for quantum computing devices are many and varied. They each have unique noise processes that make none of them fully reliable at this time. There are several error correction/avoidance techniques which are valuable for reducing…
The theory of entanglement-assisted quantum error-correcting codes (EAQECCs) is a generalization of the standard stabilizer quantum error-correcting codes, which can be possibly constructed from any classical codes by relaxing the duality…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
Experimental realization of automated error correction is demonstrated through IBM Quantum Experience for Bell and GHZ states using a measurement based approach upon ancilla qubits. The measurement automatically activates error correcting…
Entanglement-assisted quantum error correcting codes (EAQECCs) play a significant role in protecting quantum information from decoherence and quantum noise. Recently, constructing entanglement-assisted quantum maximum distance separable…
A quantum error correcting code is a subspace $\mathcal{C}$ such that allowed errors acting on any state in $\mathcal{C}$ can be corrected. A quantum code for which state recovery is only required up to a logical rotation within…
I give an overview of the basic concepts behind quantum error correction and quantum fault tolerance. This includes the quantum error correction conditions, stabilizer codes, CSS codes, transversal gates, fault-tolerant error correction,…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…