Related papers: An Introduction to Topological Quantum Codes
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are LDPC codes with linear rate and distance $n^\epsilon$. Their rate is evaluated via Euler characteristic…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
We present a general formalism for quantum error-correcting codes that encode both classical and quantum information (the EACQ formalism). This formalism unifies the entanglement-assisted formalism and classical error correction, and…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
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…
We generalize the construction of quantum error-correcting codes from GF(4)-linear codes by Calderbank et al. to p^m-state systems. Then we show how to determine the error from a syndrome. Finally we discuss a systematic construction of…
This Letter discusses topological quantum computation with gapped boundaries of two-dimensional topological phases. Systematic methods are presented to encode quantum information topologically using gapped boundaries, and to perform…
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 present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated…
A general theory of quantum error avoiding codes is established, and new light is shed on the relation between quantum error avoiding and correcting codes. Quantum error avoiding codes are found to be a special type of highly degenerate…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Elementary review article on quantum cryptography.
This is an essay review of the book by D. Home: "Conceptual Foundations of Quantum Physics: An Overview from Modern Perspectives" (New York: Plenum Press, 1997), xvii+386 pp., ISBN 0-306-45660-5.
Quantum computation is a subject of much theoretical promise, but has not been realized in large scale, despite the discovery of fault-tolerant procedures to overcome decoherence. Part of the reason is that the theoretically modest…
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…
Quantum error correction plays an important role in fault-tolerant quantum information processing. It is usually difficult to experimentally realize quantum error correction, as it requires multiple qubits and quantum gates with high…
The following open problems, which concern a fundamental limit on coding properties of quantum codes with realistic physical constraints, are analyzed and partially answered here: (a) the upper bound on code distances of quantum…
Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their groundspaces. More…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…