Related papers: Stabilizer formalism for generalized concatenated …
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 propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code;…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
The stabilizer formalism is a scheme, generalizing well-known techniques developed by Gottesman [quant-ph/9705052] in the case of qubits, to efficiently simulate a class of transformations ("stabilizer circuits", which include the quantum…
In this work, we introduce a technique for reducing the length of a quantum stabilizer code, and we call this deflation of the code. Deflation can be seen as a generalization of the well-known puncturing and shortening techniques in cases…
Large-scale quantum computation is likely to require massive quantum error correction (QEC). QEC codes and circuits are described via the stabilizer formalism, which represents stabilizer states by keeping track of the operators that…
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…
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…
We introduce a framework for entanglement-assisted quantum error correcting codes that unifies the three original frameworks for such codes called EAQEC, EAOQEC, and EACQ under a single umbrella. The unification is arrived at by viewing…
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…
In the previous research by Grassl, Huber and Winter, they proved a theorem which can make entanglement-assisted quantum error-correcting codes (EAQECC) from general quantum error-correcting codes (QECC). In this paper, we prove that the…
There is a connection between classical codes, highly entangled pure states (called k-uniform or absolutely maximally entangled (AME) states), and quantum error correcting codes (QECCs). This leads to a systematic method to construct…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Quantum computing is an emerging technology that has the potential to achieve exponential speedups over their classical counterparts. To achieve quantum advantage, quantum principles are being applied to fields such as communications,…
Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve…
Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given there are several bosonic codes and…
In this paper, we introduce a unified framework to construct entanglement-assisted quantum error-correcting codes, including additive and nonadditive codes, based on the codeword stabilized framework on subsystems. The codeword stabilized…
In quantum coding theory, stabilizer codes are probably the most important class of quantum codes. They are regarded as the quantum analogue of the classical linear codes and the properties of stabilizer codes have been carefully studied in…
Protection of quantum information from noise is a massive challenge. One avenue people have begun to explore is reducing the number of particles needing to be protected from noise and instead use systems with more states, so called qudit…
A generalization of the stabilizer code construction presented by Gottesman is described, which allows for the construction of quantum error-correcting codes for continuous-variable systems. This formalism describes all continuous-variable…