Related papers: Asymmetric Quantum Codes on Toric Surfaces
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
Algebraic-geometric codes on Garcia-Stichtenoth family of curves are used to construct the asymptotically good quantum codes.
Quantum computing holds transformative potential for various fields, yet its practical application is hindered by the susceptibility to errors. This study makes a pioneering contribution by applying quantum error correction codes (QECCs)…
The problem of finding quantum error-correcting codes is transformed into the problem of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product. Many new codes and new bounds are…
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 construct a family of quantum low-density parity-check codes locally equivalent to higher-dimensional quantum hypergraph-product (QHP) codes. Similarly to QHP codes, the proposed codes have highly redundant sets of low-weight stabilizer…
Quantum error correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of finite per-qubit error rate that have been proven for…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
Most of the research done on quantum error correction studies an error model in which each qubit is affected by noise, independently of the other qubits. In this paper we study a different noise model -- one in which the noise may be…
Quantum computers hold the promise of solving computational problems which are intractable using conventional methods. For fault-tolerant operation quantum computers must correct errors occurring due to unavoidable decoherence and limited…
We describe the popular BB84 protocol and critically examine its security proof as presented by Shor and Preskill. The proof requires the use of quantum error correcting codes called the Calderbank-Shor-Steanne (CSS) quantum codes. These…
Errors are inevitable during all kinds quantum informational tasks and quantum error-correcting codes (QECCs) are powerful tools to fight various quantum noises. For standard QECCs physical systems have the same number of energy levels.…
Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the…
Fault-tolerant quantum error correction requires the measurement of error syndromes in a way that minimizes correlated errors on the quantum data. Steane and Shor ancilla are two well-known methods for fault-tolerant syndrome extraction. In…
Surface codes$\unicode{x2014}$leading candidates for quantum error correction (QEC)$\unicode{x2014}$and entanglement phases$\unicode{x2014}$a key notion for many-body quantum dynamics$\unicode{x2014}$have heretofore been unrelated. Here, we…
Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [googlemachine,gambetta2015building], and several-hundred-qubit machines are around the corner.…
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…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…