Related papers: Low-overhead quantum error correction codes with a…
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…
The five-qubit quantum error correcting code encodes one logical qubit to five physical qubits, and protects the code from a single error. It was one of the first quantum codes to be invented, and various encoding circuits have been…
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…
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 error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…
The realization of quantum error correction is an essential ingredient for reaching the full potential of fault-tolerant universal quantum computation. Using a range of different schemes, logical qubits can be redundantly encoded in a set…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Multi-valued quantum systems can store more information than binary ones for a given number of quantum states. For reliable operation of multi-valued quantum systems, error correction is mandated. In this paper, we propose a 5-qutrit…
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…
Experimental realization of stabilizer-based quantum error correction (QEC) codes that would yield superior logical qubit performance is one of the formidable task for state-of-the-art quantum processors. A major obstacle towards realizing…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…
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 error correction is an essential ingredient for universal quantum computing. Despite tremendous experimental efforts in the study of quantum error correction, to date, there has been no demonstration in the realisation of universal…
Active quantum error correction using qubit stabilizer codes has emerged as a promising, but experimentally challenging, engineering program for building a universal quantum computer. In this review we consider the formalism of qubit…
Quantum error correction (QEC) is crucial for ensuring the reliability of quantum computers. However, implementing QEC often requires a significant number of qubits, leading to substantial overhead. One of the major challenges in quantum…
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder…
Quantum error correction (QEC) is considered a deciding component in enabling practical quantum computing. Stabilizer codes, and in particular topological surface codes, are promising candidates for implementing QEC by redundantly encoding…
The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum…