Related papers: Nested Quantum Error Correction Codes
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of quantum error correction based on encoding…
I report two general methods to construct quantum convolutional codes for $N$-state quantum systems. Using these general methods, I construct a quantum convolutional code of rate 1/4, which can correct one quantum error for every eight…
We describe the theory of quantum convolutional error correcting codes. These codes are aimed at protecting a flow of quantum information over long distance communication. They are largely inspired by their classical analogs which are used…
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.…
The goal of this paper is to review the theoretical basis for achieving a faithful quantum information transmission and processing in the presence of noise. Initially encoding and decoding, implementing gates and quantum error correction…
Quantum error correcting codes (QECC) is becoming an increasingly important branch of coding theory. For classical block codes, a \href{codetables.de} {comprehensive database of best known codes} exists which is available online at…
In the early years of fault-tolerant quantum computing (FTQC), it is expected that the available code distance and the number of magic states will be restricted due to the limited scalability of quantum devices and the insufficient…
Recent progress in quantum computing has enabled systems with tens of reliable logical qubits, built from thousands of noisy physical qubits. However, many impactful applications demand quantum computations with millions of logical qubits,…
Fault tolerant quantum computing methods which work with efficient quantum error correcting codes are discussed. Several new techniques are introduced to restrict accumulation of errors before or during the recovery. Classes of eligible…
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have…
This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed.…
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…
Quantum error correction is capable of digitizing quantum noise and increasing the robustness of qubits. Typically, error correction is designed with the target of eliminating all errors - making an error so unlikely it can be assumed that…
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 recently introduced detected-jump correcting quantum codes are capable of stabilizing qubit-systems against spontaneous decay processes arising from couplings to statistically independent reservoirs. These embedded quantum codes exploit…
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,…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Though the theory of quantum error correction is intimately related to the classical coding theory, in particular, one can construct quantum error correction codes (QECCs) from classical codes with the dual containing property, this does…
Quantum computers require error correction to achieve universal quantum computing. However, current decoding of quantum error-correcting codes relies on classical computation, which is slower than quantum operations in superconducting…