Related papers: Fault-tolerant quantum error correction using erro…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
Quantum error correction of a surface code or repetition code requires the pairwise matching of error events in a space-time graph of qubit measurements, such that the total weight of the matching is minimized. The input weights follow from…
I make a rough estimate of the accuracy threshold for fault tolerant quantum computing with concatenated codes. First I consider only gate errors and use the depolarizing channel error model. I will follow P.Shor (quant-ph/9505011) for…
Quantum Error Correction (QEC) is essential for fault-tolerant quantum copmutation, and its implementation is a very sophisticated process involving both quantum and classical hardware. Formulating and verifying the decomposition of logical…
Quantum error correction (QEC) is essential for realizing scalable quantum computation. However, when evaluating its benefits, most analyses assume idealized components, overlooking the imperfections inherent in realistic fault-tolerant…
Classical simulations of noisy stabilizer circuits are often used to estimate the threshold of a quantum error-correcting code. Physical noise sources are efficiently approximated by random insertions of Pauli operators. For a single qubit,…
In this paper, we utilize a concatenation scheme to construct new families of quantum error correction codes achieving the quantum Gilbert-Varshamov (GV) bound asymptotically. We concatenate alternant codes with any linear code achieving…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
Recently a framework for assisted quantum error correction was proposed in which a specific type of error is allowed to occur on auxiliary qubits, which is in contrast to standard entanglement assistance that requires noiseless auxiliary…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
We present a construction scheme for quantum error correcting codes. The basic ingredients are a graph and a finite abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph…
The performance of quantum error correction can be significantly improved if detailed information about the noise is available, allowing to optimize both codes and decoders. It has been proposed to estimate error rates from the syndrome…
Correcting errors is a vital but expensive component of fault tolerant quantum computation. Standard fault tolerant protocol assumes the implementation of error correction, via syndrome measurements and possible recovery operations, after…
Quantum error correction allows for faulty quantum systems to behave in an effectively error free manner. One important class of techniques for quantum error correction is the class of quantum subsystem codes, which are relevant both to…
A universal and fault tolerant scheme for quantum computation is proposed which utilizes a class of error correcting codes that is based on the detection of spontaneous emission (of, e.g., photons, phonons, and ripplons). The scheme is…
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…
The realization of quantum error correction protocols whose logical error rates are suppressed far below physical error rates relies on an intricate combination: the error-correcting code's efficiency, the syndrome extraction circuit's…
A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a…
One-way quantum repeaters where loss and operational errors are counteracted by quantum error correcting codes can ensure fast and reliable qubit transmission in quantum networks. It is crucial that the resource requirements of such…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…