Related papers: Quantum Error-Correcting Codes for Qudit Amplitude…
Quantum error correction protocols have been developed to offset the high sensitivity to noise inherent in quantum systems. However, much is still unknown about the behaviour of a quantum error-correcting code under general noise, including…
Quantum burst error correction codes (QBECCs) are of great importance to deal with the memory effect in quantum channels. As the most important family of QBECCs, quantum cyclic codes (QCCs) play a vital role in the correction of burst…
We show that quantum feedback control can be used as a quantum error correction process for errors induced by weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per…
We define and investigate a notion of entropy for quantum error correcting codes. The entropy of a code for a given quantum channel has a number of equivalent realisations, such as through the coefficients associated with the Knill-Laflamme…
Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC)…
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.…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
A protocol of quantum dense coding protection of two qubits is proposed in amplitude damping (AD) channel using weak measurement and reversal measurement. It is found that the capacity of quantum dense coding under the weak measurement and…
We discuss a method to construct quantum codes correcting amplitude damping errors via code concatenation. The inner codes are chosen as asymmetric Calderbank-Shor-Steane (CSS) codes. By concatenating with outer codes correcting symmetric…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
The problem of recovering from qubit erasures has recently gained attention as erasures occur in many physical systems such as photonic systems, trapped ions, superconducting qubits and circuit quantum electrodynamics. While several…
Noise-biased qubits are a promising route toward significantly reducing the hardware overhead associated with quantum error correction. The squeezed cat code, a non-local encoding in phase space based on squeezed coherent states, is an…
Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we…
Fault-tolerant quantum error correction is a necessity for any quantum architecture destined to tackle interesting, large-scale problems. Its theoretical formalism has been well founded for nearly two decades. However, we still do not have…
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…
Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian…
In the era of noisy intermediate-scale quantum (NISQ) devices, the number of controllable hardware qubits is insufficient to implement quantum error correction (QEC). As an alternative, quantum error mitigation (QEM) can suppress errors in…
As quantum computing hardware steadily increases in qubit count and quality, one important question is how to allocate these resources to mitigate the effects of hardware noise. In a transitional era between noisy small-scale and fully…
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…