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We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and…
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
We show that within any quantum stabilizer code there lurks a classical binary linear code with similar error-correcting capabilities, thereby demonstrating new connections between quantum codes and classical codes. Using this result --…
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…
Quantum entanglement is a unique criterion of the quantum realm and an essential tool to secure quantum communication. Ensuring high-fidelity entanglement has always been a challenging task owing to interaction with the hostile channel…
Understanding fault-tolerant properties of quantum circuits is important for the design of large-scale quantum information processors. In particular, simulating properties of encoded circuits is a crucial tool for investigating the…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
Encoding and decoding quantum information in a multipartite quantum system are indispensable for quantum error correction and also play crucial roles in multiparty tasks in distributed quantum information processing such as quantum secret…
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…
We introduce a construction for entanglement-assisted quantum error-correcting codes (EAQECCs) that saturates the classical Singleton bound with less shared entanglement than any known method for code rates below $ \frac{k}{n} = \frac{1}{3}…
We construct a theory of continuous-variable entanglement-assisted quantum error correction. We present an example of a continuous-variable entanglement-assisted code that corrects for an arbitrary single-mode error. We also show how to…
The states needed in a quantum computation are extremely affected by decoherence. Several methods have been proposed to control error spreading. They use two main tools: fault-tolerant constructions and concatenated quantum error correcting…
Construction of quantum codes and entanglement-assisted quantum codes with good parameters via classical codes is an important task for quantum computing and quantum information. In this paper, by a family of one-generator quasi-cyclic…
We investigate an efficient quantum error correction of a fully correlated noise. Suppose the noise is characterized by a quantum channel whose error operators take fully correlated forms given by $\sigma_x^{\otimes n}$, $\sigma_y^{\otimes…
Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error…
Quantum data is susceptible to decoherence induced by the environment and to errors in the hardware processing it. A future fault-tolerant quantum computer will use quantum error correction (QEC) to actively protect against both. In the…
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…
Decoding algorithms are essential to fault-tolerant quantum-computing architectures. In this perspective we explore decoding algorithms for the surface code; a prototypical quantum low-density parity-check code that underlies many of the…
The task of preserving entanglement against noises is of crucial importance for both quantum communication and quantum information transfer. To this aim, quantum error correction (QEC) codes may be employed to compensate, at least…
We outline a quantum convolutional coding technique for protecting a stream of classical bits and qubits. Our goal is to provide a framework for designing codes that approach the ``grandfather'' capacity of an entanglement-assisted quantum…