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Surface codes are versatile quantum error-correcting codes known for their planar geometry, making them ideal for practical implementations. While the original proposal used Pauli $X$ or Pauli $Z$ operators in a square structure, these…
DNA storage has emerged as a promising solution for large-scale and long-term data preservation. Among various error types, insertions are the most frequent errors occurring in DNA sequences, where the inserted symbol is often identical or…
The unavoidable presence of noise is a crucial roadblock for the development of large-scale quantum computers and the ability to characterize quantum noise reliably and efficiently with high precision is essential to scale quantum…
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and quantum outputs. Although they demonstrated…
Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of…
The low coding rate of quantum stabilizer codes results in formidable physical qubit overhead when realizing quantum error correcting in engineering. In this letter, we propose a new class of hypergraph-product code called…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information…
We present a rate-compatible polar coding scheme that achieves the capacity of any family of channels. Our solution generalizes the previous results [1], [2] that provide capacity-achieving rate-compatible polar codes for a degraded family…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
Protecting information in systems that have more than two basis states (qudits) not only offers a promising route for reducing the number of individual quantum locations that must be protected, while more accurately reflecting the structure…
We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such…
We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how…
Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical…
This paper presents a coding scheme for an insertion deletion substitution channel. We extend a previous scheme for the deletion channel where polar codes are modified by adding "guard bands" between segments. In the new scheme, each guard…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Learning unknown processes affecting a quantum system reveals underlying physical mechanisms and enables suppression, mitigation, and correction of unwanted effects. Describing a general quantum process requires an exponentially large…
In some quantum computing architectures, Pauli noise is highly biased. Tailoring Quantum error-correcting codes to the biased noise may benefit reducing the physical qubit overhead without reducing the logical error rate. In this paper, we…
Quantum information is fragile and must be protected by a quantum error-correcting code for large-scale practical applications. Recently, highly efficient quantum codes have been discovered which require a high degree of spatial…
Quantum stabilizer codes (QSCs) suffer from a low quantum coding rate, since they have to recover the quantum bits (qubits) in the face of both bit-flip and phase-flip errors. In this treatise, we conceive a low-complexity concatenated…