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Quantum error correction is essential for realizing scalable quantum computation. Among various approaches, low-density parity-check codes over higher-order Galois fields have shown promising performance due to their structured sparsity and…
We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…
This is an expository article aiming to introduce the reader to the underlying mathematics and geometry of quantum error correction. Information stored on quantum particles is subject to noise and interference from the environment. Quantum…
Leveraging quantum effects in metrology such as entanglement and coherence allows one to measure parameters with enhanced sensitivity. However, time-dependent noise can disrupt such Heisenberg-limited amplification. We propose a…
High-dimensional Hilbert spaces possess large information encoding and transmission capabilities. Characterizing exactly the real potential of high-dimensional entangled systems is a cornerstone of tomography and quantum imaging. The…
Self-calibrating quantum state tomography aims at reconstructing the unknown quantum state and certain properties of the measurement devices from the same data. Since the estimates of the state and device parameters come from the same data,…
It has been known that quantum error correction via concatenated codes can be done with exponentially small failure rate if the error rate for physical qubits is below a certain accuracy threshold. Other, unconcatenated codes with their own…
I. This paper is devoted to the problem of error detection with quantum codes. In the first part we examine possible problem settings for quantum error detection. Our goal is to derive a functional that describes the probability of…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the…
The field of quantum computing has experienced a rapid expansion in recent years, with ongoing exploration of new technologies, a decrease in error rates, and a growth in the number of qubits available in quantum processors. However,…
High-rate and large-distance quantum codes are expected to make fault-tolerant quantum computing more efficient, but most of them lack efficient fault-tolerant encoded-state preparation methods. We propose such a fault-tolerant encoder for…
Color codes are a leading class of topological quantum error-correcting codes with modest error thresholds and structural compatibility with two-dimensional architectures, which make them well-suited for fault-tolerant quantum computing…
High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical…
Convexity properties of error rates of a class of decoders, including the ML/min-distance one as a special case, are studied for arbitrary constellations, bit mapping and coding. Earlier results obtained for the AWGN channel are extended to…
The surface code is one the most promising alternatives for implementing fault-tolerant, large-scale quantum information processing. Its high threshold for single-qubit errors under stochastic noise is one of its most attrative features. We…
A quantum error correction code is assessed over its ability to correct errors in noisy quantum circuits. This task requires extensive simulations of faulty quantum circuits, which are often made tractable by considering stochastic Pauli…
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,…
Quantum computers face significant challenges from quantum deviations or coherent noise, particularly during gate operations, which pose a complex threat to the efficacy of quantum error correction (QEC) protocols. In this study, we…
The Hamiltonian model of quantum error correction code in the literature is often constructed with the help of its stabilizer formalism. But there have been many known examples of nonadditive codes which are beyond the standard quantum…