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The design of decoding algorithms is a significant technological component in the development of fault-tolerant quantum computers. Often design of quantum decoders is inspired by classical decoding algorithms, but there are no general…
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 machine learning (QML) has emerged as a promising direction in the noisy intermediate-scale quantum (NISQ) era, offering computational and memory advantages by harnessing superposition and entanglement. However, QML models often…
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…
A quantum error correcting protocol can be substantially improved by taking into account features of the physical noise process. We present an efficient decoder for the surface code which can account for general noise features, including…
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…
In Optical Coherence Tomography (OCT), speckle noise significantly hampers image quality, affecting diagnostic accuracy. Current methods, including traditional filtering and deep learning techniques, have limitations in noise reduction and…
Byte-based machine translation systems have shown significant potential in massively multilingual settings. Unicode encoding, which maps each character to specific byte(s), eliminates the emergence of unknown words, even in new languages.…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Topological quantum codes, such as toric and surface codes, are excellent candidates for hardware implementation due to their robustness against errors and their local interactions between qubits. However, decoding these codes efficiently…
Neural decoders for quantum error correction (QEC) rely on neural networks to classify syndromes extracted from error correction codes and find appropriate recovery operators to protect logical information against errors. Its ability to…
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…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
Qubit loss is a major source of error in quantum computation, as it invalidates the algebraic structure of the standard stabilizer formalism for quantum error-correcting codes. On the one hand, it complicates decoding; on the other hand, it…
Quantum error correction is one of the fundamental building blocks of digital quantum computation. The Quantum Lego formalism has introduced a systematic way of constructing new stabilizer codes out of basic lego-like building blocks, which…
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…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
Unifying multimodal understanding, generation and reconstruction representation in a single tokenizer remains a key challenge in building unified models. Previous research predominantly attempts to address this in a dual encoder paradigm,…
In this article we address the computational hardness of optimally decoding a quantum stabilizer code. Much like classical linear codes, errors are detected by measuring certain check operators which yield an error syndrome, and the…
Quantum error-correcting codes aim to protect information in quantum systems to enable fault-tolerant quantum computations. The most prevalent method, stabilizer codes, has been well developed for many varieties of systems, however, largely…