Related papers: Calderbank-Steane-Shor Holographic Quantum Error C…
The construction of a quantum computer remains a fundamental scientific and technological challenge, in particular due to unavoidable noise. Quantum states and operations can be protected from errors using protocols for fault-tolerant…
Steane's seven-qubit quantum code is a natural choice for fault-tolerance experiments because it is small and just two extra qubits are enough to correct errors. However, the two-qubit error-correction technique, known as "flagged" syndrome…
We consider a class of holographic tensor networks that are efficiently contractible variational ansatze, manifestly (approximate) quantum error correction codes, and can support power-law correlation functions. In the case when the network…
After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
Steganography is an information hiding application which aims to hide secret data imperceptibly into a commonly used media. Unfortunately, the theoretical hiding asymptotical capacity of steganographic systems is not attained by algorithms…
We propose a decoder for the correction of erasures with hypergraph product codes, which form one of the most popular families of quantum LDPC codes. Our numerical simulations show that this decoder provides a close approximation of the…
Self-orthogonal codes have received great attention due to their important applications in quantum codes, LCD codes and lattices. Recently, several families of self-orthogonal codes containing the all-$1$ vector were constructed by…
A classical coding across a block of logical qubits is presented. We characterize subgroups of the product stabilizer group on a block of logical qubits corresponding to dual codes of classical error correcting codes. We prove conditions on…
We solve the fundamental quantum error correction problem for bi-unitary channels on two-qubit Hilbert space. By solving an algebraic compression problem, we construct qubit codes for such channels on arbitrary dimension Hilbert space, and…
Holographic quantum error-correcting codes have been proposed as toy models that describe key aspects of the AdS/CFT correspondence. In this work, we introduce a versatile framework of Majorana dimers capturing the intersection of…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
Quantum error-correcting codes with high encoding rate are good candidates for large-scale quantum computers as they use physical qubits more efficiently than codes of the same distance that encode only a few logical qubits. Some logical…
We investigate the usage of highly efficient error correcting codes of multilevel systems to protect encoded quantum information from erasure errors and implementation to repetitively correct these errors. Our scheme makes use of quantum…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of…
Quantum error correction (QEC) is essential for fault-tolerant quantum computation. Often in QEC errors are assumed to be independent and identically distributed and can be discretised to a random Pauli error during the execution of a…
A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing…
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)…
Zero-knowledge codes, introduced by Decatur, Goldreich, and Ron (ePrint 1997), are error-correcting codes in which few codeword symbols reveal no information about the encoded message, and have been extensively used in cryptographic…