Related papers: On Quantum Weight Reduction
Random classical linear codes are widely believed to be hard to decode. While slightly sub-exponential time algorithms exist when the coding rate vanishes sufficiently rapidly, all known algorithms at constant rate require exponential time.…
Fault tolerance in quantum protocols requires contributions from error-correcting codes and their suitable decoders. Quantum Low-Density Parity Check (QLDPC) codes are one of the most explored quantum codes that have good coding rate and…
We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to…
To make practical quantum algorithms work, large-scale quantum processors protected by error-correcting codes are required to resist noise and ensure reliable computational outcomes. However, a major challenge arises from defects in…
We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes,…
Classical low-density parity-check (LDPC) codes are a widely deployed and well-established technology, forming the backbone of modern communication and storage systems. It is well known that, in this classical setting, increasing the girth…
We present a framework for minimizing costs in constant weight codes while maintaining a certain amount of differentiable codewords. Our calculations are based on a combinatorial view of constant weight codes and relay on simple…
We give a construction of quantum LDPC codes of dimension $\Theta(\log N)$ and distance $\Theta(N/\log N)$ as the code length $N\to\infty$. Using a product of chain complexes this construction also provides a family of quantum LDPC codes of…
Quantum computation holds the promise of solving certain complex problems exponentially faster than classical computers. However, the high prevalent noise in current quantum devices impedes the accurate execution of even basic algorithms.…
Quantum convolutional code was introduced recently as an alternative way to protect vital quantum information. To complete the analysis of quantum convolutional code, I report a way to decode certain quantum convolutional codes based on the…
Having protected quantum information is essential to perform quantum computations. One possibility is to reduce the number of particles needing to be protected from noise and instead use systems with more states, so called qudit quantum…
Quantum error correction is the building block for constructing fault-tolerant quantum processors that can operate reliably even if its constituting elements are corrupted by decoherence. In this context, real-time decoding is a necessity…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
This paper presents novel techniques for improving the error correction performance and reducing the complexity of coarsely quantized 5G-LDPC decoders. The proposed decoder design supports arbitrary message-passing schedules on a…
Quantum error-correcting codes protect fragile quantum information by encoding it redundantly, but identifying codes that perform well in practice with minimal overhead remains difficult due to the combinatorial search space and the high…
We address the task of verifying whether a quantum computer, designed to be protected by a specific stabilizer code, correctly encodes the corresponding logical qubits. To achieve this, we develop a general framework for subspace…
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…
Quantum error correction (QEC) is critical for practical realization of fault-tolerant quantum computing, and recently proposed families of quantum low-density parity-check (QLDPC) code are prime candidates for advanced QEC hardware…
Quantum error correction (QEC) is crucial for ensuring the reliability of quantum computers. However, implementing QEC often requires a significant number of qubits, leading to substantial overhead. One of the major challenges in quantum…
Quantum low density parity check (qLDPC) codes are an attractive alternative to the surface code due to their relatively high code rate and distance. However, unlike the surface code which has simple, geometrically local, stabilizer checks,…