Related papers: Quantum Error Correction near the Coding Theoretic…
Noise is one of the central obstacles to building useful quantum computers, and quantum error correction (QEC) provides the framework for protecting quantum information against it. Unlike classical error correction, QEC must preserve…
Efficient and high-performance quantum error correction is essential for achieving fault-tolerant quantum computing. Low-depth random circuits offer a promising approach to identifying effective and practical encoding strategies. In this…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
With the development of quantum error correction techniques, quantum low density parity check (QLDPC) codes become a promising area in quantum error correction codes. In this paper, the requirements of QLDPC codes based on points except the…
Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance. A natural question concerns the efficient decodability of these codes. In this paper, we present a linear…
Practical quantum computing will require error rates that are well below what is achievable with physical qubits. Quantum error correction offers a path to algorithmically-relevant error rates by encoding logical qubits within many physical…
Fault-tolerant quantum computing demands many qubits with long lifetimes to conduct accurate quantum gate operations. However, external noise limits the computing time of physical qubits. Quantum error correction codes may extend such…
The quantum computing devices of today have tens to hundreds of qubits that are highly susceptible to noise due to unwanted interactions with their environment. The theory of quantum error correction provides a scheme by which the effects…
Recent progress in quantum cryptography and quantum computers has given hope to their imminent practical realization. An essential element at the heart of the application of these quantum systems is a quantum error correction scheme. We…
We present a fault-tolerant universal quantum computing architecture based on a code concatenation of biased-noise qubits and the parity architecture. The parity architecture can be understood as an LDPC code tailored specifically to obtain…
Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from…
We propose a fault-tolerant quantum computation scheme that is broadly applicable to quantum low-density parity-check (qLDPC) codes. The scheme achieves constant qubit overhead and a time overhead of $O(d^{a+o(1)})$ for any $[[n,k,d]]$…
Quantum error correction is necessary to perform large-scale quantum computation, but requires extremely large overheads in both space and time. High-rate quantum low-density-parity-check (qLDPC) codes promise a route to reduce qubit…
Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be…
In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated…
Quantum error correction protocols will play a central role in the realisation of quantum computing; the choice of error correction code will influence the full quantum computing stack, from the layout of qubits at the physical level to…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
We face the following dilemma for designing low-density parity-check codes (LDPC) for quantum error correction. 1) The row weights of parity-check should be large: The minimum distances are bounded above by the minimum row weights of…
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…