Related papers: Towards Ultra-High-Rate Quantum Error Correction w…
We introduce heterogeneous quantum error-correcting codes composed of qubit types with distinct error channels and study their performance in the code-capacity regime using maximum-likelihood tensor network decoding. In the regime where…
Quantum low-density parity-check codes are promising candidates for low-overhead fault-tolerant quantum computing, but degeneracy is known to impair the convergence of belief-propagation (BP) decoding of these codes. In this work, we show…
Quantum error correction methods use processing power to combat noise. The noise level which can be tolerated in a fault-tolerant method is therefore a function of the computational resources available, especially the size of computer and…
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…
Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit, where the logical error rate is suppressed exponentially as more qubits are added. However, this…
Noise poses a challenge for any real-world implementation in quantum information science. The theory of quantum error correction deals with this problem via methods to encode and recover quantum information in a way that is resilient…
It is widely accepted that quantum error correction is essential for realizing large-scale fault-tolerant quantum computing. Recent experiments have demonstrated error correction codes operating below threshold, primarily using local planar…
High-rate quantum error correcting (QEC) codes with moderate overheads in qubit number and control complexity are highly desirable for achieving fault-tolerant quantum computing. Recently, quantum error correction has experienced…
A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential…
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…
Recently Shor showed how to perform fault tolerant quantum computation when the error probability is logarithmically small. We improve this bound and describe fault tolerant quantum computation when the error probability is smaller than…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. Practical quantum error correction codes, such as stabilizer codes, are generally structured to suit a specific use, and…
Quantum error-correcting codes (QECCs) can eliminate the negative effects of quantum noise, the major obstacle to the execution of quantum algorithms. However, realizing practical quantum error correction (QEC) requires resolving many…
Quantum error correction is an important ingredient for scalable quantum computing. Stabilizer codes are one of the most promising and straightforward ways to correct quantum errors, are convenient for logical operations, and improve…
Quantum error correction is necessary to perform large-scale quantum computations in the presence of noise and decoherence. As a result, several aspects of quantum error correction have already been explored. These have been primarily…
Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…
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 $[[n,k,d]]$…
We examine the transformation of noise under a quantum error correcting code (QECC) concatenated repeatedly with itself, by analyzing the effects of a quantum channel after each level of concatenation using recovery operators that are…
A major milestone of quantum error correction is to achieve the fault-tolerance threshold beyond which quantum computers can be made arbitrarily accurate. This requires extraordinary resources and engineering efforts. We show that even…