Related papers: A simple approach to approximate quantum error cor…
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…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…
Current quantum processors are fragile, noisy and fairly limited in both quantity and quality with tens of qubits and physical error rates of around 10^-3. To realize practical quantum applications, however, error rates need to be below…
In this work, we develop the theory of quasi-exact fault-tolerant quantum (QEQ) computation, which uses qubits encoded into quasi-exact quantum error-correction codes ("quasi codes"). By definition, a quasi code is a parametric approximate…
The overhead of quantum error correction (QEC) poses a major bottleneck for realizing fault-tolerant computation. To reduce this overhead, we exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into…
We identify optimal quantum error correction codes for situations that do not admit perfect correction. We provide analytic n-qubit results for standard cases with correlated errors on multiple qubits and demonstrate significant…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building…
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)…
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…
Large-scale quantum computers will inevitably need quantum error correction to protect information against decoherence. Traditional error correction typically requires many qubits, along with high-efficiency error syndrome measurement and…
There is no unique way to encode a quantum algorithm into a quantum circuit. With limited qubit counts, connectivities, and coherence times, circuit optimization is essential to make the best use of near-term quantum devices. We introduce…
We study relaxations of entanglement-assisted quantum channel coding and establish that non-signaling assistance and a natural semi-definite programming relaxation\, -- \,termed meta-converse\, -- \,are equivalent in terms of success…
Quantum error correction (QEC) is an essential step towards realising scalable quantum computers. Theoretically, it is possible to achieve arbitrarily long protection of quantum information from corruption due to decoherence or imperfect…
Quantum error correction is crucial for protecting quantum information against decoherence. Traditional codes like the surface code require substantial overhead, making them impractical for near-term, early fault-tolerant devices. We…
We present a comparative analysis of exact and approximate quantum error correction by means of simple unabridged analytical computations. For the sake of clarity, using primitive quantum codes, we study the exact and approximate error…
Quantum error correction is an essential tool for reliably performing tasks for processing quantum information on a large scale. However, integration into quantum circuits to achieve these tasks is problematic when one realizes that…
The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a…
We describe a quantum error correction scheme aimed at protecting a flow of quantum information over long distance communication. It is largely inspired by the theory of classical convolutional codes which are used in similar circumstances…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…