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Quantum computers theoretically are able to solve certain problems more quickly than any deterministic or probabilistic computers. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, one has to…
We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based…
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies…
The AND gate is not reversible$\unicode{x2014}$on qubits. However, it is reversible on qutrits, making it a building block for efficient simulation of qubit computation using qutrits. We first observe that there are multiple two-qutrit…
Quantum repeaters have promised efficient scaling of quantum networks for over two decades. Despite numerous platforms proclaiming functional repeaters, the realization of large-scale networks remains elusive, indicating that the resources…
In this note we show that the weight enumerators of a real quantum error correcting code with $ X $ and $ Z $ exactly transversal must satisfy certain identities. One consequence of these identities is that if the code is error detecting…
A quantum repeater scheme based on cavity-QED and quantum error correction of channel loss via rotation-symmetric bosonic codes (RSBC) is proposed to distribute atomic entangled states over long distances without memories and at high clock…
We investigate the advantage of coherent superposition of two different coded channels in quantum metrology. In a continuous variable system, we show that the Heisenberg limit $1/N$ can be beaten by the coherent superposition without the…
We present a new propagation rule for CSS codes. Starting with a CSS code $[\![n,k,d]\!]_q$, we construct a CSS code with parameters $[\![n-2,k,d-1]\!]_q$. In general, one would only obtain a code with parameters $[\![n-2,k,d-2]\!]_q$. The…
Classical turbo codes efficiently approach the Shannon limit, and so bringing these over to the quantum scenario would allow for rapid transmission of quantum information. Early on in the work of defining the quantum analogue, it was shown…
It is conjectured that quantum computers are able to solve certain problems more quickly than any deterministic or probabilistic computer. A quantum computer exploits the rules of quantum mechanics to speed up computations. However, it is a…
We show how good quantum error-correcting codes can be constructed using generalized concatenation. The inner codes are quantum codes, the outer codes can be linear or nonlinear classical codes. Many new good codes are found, including both…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
In quantum repeater protocols, measurements are performed in multiple relay points. Classical communications are used to convey the measurement results. It is important to improve the way of conveying the measurement results so that EPR…
We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable…
To realize long-distance quantum communication, it is crucial to design quantum repeater architectures that can deal with transmission losses and operational errors. Code concatenation of photonic graph codes is a promising way to achieve…
Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors,…
Quantum repeaters are essential ingredients for quantum networks that link distant quantum modules such as quantum computers and sensors. Motivated by distributed quantum computing and communication, quantum repeaters that relay…
Quantum error-correcting codes (QECCs) and decoherence-free subspace (DFS) codes provide active and passive means, respectively, to address certain types of errors that arise during quantum computation. The latter technique is suitable to…
Error-correction codes are central for fault-tolerant information processing. Here we develop a rigorous framework to describe various coding models based on quantum resource theory of superchannels. We find, by treating codings as…