Related papers: A Combinatorial Approach to Quantum Error Correcti…
The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…
Combinatorial optimization is among the main applications envisioned for near-term and fault-tolerant quantum computers. In this work, we consider a well-studied quantum algorithm for combinatorial optimization: the Quantum Approximate…
The longstanding open problem of approximating all singular vertex couplings in a quantum graph is solved. We present a construction in which the edges are decoupled; an each pair of their endpoints is joined by an edge carrying a $\delta$…
Quantum Error-Correcting Codes (QECCs) play a crucial role in enhancing the robustness of quantum computing and communication systems against errors. Within the realm of QECCs, stabilizer codes, and specifically graph codes, stand out for…
Asymmetric quantum error-correcting codes are quantum codes defined over biased quantum channels: qubit-flip and phase-shift errors may have equal or different probabilities. The code construction is the Calderbank-Shor-Steane construction…
This paper studies the problem of proper-walk connection number: given an undirected connected graph, our aim is to colour its edges with as few colours as possible so that there exists a properly coloured walk between every pair of…
Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$…
A short introduction to quantum error correction is given, and it is shown that zero-dimensional quantum codes can be represented as self-dual additive codes over GF(4) and also as graphs. We show that graphs representing several such codes…
We give an introduction to the theory of quantum error correction using stabilizer codes that is geared towards the working computer scientists and mathematicians with an interest in exploring this area. To this end, we begin with an…
As two fundamental problems, graph cuts and graph matching have been investigated over decades, resulting in vast literature in these two topics respectively. However the way of jointly applying and solving graph cuts and matching receives…
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…
Quantum error correction and the use of quantum error correction codes is likely to be essential for the realisation of practical quantum computing. Because the error models of quantum devices vary widely, quantum codes which are tailored…
Concatenated coding provides a general strategy to achieve the desired level of noise protection in quantum information storage and transmission. We report the implementation of a concatenated quantum error-correcting code able to correct…
Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin--Knill theorem,…
Binary codes are constructed from incidence matrices of hypergraphs. A combinatroial description is given for the minimum distances of such codes via a combinatorial tool called ``eonv". This combinatorial approach provides a faster…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…