相关论文: Extended Quantum Color Coding
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a…
We develop further the new versions of quantum chromatic numbers of graphs introduced by the first and fourth authors. We prove that the problem of computation of the commuting quantum chromatic number of a graph is solvable by an SDP…
Quantum optical frequency combs provide an intriguing approach to high-dimensional quantum states. Because of the need to move probabilities among different colors, the realization of gates appropriate to multicolor photons requires…
In this paper, we explore the possibility of constructing the quantum chromodynamics of a massive color-octet vector field without introducing higher structures like extended gauge symmetries, extra dimensions or scalar fields. We show that…
The Four color problem is closely related to other branches of mathematics and practical applications. More than 20 of its reformulations are known, which connect this problem with problems of algebra, statistical mechanics and planning.…
Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity…
The parameters of a quantum system grow exponentially with the number of involved quantum particles. Hence, the associated memory requirement goes well beyond the limit of best classic computers for quantum systems composed of a few dozen…
We prove that a wide class of random quantum channels with few Kraus operators, sampled as random matrices with some sparsity and moment assumptions, typically exhibit a large spectral gap, and are therefore optimal quantum expanders. In…
A homomorphism from a graph $X$ to a graph $Y$ is an adjacency preserving mapping $f:V(X) \rightarrow V(Y)$. We consider a nonlocal game in which Alice and Bob are trying to convince a verifier with certainty that a graph $X$ admits a…
The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of GRUNDY COLORING, the problem of determining whether a…
Here, we study the capacity of a quantum channel, assuming linear optical encoding, as a function of available photons and optical modes. First, we observe that substantial improvement is made possible by not restricting ourselves to a…
Recent developments in approximate counting have made startling progress in developing fast algorithmic methods for approximating the number of solutions to constraint satisfaction problems (CSPs) with large arities, using connections to…
Irregular computations on unstructured data are an important class of problems for parallel programming. Graph coloring is often an important preprocessing step, e.g. as a way to perform dependency analysis for safe parallel execution. The…
Many protocols of quantum information processing, like quantum key distribution or measurement-based quantum computation, "consume" entangled quantum states during their execution. When participants are located at distant sites, these…
Approximate random k-colouring of a graph G=(V,E) is a very well studied problem in computer science and statistical physics. It amounts to constructing a k-colouring of G which is distributed close to Gibbs distribution, i.e. the uniform…
There is an extensive history of scholarship into what constitutes a "basic" color term, as well as a broadly attested acquisition sequence of basic color terms across many languages, as articulated in the seminal work of Berlin and Kay…
It is shown that the large $N_c$ limit of QCD with quarks in the two-index antisymmetric color representation [QCD(AS)] has narrow tetraquark states with exotic flavor quantum numbers. They decay into mesons with a width that is…
The generalized coloring numbers of Kierstead and Yang (Order 2003) offer an algorithmically-useful characterization of graph classes with bounded expansion. In this work, we consider the hardness and approximability of these parameters.…
The emergence of quantum computing has introduced unprecedented security challenges to conventional cryptographic systems, particularly in the domain of optical communications. This research addresses these challenges by innovatively…
In this work we consider the \emph{infinite color urn model} associated with a bounded increment random walk on $\Zbold^d$. This model was first introduced by Bandyopadhyay and Thacker (2013). We prove that the rate of convergence of the…