相关论文: Random-projector quantum diagnostics of Ramsey num…
Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to…
The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey…
We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a…
Ramsey theory enables re-shaping of the basic ideas of quantum mechanics. Quantum observables represented by linear Hermitian operators are seen as the vertices of a graph. Relations of commutation define the coloring of edges linking the…
Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently presented a quantum algorithm for the computation of the Ramsey numbers R(m, n) using adiabatic quantum evolution. We consider that the two-color Ramsey numbers R(m, n; r)…
Bayesian inference is a widely used technique for real-time characterization of quantum systems. It excels in experimental characterization in the low data regime, and when the measurements have degrees of freedom. A decisive factor for its…
Quantum annealing has recently been used to determine the Ramsey numbers R(m,2) for 3 < m < 9 and R(3,3) [Bian et al. (2013) PRL 111, 130505]. This was greatly celebrated as the largest experimental implementation of an adiabatic evolution…
Ramsey theory is an active research area in combinatorics whose central theme is the emergence of order in large disordered structures, with Ramsey numbers marking the threshold at which this order first appears. For generalized Ramsey…
Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently shown a quantum algorithm for the computation of the Ramsey numbers using adiabatic quantum evolution. We present a quantum algorithm to compute the two-color Ramsey…
The method of random projection (RP) is the standard technique in machine learning and many other areas, for dimensionality reduction, approximate near neighbor search, compressed sensing, etc. Basically, RP provides a simple and effective…
Quantum annealing is a powerful tool for solving and approximating combinatorial optimization problems such as graph partitioning, community detection, centrality, routing problems, and more. In this paper we explore the use of quantum…
Ramsey's theorem, concerning the guarantee of certain monochromatic patterns in large enough edge-coloured complete graphs, is a fundamental result in combinatorial mathematics. In this work, we highlight the connection between this…
Ramsey interferometry, a cornerstone technique in quantum spectroscopy, traditionally operates with qubits for high precision measurements. In this work we build on Ramsey interferometry, extending it to qudits in Wigner-Majorana (WM)…
In this thesis, we investigate the computational content and the logical strength of Ramsey's theorem and its consequences. For this, we use the frameworks of reverse mathematics and of computable reducibility. We proceed to a systematic…
We prove that the Ramsey number $R(5,5)$ is less than or equal to~$46$. The proof uses a combination of linear programming and checking a large number of cases by computer. All of the computations were independently implemented by both…
We proposed a spectroscopic method that extends Ramsey's atomic spectroscopy to detect the transition frequency of a qubit fabricated on a superconducting circuit. The method uses a multi-interval train of qubit biases to implement an…
The Ramsey sequence is a canonical example of a quantum phase measurement for a spin qubit. In Ramsey measurements, the measurement efficiency can be optimized through careful selection of settings for the phase accumulation time setting,…
We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing…
In this paper we introduce a general framework for proving lower bounds for various Ramsey type problems within random settings. The main idea is to view the problem from an algorithmic perspective: we aim at providing an algorithm that…
Let V be a linear subspace of M_n(C) which contains the identity matrix and is stable under the formation of Hermitian adjoints. We prove that if n is sufficiently large then there exists a rank k orthogonal projection P such that dim(PVP)…