Related papers: Large Deviation Bounds for k-designs
Generating data from discrete distributions is important for a number of application domains including text, tabular data, and genomic data. Several groups have recently used random $k$-satisfiability ($k$-SAT) as a synthetic benchmark for…
Unitary designs are essential tools in several quantum information protocols. Similarly to other design concepts, unitary designs are mainly used to facilitate averaging over a relevant space, in this case, the unitary group…
We prove several new results on the Hamming weight of bounded uniform and small-bias distributions. We exhibit bounded-uniform distributions whose weight is anti-concentrated, matching existing concentration inequalities. This construction…
Randomization of quantum states is the quantum analogue of the classical one-time pad. We present an improved, efficient construction of an approximately randomizing map that uses O(d/epsilon^2) Pauli operators to map any d-dimensional…
We study the utility and limitations of using $k$-uniform hypergraphs $H = ([n], E)$ ($n \ge \mathrm{poly}(k)$) in the context of error reduction for randomized algorithms for decision problems with one- or two-sided error. Our error…
We propose a framework to study models of computation of indeterministic data, represented by abstract "distributions". In these distributions, probabilities are replaced by "amplitudes" drawn from a fixed semi-ring $S$, of which the…
Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and…
The performance of quantum key distribution (QKD) heavily depends on statistical inference. For a broad class of protocols, the central statistical task is a random sampling problem, customarily addressed using a hypergeometric tail bound…
Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and…
We develop a new formulation of Stein's method to obtain computable upper bounds on the total variation distance between the geometric distribution and a distribution of interest. Our framework reduces the problem to the construction of a…
In computational physics it is standard to approximate continuum systems with discretised representations. Here we consider a specific discretisation of the continuum complex Hilbert space of quantum mechanics - a discretisation where…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…
Unitary $t$-designs are `good' finite subsets of the unitary group $U(d)$ that approximate the whole unitary group $U(d)$ well. Unitary $t$-designs have been applied in randomized benchmarking, tomography, quantum cryptography and many…
Random circuits giving rise to unitary designs are key tools in quantum information science and many-body physics. In this work, we investigate a class of random quantum circuits with a specific gate structure. Within this framework, we…
The k-defensive domination problem is a powerful modeling tool for strategic decision-making in network security and disaster/emergency management, where multiple nodes may be simultaneously under attack. Despite its practical relevance,…
We design a Quasi-Polynomial time deterministic approximation algorithm for computing the integral of a multi-dimensional separable function, supported by some underlying hyper-graph structure, appropriately defined. Equivalently, our…
Randomized methods, such as the randomized SVD (singular value decomposition) and Nystr\"om approximation, are an effective way to compute low-rank approximations of large matrices. Motivated by applications to operator learning, Boull\'e…
We establish a large deviation principle (LDP) for probability graphons, which are symmetric functions from the unit square into the space of probability measures. This notion extends classical graphons and provides a flexible framework for…