Related papers: Near optimal quantum algorithm for estimating Shan…
We consider estimating the Shannon entropy of a discrete distribution $P$ from $n$ i.i.d. samples. Recently, Jiao, Venkat, Han, and Weissman, and Wu and Yang constructed approximation theoretic estimators that achieve the minimax $L_2$…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
We present an algorithm for efficiently approximating of qubit unitaries over gate sets derived from totally definite quaternion algebras. It achieves $\varepsilon$-approximations using circuits of length $O(\log(1/\varepsilon))$, which is…
The weak law of large numbers implies that, under mild assumptions on the source, the Renyi entropy per produced symbol converges (in probability) towards the Shannon entropy rate. This paper quantifies the speed of this convergence for…
We investigate the theoretical foundations of a recently introduced entropy-based formulation of weighted least squares for the approximation of overdetermined linear systems, motivated by robust data fitting in the presence of sparse gross…
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary…
The Shannon entropy is a fundamental measure for quantifying diversity and model complexity in fields such as information theory, ecology, and genetics. However, many existing studies assume that the number of species is known, an…
The estimation of entropy rates for stationary discrete-valued stochastic processes is a well studied problem in information theory. However, estimating the entropy rate for stationary continuous-valued stochastic processes has not received…
We propose a general framework for solving quantum state estimation problems using the minimum relative entropy criterion. A convex optimization approach allows us to decide the feasibility of the problem given the data and, whenever…
This paper studies the problem of estimating the differential entropy $h(S+Z)$, where $S$ and $Z$ are independent $d$-dimensional random variables with $Z\sim\mathcal{N}(0,\sigma^2 \mathrm{I}_d)$. The distribution of $S$ is unknown, but $n$…
Maximum entropy inference and learning of graphical models are pivotal tasks in learning theory and optimization. This work extends algorithms for these problems, including generalized iterative scaling (GIS) and gradient descent (GD), to…
In this paper, we show an interesting connection between a quantum sampling technique and quantum uncertainty. Namely, we use the quantum sampling technique, introduced by Bouman and Fehr, to derive a novel entropic uncertainty relation…
We consider the problem of estimating the partition function $Z(\beta)=\sum_x \exp(-\beta(H(x))$ of a Gibbs distribution with a Hamilton $H(\cdot)$, or more precisely the logarithm of the ratio $q=\ln Z(0)/Z(\beta)$. It has been recently…
It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start…
In this paper, we introduce a new quantum query lower bound framework. It is inspired by Zhandry's compressed oracle technique, but it also subsumes the polynomial method as a special case. Compared to Zhandry's technique, our approach has…
We describe a quantum algorithm based on an interior point method for solving a linear program with $n$ inequality constraints on $d$ variables. The algorithm explicitly returns a feasible solution that is $\varepsilon$-close to optimal,…
The quality of image encryption is commonly measured by the Shannon entropy over the ciphertext image. However, this measurement does not consider to the randomness of local image blocks and is inappropriate for scrambling based image…
Using the bitstring probabilities of ground states of bipartitioned ladders of Rydberg atoms, we calculate the mutual information, which is a lower bound on the corresponding bipartite von Neumann quantum entanglement entropy $S^{vN}_A$. We…
Amplitude estimation is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. The main drawback from the…
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error. First, we give a tight analysis of the trade-offs between the number of queries of quantum search…