Related papers: Near optimal quantum algorithm for estimating Shan…
We give a technique to reduce the error probability of quantum algorithms that determine whether its input has a specified property of interest. The standard process of reducing this error is statistical processing of the results of…
Entropy is a measure of the randomness of a system. Estimating the entropy of a quantum state is a basic problem in quantum information. In this paper, we introduce a time-efficient quantum approach to estimating the von Neumann entropy…
One of the crucial generic techniques for quantum computation is amplitude encoding. Although several approaches have been proposed, each of them often requires exponential classical-computational cost or an oracle whose explicit…
We introduce a variational algorithm based on the quantum alternating operator ansatz (QAOA) for the approximate solution of computationally hard counting problems. Our algorithm, dubbed VQCount, is based on the equivalence between random…
We propose a new finding $k$-minima algorithm and prove that its query complexity is $\mathcal{O}(\sqrt{kN})$, where $N$ is the number of data indices. Though the complexity is equivalent to that of an existing method, the proposed is…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
Estimating the Shannon entropy of a discrete distribution from which we have only observed a small sample is challenging. Estimating other information-theoretic metrics, such as the Kullback-Leibler divergence between two sparsely sampled…
Recent theoretical developments revived the interest in charged particle multiplicities and their wide-spread parametrization, the negative binomial distribution (NBD). The central observable of the studies is the Shannon entropy of the…
The quantification and classification of quantum entanglement is a very important and still open question of quantum information theory. In this paper, we describe an entanglement measure for multipartite pure states (the minimum of…
We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on…
We explore a supervised machine learning approach to estimate the entanglement entropy of multi-qubit systems from few experimental samples. We put a particular focus on estimating both aleatoric and epistemic uncertainty of the network's…
Estimating properties of quantum states, such as fidelities, molecular energies, and correlation functions, is a fundamental task in quantum information science. Due to the limitation of practical quantum devices, including limited circuit…
We present a quantum algorithm to solve systems of linear equations of the form $A\mathbf{x}=\mathbf{b}$, where $A$ is a tridiagonal Toeplitz matrix and $\mathbf{b}$ results from discretizing an analytic function, with a circuit complexity…
We present a study of the equilibration process of nonequilibrium systems by means of molecular dynamics simulation technique. The nonequilibrium conditions are achieved in systems by defining velocity components of the constituent atoms…
An $n$-qubit quantum circuit is said to be peaked if it has an output probability that is at least inverse-polynomially large as a function of $n$. We describe a classical algorithm with quasipolynomial runtime $n^{O(\log{n})}$ that…
The present study aims to explore the feasibility of language translation using quantum natural language processing algorithms on noisy intermediate-scale quantum (NISQ) devices. Classical methods in natural language processing (NLP)…
The statistics of work done on a quantum system can be quantified by the two-point measurement scheme. We show how the Shannon entropy of the work distribution admits a general upper bound depending on the initial diagonal entropy, and a…
We prove a query complexity lower bound for $\mathsf{QMA}$ protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle $A$ such that $\mathsf{SBP}^A \not\subset…
We present a sampling-based trajectory optimization method derived from the maximum entropy formulation of Differential Dynamic Programming with Tsallis entropy. This method is a generalization of the legacy work with Shannon entropy, which…
We investigate the computational hardness of estimating the quantum $\alpha$-R\'enyi entropy ${\rm S}^{\tt R}_{\alpha}(\rho) = \frac{\ln {\rm Tr}(\rho^\alpha)}{1-\alpha}$ and the quantum $q$-Tsallis entropy ${\rm S}^{\tt T}_q(\rho) =…