Related papers: Quantum algorithms for testing properties of distr…
Consider the problem of estimating the median of N items to a precision epsilon, i.e., the estimate should be such that, with a high probability, the number of items, with values both smaller than and larger than this estimate, is less than…
Quantum key distribution, which allows two distant parties to share an unconditionally secure cryptographic key, promises to play an important role in the future of communication. For this reason such technique has attracted many…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
We provide a distribution-free test that can be used to determine whether any two joint distributions $p$ and $q$ are statistically different by inspection of a large enough set of samples. Following recent efforts from Long et al. [1], we…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to…
The curvelet transform is a directional wavelet transform over R^n, which is used to analyze functions that have singularities along smooth surfaces (Candes and Donoho, 2002). I demonstrate how this can lead to new quantum algorithms. I…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a…
In this work, we initiate the study of learning quantum processes from quantum statistical queries. We focus on two fundamental learning tasks in this new access model: shadow tomography of quantum processes and process tomography with…
Efficient sampling from a classical Gibbs distribution is an important computational problem with applications ranging from statistical physics over Monte Carlo and optimization algorithms to machine learning. We introduce a family of…
In practical situations, the reliability of quantum resources can be compromised due to complex generation processes or adversarial manipulations during transmission. Consequently, the trials generated sequentially in an experiment may…
Experimental characterizations of a quantum system involve the measurement of expectation values of observables for a preparable state |psi> of the quantum system. Such expectation values can be measured by repeatedly preparing |psi> and…
The quantum computer algorithm by Peter Shor for factorization of integers is studied. The quantum nature of a QC makes its outcome random. The output probability distribution is investigated and the chances of a successful operation is…
Quantum mechanics permits certain kinds of non-local effects. This paper demonstrates how these can be used for distributed computation with minimal communication between various processors. The problem considered is that of estimating the…
We introduce a protocol addressing the conformance test problem, which consists in determining whether a process under test conforms to a reference one. We consider a process to be characterized by the set of end-product it produces, which…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
In classical statistics and distribution testing, it is often assumed that elements can be sampled from some distribution $P$, and that when an element $x$ is sampled, the probability $P$ of sampling $x$ is also known. Recent work in…
Quantum circuits generating probability distributions has applications in several areas. Areas like finance require quantum circuits that can generate distributions that mimic some given data pattern. Hamiltonian simulations require…