Related papers: On the sampling complexity of coherent superpositi…
Approximate inference in dynamic systems is the problem of estimating the state of the system given a sequence of actions and partial observations. High precision estimation is fundamental in many applications like diagnosis, natural…
Similarly to quantum states, also quantum measurements can be "mixed", corresponding to a random choice within an ensemble of measuring apparatuses. Such mixing is equivalent to a sort of hidden variable, which produces a noise of purely…
It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…
Subset sampling (also known as Poisson sampling), where the decision to include any specific element in the sample is made independently of all others, is a fundamental primitive in data analytics, enabling efficient approximation by…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Most current sampling algorithms for high-dimensional distributions are based on MCMC techniques and are approximate in the sense that they are valid only asymptotically. Rejection sampling, on the other hand, produces valid samples, but is…
Boson-Sampling is a classically computationally hard problem that can - in principle - be efficiently solved with quantum linear optical networks. Very recently, a rush of experimental activity has ignited with the aim of developing such…
Sampling a random permutation with restricted positions, or equivalently approximating the permanent of a 0-1 matrix, is a fundamental problem in computer science, with several notable results achieved over the years. However, existing…
We study the problem of sampling from a distribution $\mu$ with density $\propto e^{-V}$ for some potential function $V:\mathbb R^d\to \mathbb R$ with query access to $V$ and $\nabla V$. We start with the following standard assumptions: (1)…
We consider the statistical properties of photon detection with imperfect detectors that exhibit dark counts and less than unit efficiency, in the context of tomographic reconstruction. In this context, the detectors are used to implement…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
Quantum dynamical simulations of statistical ensembles pose a significant computational challenge due to the fact that mixed states need to be represented. If the underlying dynamics is fully unitary, for example in ultrafast coherent…
We give a fast algorithm for sampling uniform solutions of general constraint satisfaction problems (CSPs) in a local lemma regime. Suppose that the CSP has $n$ variables with domain size at most q, each constraint contains at most k…
We study the complexity of classically sampling from the output distribution of an Ising spin model, which can be implemented naturally in a variety of atomic, molecular, and optical systems. In particular, we construct a specific example…
Boson sampling has emerged as an important tool to demonstrate the difference between quantum and classical computers and has attracted the interest of experimentalists and theoreticians. In this work we study Boson sampling from general,…
We consider the problem of learning an $\varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Given access to a generative model, we achieve rate-optimal sample…
Considering the problem of sampling from the output photon-counting probability distribution of a linear-optical network for input Gaussian states, we obtain results that are of interest from both quantum theory and the computational…
We study the hardness of classically simulating Gaussian boson sampling at nonzero photon distinguishability. We find that similar to regular boson sampling, distinguishability causes exponential attenuation of the many-photon interference…
We show that measuring any two quantum states by a random POVM, under a suitable definition of randomness, gives probability distributions having total variation distance at least a universal constant times the Frobenius distance between…
We study the fundamental problem of sampling independent events, called subset sampling. Specifically, consider a set of $n$ events $S=\{x_1, \ldots, x_n\}$, where each event $x_i$ has an associated probability $p(x_i)$. The subset sampling…