Related papers: Quantum Sampling and Moment Estimation for Transfo…
Consider a fixed universe of $N=2^n$ elements and the uniform distribution over elements of some subset of size $K$. Given samples from this distribution, the task of complement sampling is to provide a sample from the complementary subset.…
Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
Many applications of Gaussian random fields and Gaussian random processes are limited by the computational complexity of evaluating the probability density function, which involves inverting the relevant covariance matrix. In this work, we…
A model of quantum measurement, illustrated using the spin--boson model, is formulated in terms of a cascading pair of quantum phase transitions. The first produces the desired superposition of macroscopic responses to the microscopic state…
Quantum computer algorithms can exploit the structure of random satisfiability problems. This paper extends a previous empirical evaluation of such an algorithm and gives an approximate asymptotic analysis accounting for both the average…
We consider the problem of uniform sampling of points on an algebraic variety. Specifically, we develop a randomized algorithm that, given a small set of multivariate polynomials over a sufficiently large finite field, produces a common…
We develop Monte Carlo methods for sampling random states and corresponding bit strings in qubit systems. To this end, we derive exact probability density functions that yield the Porter-Thomas distribution in the limit of large systems. We…
Quantum supremacy poses that a realistic quantum computer can perform a calculation that classical computers cannot in any reasonable amount of time. It has become a topic of significant research interest since the birth of the field, and…
The resources required to characterise the dynamics of engineered quantum systems-such as quantum computers and quantum sensors-grow exponentially with system size. Here we adapt techniques from compressive sensing to exponentially reduce…
Quantum state tomography is the problem of estimating a given quantum state. Usually, it is required to run the quantum experiment - state preparation, state evolution, measurement - several times to be able to estimate the output quantum…
Variational quantum circuits characterise the state of a quantum system through the use of parameters that are optimised using classical optimisation procedures that typically rely on gradient information. The circuit-execution complexity…
Current statistics literature on statistical inference of random fields typically assumes that the fields are stationary or focuses on models of non-stationary Gaussian fields with parametric/semiparametric covariance families, which may…
We present randomized algorithms for sampling the standard Gaussian distribution restricted to a convex set and for estimating the Gaussian measure of a convex set, in the general membership oracle model. The complexity of integration is…
Discrete Gaussian Sampling on lattices is a fundamental problem in lattice-based cryptography. It appears both in basic cryptographic primitives such as digital signatures and as an important cryptanalysis building block for solving hard…
Gaussian couplings of partial sum processes are derived for the high-dimensional regime $d=o(n^{1/3})$. The coupling is derived for sums of independent random vectors and subsequently extended to nonstationary time series. Our inequalities…
We provide a graphical method to describe and analyze non-Gaussian quantum states using a hypergraph framework. These states are pivotal resources for quantum computing, communication, and metrology, but their characterization is hindered…
Gaussian boson sampling (GBS) is considered a candidate problem for demonstrating quantum advantage. We propose an algorithm for approximate classical simulation of a lossy GBS instance. The algorithm relies on the Taylor series expansion,…