Related papers: Quantum Gibbs Sampling Using Szegedy Operators
Lindblad dynamics and other open-system dynamics provide a promising path towards efficient Gibbs sampling on quantum computers. In these proposals, the Lindbladian is obtained via an algorithmic construction akin to designing an artificial…
Identifying the boundary beyond which quantum machines provide a computational advantage over their classical counterparts is a crucial step in charting their usefulness. Gaussian Boson Sampling (GBS), in which photons are measured from a…
Quantum computers solve intractable problems which classically require an exponentially long time to compute. With the development of large-scale experiments that claim quantum advantage, a vital issue has now emerged. What are the errors,…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
Quantum amplitude estimation is a key sub-routine of a number of quantum algorithms with various applications. We propose an adaptive algorithm for interval estimation of amplitudes. The quantum part of the algorithm is based only on…
A canonical approach to approximating the partition function of a Gibbs distribution via sampling is simulated annealing. This method has led to efficient reductions from counting to sampling, including: $\bullet$ classic non-adaptive…
We operate a superconducting quantum processor consisting of two tunable transmon qubits coupled by a swapping interaction, and equipped with non destructive single-shot readout of the two qubits. With this processor, we run the Grover…
The aim of this paper is to develop novel quantum algorithms for Gaussian process quadrature methods. Gaussian process quadratures are numerical integration methods where Gaussian processes are used as functional priors for the integrands…
Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fundamental properties, such as relations between convergence characteristics of their various…
Quantum algorithms use the principles of quantum mechanics, as for example quantum superposition, in order to solve particular problems outperforming standard computation. They are developed for cryptography, searching, optimisation,…
Computational validation is vital for all large-scale quantum computers. One needs computers that are both fast and accurate. Here we apply precise, scalable, high order statistical tests to data from large Gaussian boson sampling (GBS)…
We show a certain kind of non-local operations can be simulated by sampling a set of local operations with a quasi-probability distribution when the task of a quantum circuit is to evaluate an expectation value of observables. Utilizing the…
The Gibbs sampler (GS) is a crucial algorithm for approximating complex calculations, and it is justified by Markov chain theory, the alternating projection theorem, and $I$-projection, separately. We explore the equivalence between these…
Gibbs sampling is a widely used Markov chain Monte Carlo (MCMC) method for numerically approximating integrals of interest in Bayesian statistics and other mathematical sciences. Many implementations of MCMC methods do not extend easily to…
In this work, we study the maximum matching problem from the perspective of sensitivity. The sensitivity of an algorithm $A$ on a graph $G$ is defined as the maximum Wasserstein distance between the output distributions of $A$ on $G$ and on…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
Szegedy's quantization of a reversible Markov chain provides a quantum walk whose spectral gap is quadratically larger than that of the classical walk. Quantum computers are therefore expected to provide a speedup of Metropolis-Hastings…
We introduce a new approach for quantum linear algebra based on quantum subspace states and present three new quantum machine learning algorithms. The first is a quantum determinant sampling algorithm that samples from the distribution…
We present a quantum algorithm for sampling random spanning trees from a weighted graph in $\widetilde{O}(\sqrt{mn})$ time, where $n$ and $m$ denote the number of vertices and edges, respectively. Our algorithm has sublinear runtime for…