Estimation and uncertainty quantification for the output from quantum simulators

Kody Law, Ajay Jasra, Ryan Bennink, Pavel Lougovski

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of estimating certain distributions over {0, 1}d is considered here. The distribution represents a quantum system of d qubits, where there are non-trivial dependencies between the qubits. A maximum entropy approach is adopted to reconstruct the distribution from exact moments or observed empirical moments. The Robbins Monro algorithm is used to solve the intractable maximum entropy problem, by constructing an unbiased estimator of the un-normalized target with a sequential Monte Carlo sampler at each iteration. In the case of empirical moments, this coincides with a maximum likelihood estimator. A Bayesian formulation is also considered in order to quantify uncertainty a posteriori. Several approaches are proposed in order to tackle this challenging problem, based on recently developed methodologies. In particular, unbiased estimators of the gradient of the log posterior are constructed and used within a provably convergent Langevin-based Markov chain Monte Carlo method. The methods are illustrated on classically simulated output from quantum simulators.
Original languageEnglish
Pages (from-to)157-176
JournalFoundations of Data Science
Volume1
Issue number2
DOIs
Publication statusPublished - 1 Jun 2019

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