Conference

Many tasks in quantum information rely on accurate knowledge of a system's Hamiltonian, including calibrating control, characterizing devices, and verifying quantum simulators. In this talk, we pose the problem of learning Hamiltonians as an instance of parameter estimation. We then solve this problem with Bayesian inference, and describe how rejection and particle filtering provide efficient numerical algorithms for learning Hamiltonians. Finally, we discuss how filtering can be combined with quantum resources to verify quantum systems beyond the reach of classical simulators. More information on this topic is available at http://www.cgranade.com/research/talks/qml/2016/

Quantum machine learning algorithms usually translate a machine learning methods into an algorithm that can exploit the advantages of quantum information processing. One approach is to tackle methods that rely on matrix inversion with the quantum linear system of equations routine. We give such a quantum algorithm based on unregularised linear regression. Opposed to closely related work from Wiebe, Braun and Lloyd [PRL 109 (2012)] our scheme focuses on a classification task and uses a different combination of core routines that allows us to process non-sparse inputs, and significantly improves the dependence on the condition number. The second part of the talk presents an idea that transcends the reproduction of classical results. Instead of considering a single trained classifier, practicioners often use ensembles of models to make predictions more robust and accurate. Under certain conditions, having infinite ensembles can lead to good results. We introduce a quantum sampling scheme that uses the parallelism inherent to a quantum computer in order to sample from 'exponentially large' ensembles that are not explicitely trained.

Supervised Machine Learning is one of the key problems that arises in modern big data tasks. In this talk, I will first describe several different classical algorithmic paradigms for classification and then contrast them with quantum algorithmic constructs. In particular, we will look at classical methods such as the nearest neighbor rule, optimization based algorithms (e.g. SVMs), Bayesian inference based techniques (e.g. Bayes point machine) and provide a unifying framework so that we can get a deeper understanding about the quantum versions of the methods.