Quantum parameter estimation via Bayesian inference (Masters project)

Alexandra Ramôa Alves | Engineering Physics - Physics of Information, University of Minho

Each folder contains several scripts, generally a .pdf file with slides showing a selection of results, and sometimes data.

The HSMC inference folder contains the application of Hamiltonian sequential Monte Carlo to the characterization of multi-parameter probabilistic functions (using sequential importance resampling, with the prior distribution as importance function).

The HSMC-ECS (annealing) folder implements energy conserving subsampling HSMC, using a block pseudo marginal approach (in a tempered likelihood setting).

The IBMQ experiments folder contains a Jupyter notebook with several characterization experiments on IBMQ's backends (performed using OpenPulse), along with a selection of the data gathered from them and some files adapted to perform inference based on these data.

The Phase estimation folder contains scripts that estimate a phase using 2 different approaches: gaussian rejection filtering, and MCMC (with Hamiltonian Monte Carlo and random walk Metropolis transitions).

The Precession frequency estimation folder contains implementations of the estimation of a precession frequency (plus a decay factor in some cases) using 3 different approaches: SMC (with sequential importance resampling), HSMC (relying mostly on Hamiltonian Monte Carlo mutation steps) and MCMC (using Hamiltonian Monte Carlo and random walk Metropolis transitions).

The Sampling methods folder contains implementations of several Monte Carlo sampling algorithms for 3 target probability densities (a Rosenbrock function, a 6-dimensional gaussian, and a smiley face kernel density estimate).

The SG-H(S)MC (annealing) folder implements Hamiltonian dynamics based algorithms accounting for noisy gradients - e.g. from subsampling, namely stochastic gradient HMC-based SMC (in a tempered likelihood setting).

The Tempered likelihood HSMC inference folder contains the application of tempered/annealed Hamiltonian sequential Monte Carlo to the characterization of multi-parameter probabilistic functions.

The Trajectory sampling strategies folder applies several variations of HMC to a Rosenbrock function density. These variations differ in how they pick a sample from the generated trajectory (in all other files only the last state was considered, and a Metropolis correction was performed). Includes static and dynamic approaches.

The dissertation_examples jupyter notebook visually represents a few key examples to be used for illustrations.