Emanuel Casiano Diaz

Quantum Entanglement

The constituents of quantum many-body systems may exhibit correlations that cannot be classically described, a phenomenon known as quantum entanglement. In my time in graduate school, I have studied how much entanglement is there between spatial subregions of a system and also how much entanglement is there between groups of particles, regardless of their spatial subregion. We quantify this via Rényi Entanglement Entropies, a measure that can be computed exactly in small systems, but for larger systems can only be sampled using Quantum Monte Carlo algorithms. We developed the first Path-Integral Monte Carlo algorithm that allows us to compute the spatial entanglement, and how much of it can be used as a resource for quantum computing, for systems of bosons on a lattice at zero-temperature.

Machine Learning Quantum Many-Body Systems

Machine learning has proved to be a viable tool for the simulation of quantum many-body systems. Certain machine learning models have been shown to be more efficient for this task than more commonly used Monte Carlo algorithms. In particular, I’ve been exploring how generalizing a Restricted Boltzmann Machine (or RBM) into a convolutional neural network leads to better performing simulations of the Ising Model.

Accelerating Monte Carlo Simulation

Monte Carlo simulation was invented in the 40’s and many existing algorithms have been highly optimized already. Due to the ubiquity of these simulations in science, and other fields such as finance, it is of interest finding ways of accelerating this tool.

Publications

https://arxiv.org/abs/2207.11301

  1. PIGSFLI: A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons
    Emanuel Casiano-Diaz, Chris M. Herdman, Adrian Del Maestro (2022)
    arXiv:2207.11301
  2. Operationally accessible entanglement of one-dimensional spinless fermions
    Hatem Barghtahi, Emanuel Casiano-Diaz, Adrian Del Maestro (2019)
    arXiv:1905.03312
  3. Master’s Thesis - Quantum entanglement of one-dimensional spinless fermions
    Emanuel Casiano-Diaz (2019)
  4. Particle partition entanglement of one dimensional spinless fermions
    Hatem Barghathi, Emanuel Casiano-Diaz, Adrian Del Maestro (2017)
    arXiv:1703.10587v3

Recent recorded talks

1.Operationally Accessible Entanglement in the 1D Bose-Hubbard Model - APS March Meeting 2022

2.Measuring Rényi Entanglement Entropies in Lattice Worm Algorithm QMC - APS March Meeting 2020