Projects mentored

Toward the end of my master’s degree at UNAM in Mexico, I wanted to explore my research ideas through collaboration while also contributing to my alma mater, Universidad de San Carlos de Guatemala. I therefore began looking for undergraduate students there who were interested in working with me on these topics. I am pleased that one of these collaborations ultimately led to a research paper.

Undergraduate graduation projects

1. Mariana Pérez Muralles¹ (ECFM-USAC) March 2025 – August 2026
   Parrondo’s paradox in discrete-time quantum walks
   Investigation of the emergence of a genuine Parrondo’s paradox in 1D discrete-time quantum walks using homogeneous coin operators.
   
   This project includes the co-organization of a week-long hands-on introductory course on Wolfram Mathematica (course website).

2. Amado Cabrera Estrada¹ (ECFM-USAC) March 2025 – August 2026
   Imperfect measurements in discrete-time quantum walks
   Analysis of the effects of imperfect measurement apparatus, within the quantum channel-based framework of fuzzy measurements, on 1D discrete-time quantum walks.
   
   This project includes the co-organization of a week-long hands-on introductory course on Wolfram Mathematica (course website).

Undergraduate final internship projects

1. Dessiré Zapeta (ECFM-USAC) May 2026 – Present
   Quantum chaos in quantum walks:
   Investigation of the level spacing distributions of discrete-time quantum walks in billiards.

2. Saúl Najera (ECFM-USAC) September 2025 – May 2026
   Quantum chaos in the Bose–Hubbard model:
   Characterization of the integrable-to-chaos transition in the Bose–Hubbard model.
   [Final report (in Spanish)]

   

   Integrable-to-chaos transition in the Bose-Hubbard model with N=L (N: bosons, L: sites). (a) KL divergence between numerical \(P(r)\) and \(P_{\mathrm{GOE}}(r)\) (filled markers) and \(P_{\mathrm{GOE}}(r)\) (open markers). (b) Mean level spacing ratio.

3. Mariana Pérez Muralles (ECFM-USAC) August 2023 – November 2024
   Discrete-time quantum walks:
   Theoretical framework and numerical implementation of discrete-time quantum walks.
   [Final report (in Spanish)]

4. Amado Cabrera Estrada (ECFM-USAC) August 2023 – November 2024
   Discrete-time quantum walks:
   Theoretical framework and numerical implementation of discrete-time quantum walks.
   A Wolfram Language package developed by Amado during this project is available at https://github.com/AmadoCab/QW.
   [Final report (in Spanish)]