email: momercad(at)usc(dot)edu

My work is generously supported by the Astronaut Scholarship Foundation.

> Quantum Mechanics/QFT
> Condensed Matter/QI

> Analytical Recipes
> Topological mass generation vs. Higgs mechanism
> 3D gauge Ising model as string theory
> Dyson singularity
> Reparameterization symmetry, Lorentz algebras in light-cone coordinates and light-cone gauge
> Magnons and topology
> Science communication: What makes a good presentation?
> 2d TQFTs and Frobenius algebras
> Topology vs. decoherence - a case study
> Relaxation dynamics of Goldstone modes in noisy spin lattices
> Open quantum SPTs in one dimension

  • How do we phenomenologically understand topological phases out of equilibrium? (e.g. open quantum systems, periodically driven, with interactions and disorder?)
  • Can we apply state-of-the-art quantum devices (e.g. cold atom arrays, solid state simulators, spintronic devices) to study non-trivial problems in physics?
  • What are the roles of symmetries, topology, and quantum information in many-body physics? Can we experimentally probe them?
  • How do we improve mathematics and physics education to be more fun, engaging, and accessible at all levels?

2. Dynamics of symmetry-protected topological matter on a quantum computer
M. Mercado, K. Chen, P. Darekar, A. Nakano, R.D. Felice, S. Haas
Physical Review B 110 (7), 075116 (2024).

3. (Acknowledgement) Cluster expansion methods from physical concepts
P. Lammert, V. Crespi
arXiv:2210.10937 (2022)

> D62.00003: Dynamics of Symmetry-Protected Topological Phases of Matter on a Quantum Computer, oral presentation at American Physical Society March Meeting (2024) - Top Undergraduate Presenter Award.

> Stabilizing Topological Phases of Matter on Present-Day Quantum Computers, talk at Southern California Conferences for Undergraduate Research (SCCUR) (2023).

> Colloquium: Probing Topological Quantum Matter, invited speaker at Bryn Mawr College (2023).

> Many-Body Entanglement via Topological Magnons in Hybrid Quantum Multilayers, virtual poster presentation at MSRP Extension Program Virtual Showcase (2023).

> E02.00006: Hierarchy of Surface Modes in Disordered Symmetry Protected Topological Insulators, oral presentation at American Physical Society Mid-Atlantic Meeting (2023).

> Realization of Stable Topological Matter on a Noisy Quantum Computer, talk at Gulf Coast Undergraduate Research Symposium (GCURS) (2023).

> Many-Body Entanglement via Topological Magnons in Hybrid Quantum Multilayers, Poster presentation at MIT Summer Research Program Poster Symposium (2023).

> Many-Body Entanglement via Topological Magnons in Hybrid Quantum Multilayers, talk at MIT Spintronic Material and Device group (2023).

> 3d gauge Ising model as string theory, talk at USC string theory course seminar (2023)

> Topological Protection Against Disorder in Chiral Symmetric Matter, Poster presentation at USC Undergraduate Symposium for Scholarly and Creative Work (2023) - Best Overall Presentation Award.

> GCEP: A Revised Cluster Expansion Method Formulation based on Hilbert Space Geometry, Poster presentation at National Organization for the Professional Advancement of Black Chemists and Chemical Engineers Global Science Awakening Conference (2022).

> GCEP: A Geometrical Revision of Cluster Expansion Theory, Poster presentation at The Pennsylvania State REU Poster Symposium (2022).

> Revised Cluster Expansion Method based on Hilbert Space Geometry and GCEP Software Package Implementation, talk at Center for Nanoscale Science Interdiscplinary Research Group (IRG) (2022).

* I am extremely fortunate to be mentored by extraordinary people. I would like to mention: *

> Stephan Haas (USC), condensed matter theorist, physics dep. chair
> Scott MacDonald (USC), string theorist, physics/mathematics orator
> Aiichiro Nakano (USC), computational scientist, physicist, polymath
> Rosa Di Felice (USC), theoretical/computational physicist, quantum chemist
> Bhavna Sharma (USC), materials/environmental engineer, architect, designer
> Luqiao Liu (MIT), experimental physicist and device inventor
> Zhongqiang Hu (MIT), theoretical and experimental physicist, research mentor
> Abhinav Prem (IAS), condensed matter theorist/mathematical physicist
> Michael Markesbery (OROS Labs), inventor/entrepreneur, astronaut scholar

... in addition to everyone who is supporting me!