Research organized around questions, contributors, and public outputs.

Topology, TQFT

Quasicrystals possess collective phason degrees of freedom whose natural configuration space is the tiling hull and its singular strata rather than ordinary physical space. This paper constructs a topological framework to determine when closed phason cycles induce non-Abelian unitaries on the topologically degenerate Hilbert spaces of two-dimensional intrinsic topological orders. The central object of study is a projective adiabatic representation $\rho_{\text{ph}}: \pi_1(\Omega_{\text{QC}} \setminus \Delta, \lambda_0) \to \text{PU}(\mathcal{H}_{\text{top}})$, defined over a finite-local-complexity tiling hull or approximant configuration space $\Omega_{\text{QC}}$ with a discriminant locus $\Delta$ removed. By evaluating a hierarchy of models spanning toric code, quantum double $D(S_3)$, and Fibonacci Levin-Wen phases, we establish that defect-free local phason motion related by natural string-net recellulations yields at most an Abelian Berry phase. Conversely, non-Abelian holonomy arises when phason cycles enclose defects carrying nontrivial braided autoequivalences of the underlying anyon category, acting on Wilson-line algebras as twist-defect monodromies.

Rihaan Shah

Quantum Materials

The project introduces a novel quantum computing architecture that leverages the unique properties of Weyl semimetals to create highly stable qubits. By utilizing strain-induced axial gauge fields rather than traditional electromagnetic controls, the design naturally shields the circuit from common sources of environmental noise.

Rihaan Shah

Condensed Matter Physics

The research explores the theoretical intersection of chiral matter and fracton physics. It investigates what happens when quantum anomalies generate new particles in systems where the movement of isolated charges is strictly forbidden by multipole conservation laws. Instead of flowing as standard electrical currents, the newly created chiral charges are forced into restricted mobility patterns to form a fractonic chiral plasma. The study demonstrates that these charges transform into exotic states like mobile dipoles, one-dimensional lineons, or specialized surface currents, fundamentally altering our understanding of quantum transport in heavily constrained systems.

Rihaan Shah

Quantum Materials

The TopoEliashberg project introduces a computational framework designed to discover advanced quantum materials that host Majorana phases. These phases are critical for future quantum computing technologies. By combining advanced simulations of crystal structures, magnetic properties, and electron-phonon interactions, the framework maps out how superconductivity behaves at the atomic level in complex layered materials. Specifically, it investigates stacks of altermagnets, polar control interfaces, and superconductors to see if their topological properties can be electrically switched on and off. The overall goal is to provide a rigorous roadmap for predicting robust quantum states using realistic, material-specific data rather than simplified theoretical models.

Rihaan Shah

TQFT, CFT

In four-dimensional theoretical physics, domain walls can alter the fundamental properties of fields crossing them. When an axion domain wall intersects with an electromagnetic duality wall, a mathematical contradiction arises because their respective physical transformations do not commute. The project provides a theoretical framework for resolving this structural mismatch at their two-dimensional intersection. It introduces a phenomenon called categorical refraction, where quantum lines traveling through the junction split into multiple outgoing dyonic sectors. This splitting requires new localized quantum states to resolve the charge mismatch and preserve the underlying symmetry.

Rihaan Shah

TQFT, Tensor Networks

In quantum physics, scientists use mathematical tools to identify hidden symmetries in complex materials known as topological phases. Previous methods relied on simple numbers, or scalars, to measure these symmetries, which often accidentally erased crucial details about how particles interact. The current research introduces a new, matrix-based measurement tool. By keeping the full mathematical matrix rather than compressing it into a single number, physicists can now detect subtle, previously invisible interactions and structural details in non-Abelian quantum systems.

Rihaan Shah

Networking

Successfully demonstrated a new protocol for high-fidelity teleportation over long distances using entangled photon pairs.

Independent project

Quantum ML

Applying quantum kernel methods to analyze complex climate patterns and improve prediction models for extreme weather events.

Independent project

Astro-Quantum

Quantum circuit framework for modeling black hole information scrambling using OTOCs, introducing a noise-corrected method (NC-OTOC) that enables accurate extraction of scrambling dynamics and Lyapunov exponents from noisy quantum hardware.

Independent project

Topological

Successfully demonstrated methods for simulating non-Abelian anyons in controllable quantum systems, enabling observation of their braiding behavior relevant to topological quantum computation.

Rihaan Shah · Alice Johnson

Many-Body Systems

Large matrix-style Ising spin systems can be approximated by a smoother bosonic model and can undergo a topological phase transition where the structure of spin interactions changes, competing with glassy and magnetic order at low temperatures.

Independent project

Quantum Optimization

Density-Adaptive Quantum Walks and QUBO-based signal scheduling to optimize urban traffic flow. By combining dynamic routing with intersection synchronization, the framework maintains a significant congestion reduction advantage over classical Dijkstra-based baselines while remaining compatible with near-term NISQ hardware.

Independent project

Quantum Chemistry

Implementing VQE algorithms to simulate molecular ground states for drug discovery applications. Focus on optimizing ansatz.

Independent project

Quantum Finance

Quantum algorithm for pricing Asian options using the Heston model, showing how to maintain a speed advantage over classical computers by using error mitigation (Zero-Noise Extrapolation) to handle hardware noise.

Rihaan Shah