Rihaan Shah
This researcher has not added a scholarly bio yet.
8
Research projects
3
Research areas
6
Published articles
Portfolio
Research & projects
Phason Holonomy and Defect-Enriched Topological Order in Quasicrystalline String Nets
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.
Categorical Refraction at Axion–Duality Junctions
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.
Skein-Theoretic Membrane Order for Non-Abelian SET Phases
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.
Axial-Geometric Fermi-Arc Qubits
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.
Fractonic Chiral Plasma
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.
TopoEliashberg
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.
Noise-Resilient Quantum Amplitude Estimation for Asian Option Pricing
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.
Simulating Non-Abelian Anyons
Successfully demonstrated methods for simulating non-Abelian anyons in controllable quantum systems, enabling observation of their braiding behavior relevant to topological quantum computation.
Writing
Published articles
A Spin in a Molecule, a Photon in a Network: The New Chemistry of Quantum Interfaces
The molecule that links a spin to a photon A useful quantum-network node must perform two tasks that are usually optimized in different materials. It must preserve a quantum state
The Walls Remember: How Nanometre Blisters Store Ionic Information
When a channel remembers the voltage A nanometre-wide channel filled with salt water can respond differently to the same applied voltage depending on what happened a few seconds ea
Six Seconds of Gamma Rays: How Bayesian Physics Locates Invisible Sources
What six seconds of radiation can reveal A helicopter passes over a field at roughly ten metres per second. A scintillation detector aboard the aircraft records a sequence of gamma
Could Every Particle Hide a Black Hole? The Planck Boundary Between Matter and Spacetime
An elementary particle and an event horizonAn electron has mass, electric charge and angular momentum. So does a rotating, electrically charged solution of Einstein's gravitational
When a Quantum Error Crosses the Network: The First Distributed Syndrome Measurements
One logical state, two separate machines A quantum computer assembled from independent processors must do more than exchange entanglement. If a protected quantum state spans severa
When One Laser Pulse Is Not Enough: Coherent Control of a Sliding Ferroelectric
A crystal driven by the timing of lightOptical control of a crystal is often described as a problem of delivering enough energy to move its atoms. For a coherent vibration, however