Rihaan Shah
This researcher has not added a scholarly bio yet.
8
Research projects
0
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.
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.
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.
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.
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.
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.
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 Quantum Field Theory Made From 19 Atoms
A programmable chain of neutral atoms has made the excitation spectrum of conformal field theory directly measurable, turning a mathematical framework used across critical phenomen
Majorana 2: The 20-Second Bet on Topological Quantum Computing
Microsoft’s second-generation Majorana processor replaces aluminum with lead, reports parity stability thousands of times longer than its previous devices, and puts one of quantum
Dimensions You Can Program
Synthetic dimensions let physicists use spin states, frequencies, momentum modes, and driven quantum dynamics as extra coordinates, creating experimental worlds whose geometry cann
The Magnet That Creates Its Own Light
In quantum spin ice, frustrated atomic magnets can reorganize themselves into an emergent version of electrodynamics, complete with photon-like waves, fractionalized charges, monop
When Hot Quantum Systems Cool Faster
The quantum Mpemba effect reveals that distance from equilibrium does not determine how quickly a system returns to it. Sometimes the state that begins farther away gets there firs
When Empty Space Decays
Quantum field theory allows a vacuum to be only temporarily stable. Its escape does not begin everywhere at once, but through a microscopic bubble created by quantum tunneling, a p