Rihaan Shah
@zzU8diJ8
About Me
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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.
Articles & Mentions
A Quantum Field Theory Made From 19 Atoms
A programmable chain of neutral atoms has made the excitation spectrum of conformal field theory dir...
Majorana 2: The 20-Second Bet on Topological Quantum Computing
Microsoft’s second-generation Majorana processor replaces aluminum with lead, reports parity stabili...
Dimensions You Can Program
Synthetic dimensions let physicists use spin states, frequencies, momentum modes, and driven quantum...
The Magnet That Creates Its Own Light
In quantum spin ice, frustrated atomic magnets can reorganize themselves into an emergent version of...
When Hot Quantum Systems Cool Faster
The quantum Mpemba effect reveals that distance from equilibrium does not determine how quickly a sy...
When Empty Space Decays
Quantum field theory allows a vacuum to be only temporarily stable. Its escape does not begin everyw...
The Hidden Geometry Inside a Quantum State
Electrons can carry a geometry that has nothing to do with the shape of the material. That hidden ge...
The Quantum Tail
Can quantum computers find the financial disasters that Monte Carlo sees too slowly?Most financial m...
The Black Hole Atom & Quantum Clouds
How Kerr superradiance allows rotating black holes to build macroscopic quantum clouds, lose angular...
When Measurement Creates a New Phase of Quantum Matter
Repeated observation does more than disturb a quantum system. In many-body systems, measurement can ...
The Strange Geometry of Anyons
Anyons reveal a regime of quantum mechanics in which the history of how particles move around one an...
Knots, Holes, & When Shape Becomes Physics
Topology entered physics through an idea that initially seems almost too abstract to influence an ex...
Quantum Tunneling Inside the Genetic Code
Protons inside DNA can move according to quantum mechanics, briefly changing the identity of a base ...
The Quantum Systems That Refuse to Forget
Quantum many-body scars reveal rare pathways through Hilbert space where interacting quantum systems...
The Quantum-Classical Boundary Just Moved
In 2026, physicists made metal nanoparticles containing thousands of atoms interfere like waves, pus...
The Geometry Hidden Inside a Quantum Code
AdS/CFT suggests that spacetime is encoded redundantly in quantum information. New work is asking wh...
Quantum Gravity Is Coming to the Lab
After decades as one of physics’ most theoretical problems, the quantum nature of gravity may finall...
Quantum Acoustics: Computing With the Smallest Possible Sounds
Physicists are learning to control individual quanta of vibration, turning sound inside solid materi...
Twistronics: Designing New Quantum Matter With a Tiny Rotation
By stacking atomically thin materials at carefully chosen angles, physicists are learning to enginee...
Building Tiny Universes With Quantum Simulators
Quantum devices are beginning to recreate pieces of particle physics that are extraordinarily diffic...
The Quantum Technology That May Arrive Before Quantum Computers
Quantum sensors are using some of the strangest properties of atoms to measure gravity, time, motion...
Is Reality Made of Information?
Quantum physics has forced scientists to rethink what the universe is made of. What if matter and en...
Why IBM Just Bought a Quantum Lab Owned by Boeing and GM
The race to build useful quantum computers may be becoming a race to decide what a qubit should actu...
Why High School Is the Right Time for Quantum
There is a persistent myth in science education that quantum mechanics is a subject reserved for the...
Origin Wukong: A New Archetype for Quantum Intelligence
As a brand built on high-performance research and novel tech, Quantum Spark is always scan...
Forum Activity
GPU-Accelerated State Vector vs. Tensor Network Simulation
Thread starter • 4 replies • 60 points
Scaling Superconducting vs. Trapped-Ion: The Interconnect Bottleneck
Thread starter • 5 replies • 88 points
AdS/CFT Correspondence and Quantum Information Scrambling
Thread starter • 7 replies • 34 points
Threshold Theorems for the Surface Code under Non-Markovian Noise
Thread starter • 5 replies • 68 points
Majorana Zero Modes in Hybrid Superconductor-Semiconductor Nanowires
Thread starter • 5 replies • 87 points
"The bartender thinks he saw the cat, but until I read this post, he was still in a superposition of serving a drink and ..."
"If you're interested in Physics you should definitely check out the Simulating Non-Abelian Anyons paper in the research ..."
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