Abhinav Muraleedharan

PhD Student, Computer Science · University of Toronto

I'm currently a CS PhD student at the University of Toronto, where I work under the supervision of Prof. Nathan Wiebe. My research spans quantum algorithms, machine learning, and the interpretability and alignment of AI systems.

I'm especially interested in bringing ideas from physics and dynamical systems to bear on computation: designing quantum algorithms that simulate complex classical dynamics, and understanding when our tools for interpreting and steering neural networks can be trusted. In summer 2025 I was a research intern at Pacific Northwest National Laboratory (PNNL). Before my PhD, I completed an MEng at the University of Toronto Institute for Aerospace Studies, where my thesis studied retention-based autoregressive models for modelling neural dynamics.

Quantum Algorithms
Machine Learning
Interpretability
AI Alignment

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Recent Talk

Quantum Neural ODEs

Fields Institute for Research in Mathematical Sciences

Research

I work across quantum computing, AI safety, and reinforcement learning.

Quantum algorithms. Algorithms for simulating physical systems, including driven, time-dependent and nonlinear classical dynamics, and for training large-scale machine learning models.
Interpretability and alignment. Understanding when interpretability tools for large language models, such as linear probes and steering vectors, can be trusted and when they break down.
Reinforcement learning. Methods that go beyond dynamic programming to compute optimal long-horizon behavior directly, toward training generally intelligent agents.

Overview of nonlinear Schrödingerization

Simulating Time-Dependent and Nonlinear Classical Oscillators through Nonlinear Schrödingerization

Abhinav Muraleedharan, Nathan Wiebe

PreprintarXiv, 2025

Quantum computers can simulate the dynamics of 2ⁿ coupled harmonic oscillators in time polynomial in n, an exponential speedup over classical methods. Real physical systems, however, are rarely that clean: they are driven by time-dependent forces, have stiffness that changes over time, and include nonlinear interactions. Existing quantum algorithms do not cover these cases, which limits where the speedup can actually be used.

In this work we introduce nonlinear Schrödingerization. We rewrite the classical dynamics as a nonlinear Schrödinger equation, reduce it to a time-independent one using perturbative techniques, and handle weak nonlinearities by embedding them in a linear Schrödinger equation on a higher-dimensional space. Standard Hamiltonian simulation algorithms then apply. When the system can be queried and the initial state prepared efficiently, the cost is polynomial in n and nearly linear in evolution time for most systems. This extends quantum simulation to non-conservative and nonlinear classical systems.

arXiv BibTeX

Epsilon-close latents diverging with depth

On the Limits of Linear Representation Hypotheses in Large Language Models: A Dynamical Systems Analysis

Abhinav Muraleedharan

NeurIPS 2025 WorkshopMechanistic Interpretability Workshop

Linear representation hypotheses and steering vectors assume that perturbations in latent space produce predictable changes in model behavior. We give a theoretical critique of this view by treating deep residual networks as dynamical systems. We prove that two latent vectors that start ε-close can diverge exponentially within O(log(1/ε)) layers under positive Lyapunov exponents. This sensitivity to initial conditions makes linear approximations unreliable in deep networks, and gives a theoretical account of the limits of current interpretability methods.

OpenReview PDF

Beyond Dynamic Programming

Abhinav Muraleedharan

PreprintarXiv, 2023

In this paper, I introduced Score-life programming, a novel theoretical approach for solving reinforcement learning problems. In contrast with classical dynamic programming-based methods, the methods in this work can search over non-stationary policy functions, and can directly compute optimal infinite horizon action sequences from a given state.

arXiv BibTeX

Experience

Research Intern

Pacific Northwest National Laboratory (PNNL)

Summer 2025

Teaching

Teaching Assistant · University of Toronto

CSC2332HFIntroduction to Quantum Algorithms
CSC413H1S / CSC2516HSNeural Networks and Deep Learning
CSC236H1FIntroduction to the Theory of Computation
CSC165H1S-BMathematical Expression and Reasoning for Computer Science

Course Instructor · Outreach

UofT Engineering Outreach OfficeDEEP Summer Academy
UofT Math Outreach OfficeMath Outreach Programs

Honors

Finalist, Indian Innovation Challenge · 2017

Academic Service

Reviewer, Quantum Computing Theory in Practice (QCTiP) · 2026