Learning Local Gibbs States from Noisy Shallow Quantum Circuits

Understand how different noise mechanisms impact the structure of Gibbs states generated by local, shallow quantum circuits (k-local, depth O(log n)). Gibbs states represent thermal equilibrium and have relevance to both quantum simulation and quantum machine learning, but their behavior under realistic noise is not well understood.

Used tensor network methods via the Quimb library to simulate noisy quantum circuits and study their output states computationally. The main focus was depolarizing noise, which is the most physically natural model for many qubit architectures, with additional discussion of amplitude damping. Systems of up to 8 qubits were simulated, pushing the practical limits of exact classical simulation.

Full analytical validation was not tractable within the scope of the project. Instead, I performed extensive sanity checks and consistency comparisons across different circuit depths and noise strengths to build confidence in the observed behavior and the correctness of the simulation implementation.

A 40-page master's thesis and an original conjecture relating noise strength to the structure of thermal states generated by these circuits. The work sits at the intersection of quantum information theory, statistical mechanics, and numerical simulation.