PROJECTS

Quantum Monte Carlo (QMC) is a computational method to simulate many-body quantum systems. In this work, we have proposed a QMC algorithm using Permutation Matrix Representation (PMR) for arbitrary spin-1/2 Hamiltonians, and have provided a full computational package on GitHub.

Continuous weak measurement could allow one to detect errors and thereby correct them. In time-dependent Hamiltonians, we explore the performance of a quantum feedback mechanism using continuous weak measurements.

The mathematical framework of non-abelian anyons with topological defects can be explored using a framework known as G-crossed modular tensor categories. In this work, we show an intrinsic connection between topology of higher genus surfaces and fusion categories of topological defects.

The Eigenstate Thermalization Hypothesis (ETH) postulates that pure quantum systems that are chaotic do self-thermalize in the long-time limit. The presence of a large number of symmetries generally prevents a quantum system from thermalizing. We extend the ETH hypothesis to systems with non-abelian SU(2) symmetry.