NCSA staff who would like to submit an item for the calendar can email newsdesk@ncsa.illinois.edu.
Abstract: In this talk, we will discuss the quantum Heisenberg model and its generalizations. The quantum Heisenberg model is a family of spin glass Hamiltonians defined by nearest-neighbor interactions. This model, especially the antiferromagnetic variant, is well-studied in condensed matter physics and has recently gained attention in computer science since it can be seen as a quantum generalization of the Max-Cut problem. We will mostly focus on a generalization of the quantum Heisenberg model, known as Quantum Max-d-Cut, that deals with interactions of spins with local Hilbert space of dimension d. Similarly to Quantum Max-Cut, Quantum Max-d-Cut can be seen as the quantum generalization of Max-d-Cut. Additionally, this model is known to be universal and QMA-hard to optimize.
There has been a large body of literature recently that focuses on finding classical approximation algo-rithms for Quantum Max-Cut while not much is known for Quantum Max-d-Cut. In this talk, we will discuss a systematic study of Quantum Max d-Cut, as well as preliminary algorithmic results for approximating the ground state of the corresponding Hamiltonian.
Bio: I am a professor at University of California, Santa Cruz. My research focuses on Theoretical Computer Science, and more specifically, spectral graph theory, statistical physics, and quantum computing. I received my PhD from UC Berkeley, and have held faculty positions at UIUC and CU Boulder, prior to joining UC Santa Cruz.
To watch online go to the IQUIST youtube channel: https://www.youtube.com/channel/UCCzAySwQXF8J4kRolUzg2ww
For Zoom link you may check the IQUIST calendar weekly email or contact Hannah Stites (hstites2@illinois.edu). To subscribe to our weekly email for event announcements, please go to https://lists.illinois.edu/lists/subscribe/iquist-announcements.