"Simulatability and Testability of Quantum States Through an Algebraic Lens"
Abstract: The classical simulation of quantum computers is a fundamental problem with both theoretical and practical implications. While universal quantum computation is believed to be infeasible for efficient classical simulation, certain restricted models can be simulated efficiently. One notable example is quantum circuits composed of Clifford gates, which can be simulated via the Gottesman-Knill theorem.
In this talk, I discuss a generalized version of this algorithm, whose efficiency is determined by a key quantity known as the stabilizer rank of magic states. I present an improvement on the lower bound of stabilizer rank and explore its complexity-theoretic implications. Additionally, I address the problem of testing stabilizer states, a class of states essential for understanding both simulation techniques and quantum error correction. In particular, I show that there exists an efficient quantum procedure to determine whether the maximum fidelity of a given quantum state with a stabilizer state falls within one of two intervals separated by a polynomial gap.
Bio: Mehrdad Tahmasbi is a Future Faculty Fellow and postdoctoral researcher in the Department of Computer Science at the University of Illinois Urbana-Champaign (UIUC). He earned his Ph.D. in Electrical Engineering from the Georgia Institute of Technology, where his dissertation received the Sigma Xi Best Ph.D. Thesis Award. Before joining UIUC, he was a postdoctoral researcher at the University of Amsterdam and Tufts University. He holds a B.Sc. from Sharif University of Technology and an M.S. in Mathematics from Georgia Tech. His research focuses on the theoretical aspects of quantum information science, particularly quantum complexity theory and quantum information theory.
To watch online go to the IQUIST youtube channel: https://www.youtube.com/channel/UCCzAySwQXF8J4kRolUzg2ww