2D Quon Language: Unifying Framework for Cliffords, Matchgates, and Beyond
Byungmin Kang | MIT
Classical simulation of generic quantum many-body states is intractable, yet special circuit families—Clifford and matchgate—admit efficient algorithms. This talk presents a unifying diagrammatic framework, the 2D Quon language, that reveals these two families as distinct special cases of a single underlying structure. Quon combines Majorana worldlines with spacetime topology to represent quantum processes and tensor networks; it is universal, but yields efficient, visually recognizable characterizations of both Clifford and matchgate classes. Building on this, I will introduce several new families of tractable tensor networks—punctured matchgates, hybrid Clifford-matchgate-MPS, and ansatze generated from factories of tractable networks—that exhibit high non-Cliffordness, high non-matchgateness, and large bipartite entanglement entropy while remaining tractable. If time permits, I will discuss new results on applying these ansatz states to quantum many-body and quantum chemistry problems. Based on https://arxiv.org/abs/2505.06336
Location
- QNC 3206
- Online on Zoom
- Meeting ID: 947 4585 9651
- Passcode: 426855