Pauli stabilizer models of twisted quantum doubles, and a new quantum cellular automaton (May 18, 2022)

  • Published: 2022-05-15

Time: 09:00 am, (UTC/GMT+8:00, Beijing/Shanghai), May 18 (Wed.), 2022

Zoom Meeting URL:

Meeting Room ID: 949 559 7503

Passcode: 2021


Speaker: Dr. Chen, Yu-An (Maryland)



In 2d, we construct a Pauli stabilizer model for every Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z_4 toric code. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary.

In 3d, we use this technique to construct a novel three-dimensional quantum cellular automaton (QCA) based on a system with short-range entangled bulk and chiral semion boundary topological order. We argue that either the QCA is nontrivial, i.e. not a finite-depth circuit of local quantum gates, or there exists a two-dimensional commuting projector Hamiltonian realizing the chiral semion topological order (U(1)_2 Chern-Simons theory). Our QCA is obtained by first constructing the Walker-Wang Hamiltonian of a certain premodular tensor category of order four, then condensing the deconfined bulk boson at the level of lattice operators. We show that the resulting Hamiltonian hosts chiral semion surface topological order in the presence of a boundary and can be realized as a non-Pauli stabilizer code on qubits, from which the QCA is defined. The construction is then generalized to a class of QCAs defined by non-Pauli stabilizer codes on 2^n-dimensional qudits that feature surface anyons described by U(1)_{2^n} Chern-Simons theory. Our results support the conjecture that the group of nontrivial three-dimensional QCAs is isomorphic to the Witt group of non-degenerate braided fusion categories.



[1] Tyler D. Ellison, Yu-An Chen, Arpit Dua, Wilbur Shirley, Nathanan Tantivasadakarn, Dominic J. Williamson, Pauli stabilizer models of twisted quantum doubles, arXiv:2112.11394, PRX Quantum 3, 010353 (2022)
[2] Wilbur Shirley, Yu-An Chen, Arpit Dua, Tyler D. Ellison, Nathanan Tantivasadakarn, Dominic J. Williamson, Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond, arXiv:2202.05442, PRX Quantum (accepted)


About the speaker:

Yu-An is the current JQI Postdoctoral Fellow and a condensed matter theorist at the University of Maryland. He is interested in studying topological phases of matter and quantum information. His PhD work at Caltech focused on bosonization, a mapping between fermionic and bosonic systems, which is used for quantum simulation and the construction of fermionic topological phases. This approach utilizes many tools in the algebraic topology. He also joined the Google Quantum AI team, working on quantum simulations of fermions. After his PhD, he works cover topological phases, gravitational anomalies, Pauli stabilizer models, quantum cellular automata, and error-correcting codes for fermions. Yu-An’s research style is the hybridization of math, condensed matter, and quantum information.