105 citations · 614 across the 24 of their papers we have counts for
25 papers
Generalized Kitaev Spin Liquid model and Emergent Twist Defect
Bowen Yan, Penghua Chen, Shawn X. Cui
The Kitaev spin liquid model on honeycomb lattice offers an intriguing feature that encapsulates both Abelian and non-Abelian anyons. Recent studies suggest that the comprehensive…
Quantum circuits for toric code and X-cube fracton model
Penghua Chen, Bowen Yan, Shawn X. Cui
We propose a systematic and efficient quantum circuit composed solely of Clifford gates for simulating the ground state of the surface code model. This approach yields the ground s…
Ternary Logic Design in Topological Quantum Computing
Muhammad Ilyas, Shawn Cui, Marek Perkowski
A quantum computer can perform exponentially faster than its classical counterpart. It works on the principle of superposition. But due to the decoherence effect, the superposition…
Constructing Approximately Diagonal Quantum Gates
Colton Griffin, Shawn X. Cui
We study a method of producing approximately diagonal 1-qubit gates. For each positive integer, the method provides a sequence of gates that are defined iteratively from a fixed di…
From Torus Bundles to Particle-Hole Equivariantization
Shawn X. Cui, Paul Gustafson, Yang Qiu +1
We continue the program of constructing (pre)modular tensor categories from 3-manifolds first initiated by Cho-Gang-Kim using theory in physics and then mathematically studied…
Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras
Penghua Chen, Shawn X. Cui, Bowen Yan
Kitaev's quantum double model is a family of exactly solvable lattice models that realize two dimensional topological phases of matter. Originally it is based on finite groups, and…
From Three Dimensional Manifolds to Modular Tensor Categories
Shawn X. Cui, Yang Qiu, Zhenghan Wang
Using M-theory in physics, Cho, Gang, and Kim (JHEP 2020, 115 (2020) ) recently outlined a program that connects two parallel subjects of three dimensional manifolds, namely, geome…
4-Manifold Invariants From Hopf Algebras
Julian Chaidez, Jordan Cotler, Shawn X. Cui
The Kuperberg invariant is a topological invariant of closed 3-manifolds based on finite-dimensional Hopf algebras. In this paper, we initiate the program of constructing 4-manifol…
Kitaev's quantum double model as an error correcting code
Shawn X. Cui, Dawei Ding, Xizhi Han +4
Kitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum…
The Search For Leakage-free Entangling Fibonacci Braiding Gates
Shawn X. Cui, Kevin T. Tian, Jennifer F. Vasquez +2
It is an open question if there are leakage-free entangling Fibonacci braiding gates. We provide evidence to the conjecture for the negative in this paper. We also found a much sim…
On Generalized Symmetries and Structure of Modular Categories
Shawn X. Cui, Modjtaba Shokrian Zini, Zhenghan Wang
Pursuing a generalization of group symmetries of modular categories to category symmetries in topological phases of matter, we study linear Hopf monads. The main goal is a generali…
Bit Threads and Holographic Monogamy
Shawn X. Cui, Patrick Hayden, Temple He +3
Bit threads provide an alternative description of holographic entanglement, replacing the Ryu-Takayanagi minimal surface with bulk curves connecting pairs of boundary points. We us…
On Two Invariants of Three Manifolds from Hopf Algebras
Liang Chang, Shawn X. Cui
We prove a 20-year-old conjecture concerning two quantum invariants of three manifolds that are constructed from finite dimensional Hopf algebras, namely, the Kuperberg invariant a…
State Sum Invariants of Three Manifolds from Spherical Multi-fusion Categories
Shawn X. Cui, Zhenghan Wang
We define a family of quantum invariants of closed oriented -manifolds using spherical multi-fusion categories. The state sum nature of this invariant leads directly to -…
Diagonal gates in the Clifford hierarchy
Shawn X. Cui, Daniel Gottesman, Anirudh Krishna
The Clifford hierarchy is a set of gates that appears in the theory of fault-tolerant quantum computation, but its precise structure remains elusive. We give a complete characteriz…
Quantum Capacities for Entanglement Networks
Shawn X Cui, Zhengfeng Ji, Nengkun Yu +1
We discuss quantum capacities for two types of entanglement networks: for the quantum repeater network with free classical communication, and for the te…
Improved Quantum Ternary Arithmetics
Alex Bocharov, Shawn X. Cui, Martin Roetteler +1
Qutrit (or ternary) structures arise naturally in many quantum systems, particularly in certain non-abelian anyon systems. We present efficient circuits for ternary reversible and…
On Gauging Symmetry of Modular Categories
Shawn X. Cui, César Galindo, Julia Yael Plavnik +1
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase indu…
Quantum Max-flow/Min-cut
Shawn X. Cui, Michael H. Freedman, Or Sattath +2
The classical max-flow min-cut theorem describes transport through certain idealized classical networks. We consider the quantum analog for tensor networks. By associating an integ…
Generalized Graph States Based on Hadamard Matrices
Shawn X Cui, Nengkun Yu, Bei Zeng
Graph states are widely used in quantum information theory, including entanglement theory, quantum error correction, and one-way quantum computing. Graph states have a nice structu…
On Enriching the Levin-Wen model with Symmetry
Liang Chang, Meng Cheng, Shawn X. Cui +6
Symmetry protected and symmetry enriched topological phases of matter are of great interest in condensed matter physics due to new materials such as topological insulators. The Lev…
Framed Cord Algebra Invariant of Knots in
Shawn X. Cui, Zhenghan Wang
We generalize Ng's two-variable algebraic/combinatorial -th framed knot contact homology for framed oriented knots in to knots in , and prove that the resu…
Universal Quantum Computation with Metaplectic Anyons
Shawn X. Cui, Zhenghan Wang
We show that braidings of the metaplectic anyons in with their total charge equal to the metaplectic mode supplemented with measurements of the total ch…
Universal quantum computation with weakly integral anyons
Shawn X. Cui, Seung-Moon Hong, Zhenghan Wang
Harnessing non-abelian statistics of anyons to perform quantum computational tasks is getting closer to reality. While the existence of universal anyons by braiding alone such as t…