中国科学技术大学：Simulation for the feature of non-Abelian anyons in quantum double model using quantum state preparation

Simulation for the feature of non abelian anyons in quantum double model using quantum state preparation Zheng-Wei zhou(周正威) Key Lab of Quantum Information, CAS, USTC In collaboration with Univ. of sci. Tech. of china XW.Luo(罗希望) Y-J.Han(韩永建) XX.Zhou(周幸祥) G.C.Guo(郭光灿) Jinhua Aug 14, 2012

Simulation for the feature of non-Abelian anyons in quantum double model using quantum state preparation Jinhua Aug 14, 2012 Zheng-Wei Zhou(周正威） Key Lab of Quantum Information , CAS, USTC In collaboration with: Univ. of Sci. & Tech. of China X.-W. Luo (罗希望) Y.-J. Han (韩永建) X.-X. Zhou (周幸祥) G.-C. Guo (郭光灿)

Outline a. Some backgrounds on Quantum simulation Introduction to topological quantum computing based on Kitaev's group algebra(quantum double)model a Il. Simulation for the feature of non-abelian anyons in quantum double model using quantum state preparation a Summary

Outline ◼ I. Some Backgrounds on Quantum Simulation ◼ II. Introduction to topological quantum computing based on Kitaev’s group algebra (quantum double) model ◼ III. Simulation for the feature of non-Abelian anyons in quantum double model using quantum state preparation ◼ Summary

. Backgrounds on Quantum Simulation

I. Backgrounds on Quantum Simulation

Nature isnt classical. and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and it's a wonderful problem, because it doesn 't look so easy. (Richard Feynman) KI+ l,+1] Ⅳ7)=exp(-iHnT)y0

“Nature isn't classical, and if you want to make a simulation of Nature, you'd better make it quantum mechanical, and it's a wonderful problem, because it doesn't look so easy.” (Richard Feynman)

Why Quantum Simulation? Answer 1: Where present many body theory fails . so far Example: 2D Fermi Hubbard Fermi liquid H=-t2(ci o +cfo Cio)+u2n, n, i,0 doped resonant valence bond(rvb)state(?) half-filling(parent compounds hole-doping superposition of singlet coverings hole pairs condense(BCs) 只+… other: time dependent problems, quantum chemistry, quantum simulation as interplay between theory and experiment

Why quantum simulation is important? Answer 2: simulate and build new virtual quantum materials Kitaev's models 3.5 ky/T P2 PI 05 H=∑(1-4s)+∑(1-B(p) ∑A topological quantum v=x, ),z:,/ computing

Why quantum simulation is important? Answer 2: simulate and build new virtual quantum materials. Kitaev’s models topological quantum computing

Physical Realizations for quantum simulation Atoms lons Electrons G B E H 2 lulia buluta and franco nor Science 326.108

Physical Realizations for quantum simulation Iulia Buluta and Franco Nori, Science 326,108

lI. Introduction to topological quantum computing based on Kitaev's group algebra quantum double) model

II. Introduction to topological quantum computing based on Kitaev’s group algebra (quantum double) model

A: Toric codes and the corresponding hamiltonians plague operators 7=ⅡIze e∈p ertex operators qubits on links e∈ 01 0-1 10 IX H=-(∑S+∑S

A: Toric codes and the corresponding Hamiltonians qubits on links plaque operators: vertex operators:

Hamiltonian and ground states: plaque operators H ∑Sp+∑S Sp=llZe e∈p Sv)=spv)sp∈{-1,+1 vertex operators X Sy)=slv)S∈{-1,+1 e∈0 ground state has all Sp= Sv=+l 仁亡L II Sp=I I Su=I every energy level is 4-fold degenerate

Hamiltonian and ground states: ground state has all plaque operators: vertex operators: every energy level is 4-fold degenerate!!