题 目： Experimentally Identifying Topological Order by Measuring the Modular Matrices

时 间： 11月30日（周三）下午4：00

报告人： 彭新华 教授

中国科学技术大学 国家杰出青年基金获得者

地 点： 量子楼410报告厅

报告简介：Experimentally Identifying Topological Order by Measuring the Modular Matrices

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered state in fractional quantum Hall systems in the 1980s. Topological orders are exotic states of matter characterized by patterns of long-range entanglement that lie beyond Landau's symmetry breaking paradigm \cite{Wen1990TO}. One important theoretical question is how we should characterize these phases. In 2+1 dimensions, plenty of numerical evidence suggests that the \emph{modular matrices}, S and T \cite{WenPRL2015}, suffice to characterize the order completely, which has more advantages than topological entanglement entropy \cite{TEE2}. However, we are not aware of any prior experimental progress in this direction.

Along the lines suggested by Feynman \cite{Feynman1982}, complex quantum systems can be efficiently simulated on quantum simulators, i.e., programmable

quantum systems whose dynamics can be efficiently controlled. Quantum simulations thus offer the possibility to investigate strongly correlated systems exhibiting topological orders and other complex quantum systems that are challenging for simulations

on classical computers.

Using a kind of nuclear magnetic resonance simulator \cite{Pengreview,Peng2014}, we propose and experimentally demonstrate, for the first time, that given just the Hamiltonian, in this case, the toric code Hamiltonian, the topological characterizing property — the modular S, T matrices — has been measured and recovered with precision without ever relying on theoretical solution of the Hamiltonian \cite{Luo2016}. This allows one to thus identify the phase uniquely purely from experimental means. This is an important proof-of-principle experiment: current technologies, combined with novel methodologies, enable one to physically identify these phases uniquely and recover these topological fingerprints. These open up new future avenues toward identifying more generic topological orders based purely on experimental measurements and open doors to possible applications (e.g., fault torrent quantum computation).