Digital Simulation of Topological Matter on Programmable Quantum Processors

Abstract

Simulating the topological phases of matter in synthetic quantum simulators is a topic of considerable interest. Given the universality of digital quantum simulators, the prospect of digitally simulating exotic topological phases is greatly enhanced. However, it is still an open question how to realize digital quantum simulation of topological phases of matter. Here, using common single- and two-qubit elementary quantum gates, we propose and demonstrate an approach to design topologically protected quantum circuits on the current generation of noisy quantum processors where spin-orbital coupling and related topological matter can be digitally simulated. In particular, a low-depth topological quantum circuit is performed on both IBM and Rigetti quantum processors. In the experiments, we not only observe but also distinguish the 0 and $\pi$ energy topological edge states by measuring qubit excitation distribution at the output of the circuits.

arXiv comment8 pages, 4 figures, Accepted by PRL

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• Stabilizing multiple topological fermions on a quantum computer
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• Observation of higher-order topological states on a quantum computer
• Doubly Modulated Optical Lattice Clock Interference and Topology
• Quench dynamics of the Schwinger model via variational quantum algorithms
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• Visualizing higher-fold topology in chiral crystals
• Robust measurement of wave function topology on NISQ quantum computers
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Quantum computing topological invariants of two-dimensional quantum matter
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• Floquet Amorphous Topological Orders in a One-dimensional Rydberg Glass
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
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• Efficient Berry Phase Calculation via Adaptive Variational Quantum Computing Approach
• Realizing non-trivial doublon formation using a quantum computer
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