Quantum simulation of topological zero modes on a 41-qubit superconducting processor

Abstract

Quantum simulation of different exotic topological phases of quantum matter on a noisy intermediate-scale quantum (NISQ) processor is attracting growing interest. Here, we develop a one-dimensional 43-qubit superconducting quantum processor, named as Chuang-tzu, to simulate and characterize emergent topological states. By engineering diagonal Aubry-Andr$\acute{\mathrm{e}}$-Harper (AAH) models, we experimentally demonstrate the Hofstadter butterfly energy spectrum. Using Floquet engineering, we verify the existence of the topological zero modes in the commensurate off-diagonal AAH models, which have never been experimentally realized before. Remarkably, the qubit number over 40 in our quantum processor is large enough to capture the substantial topological features of a quantum system from its complex band structure, including Dirac points, the energy gap's closing, the difference between even and odd number of sites, and the distinction between edge and bulk states. Our results establish a versatile hybrid quantum simulation approach to exploring quantum topological systems in the NISQ era.

Main text: 6 pages, 4 figures; Supplementary: 16 pages, 14 figures

References in corpus (6)

• Charge insensitive qubit design derived from the Cooper pair box
• Dynamical control of matter-wave tunneling in periodic potentials
• Spectral signatures of many-body localization with interacting photons
• Observation of parity-time symmetry breaking in a single spin system
• Noisy intermediate-scale quantum computers
• Observation of critical phase transition in a generalized Aubry-André-Harper model on a superconducting quantum processor with tunable couplers

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