Stabilizing multiple topological fermions on a quantum computer

Abstract

In classical and single-particle settings, non-trivial band topology always gives rise to robust boundary modes. For quantum many-body systems, however, multiple topological fermions are not always able to coexist, since Pauli exclusion prevents additional fermions from occupying the limited number of available topological modes. In this work, we show, through IBM quantum computers, how one can robustly stabilize more fermions than the number of topological modes through specially designed 2-fermion interactions. Our demonstration hinges on the realization of BDI- and D-class topological Hamiltonians of unprecedented complexity on transmon-based quantum hardware, and crucially relied on tensor network-aided circuit recompilation approaches beyond conventional trotterization. We also achieved the full reconstruction of multiple-fermion topological band structures through iterative quantum phase estimation (IQPE). All in all, our work showcases how advances in quantum algorithm implementation enables NISQ-era quantum computers to be exploited for topological stabilization beyond the context of single-particle topological invariants.

9 pages, 3 figures, 14 pages appendix

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• Dimensional transmutation from non-Hermiticity
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Zoology of non-Hermitian spectra and their graph topology
• Observation of the non-Hermitian skin effect and Fermi skin on a digital quantum computer
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Observation of higher-order topological states on a quantum computer
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Observing and braiding topological Majorana modes on programmable quantum simulators
• Filling up complex spectral regions through non-Hermitian disordered chains
• Anomalous topological edge modes in a periodically-driven trimer lattice
• Experimental validation of the Kibble-Zurek Mechanism on a Digital Quantum Computer
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
• Readout Error Mitigation for Mid-Circuit Measurements and Feedforward
• Efficient preparation of the AKLT State with Measurement-based Imaginary Time Evolution
• Experimental Realization of Special-Unitary Operations in Classical Mechanics by Nonadiabatic Evolutions
• Simulating quantum field theories on gate-based quantum computers
• Realizing non-trivial doublon formation using a quantum computer
• Dynamic thermalization on noisy quantum hardware