Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit

Area of Science:

• Quantum Computing
• Condensed Matter Physics
• Quantum Simulation

Background:

• Noisy intermediate-scale quantum (NISQ) devices are powerful for analog quantum simulation.
• Quantum computers offer precise control for implementing time-dependent Hamiltonians.

Purpose of the Study:

• To experimentally realize a temporal version of the half-Bernevig-Hughes-Zhang Chern insulator using quasiperiodic driving.
• To demonstrate topological frequency conversion on a quantum computing platform.
• To theoretically investigate the implementation of Floquet Hamiltonians in many-qubit systems.

Main Methods:

• Implementing quasiperiodic driving of a single qubit on the IBM Quantum Experience.
• Utilizing simple error mitigation techniques.
• Theoretically studying many-qubit systems and multifrequency driving.

Main Results:

• Achieved high experimental fidelities (around 97%) for the simulated topological insulator.
• Inferred the presence of a topological transition from experimental data.
• Showed the feasibility of implementing a wide class of Floquet Hamiltonians theoretically.

Conclusions:

• Experimental realization of a temporal Chern insulator and topological frequency conversion is possible on NISQ devices.
• Error mitigation is effective for achieving high fidelities in quantum simulations.
• Multifrequency driving offers a promising avenue for studying many-body systems on quantum computers, with identified promises and limitations.