Experimental Realization of non-Adiabatic Shortcut to non-Abelian Geometric Gates

When a quantum system is driven slowly through a parametric cycle in a degenerate Hilbert space, the state would acquire a non-Abelian geometric phase, which is stable and forms the foundation for holonomic quantum computation (HQC). However, in the adiabatic limit, the environmental decoherence becomes a significant source of errors. Recently, various non-adiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Here we propose and experimentally demonstrate that HQC via shortcut to adiabaticity (STA) can be constructed with only three energy levels, using a superconducting qubit. With this scheme, all holonomic single-qubit operations can be realized non-adiabatically through a single cycle evolution. As a result, we are able to experimentally benchmark the stability of STA+HQC against NHQC. The flexibility and simplicity of our scheme makes it also implementable on other quantum systems.