Experimental Realization of Nonadiabatic Shortcut to Non-Abelian Geometric Gates

Holonomic quantum computation (HQC) represents a promising solution to error suppression in controlling qubits, based on non-Abelian geometric phases resulted from adiabatic quantum evolutions as originally proposed. To improve the relatively low speed associated with such adiabatic evolutions, various non-adiabatic holonomic quantum computation schemes have been proposed,but all at the price of increased sensitivity of control errors. An alternative solution to speeding up HQC is to apply the technique of "shortcut to adiabaticity", without compromising noise resilience. However, all previous proposals employing this technique require at least four energy levels for implementation. Here we propose and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture. Within this scheme, arbitrary holonomic single-qubit operation can be realized non-adiabatically through a single cycle of state evolution. Specifically, we experimentally verified that HQC via shortcut to adiabaticity can be optimized to achieve better noise resilience compared to non-adiabatic HQC. In addition, the simplicity of our scheme makes it readily implementable on other platforms including nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance, etc. These results establish that HQC via shortcut to adiabaticity can be a practical and reliable means to improve qubit control for approaching the error threshold of fault-tolerant quantum computation.