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 nonadiabatic holonomic quantum computation (NHQC) schemes have been proposed, but all at the price of increased sensitivity to control errors. Alternatively, there exist theoretical proposals for speeding up HQC by the technique of “shortcut to adiabaticity” (STA), but no experimental demonstration has been reported so far, as these proposals involve a complicated control of four energy levels simultaneously. 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. With this scheme, all holonomic single-qubit operations can be realized nonadiabatically through a single cycle of state evolution. As a result, we are able to experimentally benchmark the stability of $\mathrm{STA}+\mathrm{HQC}$ against NHQC in the same platform. The flexibility and simplicity of our scheme makes it also implementable on other systems, such as nitrogen-vacancy center, quantum dots, and nuclear magnetic resonance. Finally, our scheme can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates.

• Received 31 July 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.080501