  Based on the geometrical nature of quantum phases, non-adiabatic holonomic
quantum control (NHQC) has become a standard technique for enhancing robustness
in constructing quantum gates. However, the conventional approach of NHQC is
sensitive to control instability, as it requires the driving pulses to cover a
fixed pulse area. Furthermore, even for small-angle rotations, all operations
need to be completed with the same duration of time. Here we experimentally
demonstrate a time-optimal and unconventional approach of NHQC (called
TOUNHQC), which can optimize the operation time of any holonomic gate. Compared
with the conventional approach, TOUNHQC provides an extra layer of robustness
to decoherence and control errors. The experiment involves a scalable
architecture of superconducting circuit, where we achieved a fidelity of 99.51%
for a single qubit gate using interleaved randomized benchmarking. Moreover, a
two-qubit holonomic control-phase gate has been implemented where the gate
error can be reduced by as much as 18% compared with NHQC.
