  High-fidelity and robust quantum manipulation is the key for scalable quantum
computation. Therefore, due to the intrinsic operational robustness, quantum
manipulation induced by geometric phases is one of the promising candidates.
However, the longer gate time for geometric operations and more
physical-implementation difficulties hinder its practical and wide
applications. Here, we propose a simplified implementation of universal
holonomic quantum gates on superconducting circuits with experimentally
demonstrated techniques, which can remove the two main challenges by
introducing the time-optimal control into the construction of quantum gates.
Remarkably, our scheme is also based on a decoherence-free subspace encoding,
with minimal physical qubit resource, which can further immune to error caused
by qubit-frequency drift, which is regarded as the main error source for large
scale superconducting circuits. Meanwhile, we deliberately design the quantum
evolution to eliminate gate error caused by unwanted leakage sources.
Therefore, our scheme is more robust than the conventional ones, and thus
provides a promising alternative strategy for scalable fault-tolerant quantum
computation.
