  Evolution time of a qubit under a Hamiltonian operation is one of the key
issues in quantum control, quantum information processing and quantum
computing. It has a lower bound in Hermitian system, which is limited by the
coupling between two states of the qubit, while it is proposed that in a
non-Hermitian system it can be made much smaller without violating the
time-energy uncertainty principle. Here we have experimentally confirmed the
proposal in a single dissipative qubit system and demonstrate that the
evolution time of a qubit from an initial state to an arbitrary state can be
controlled by tuning the dissipation intensity in a non-Hermitian
Parity-Time-Symmetric ($\mathcal{P T}$-symmetric) quantum system. It decreases
with increasing dissipation intensity and also gives a tighter bound for
quantum speed limit (QSL). We also find that the evolution time of its reversal
operation increases with the increasing dissipation intensity. These findings
give us a well-controlled knob for speeding up the qubit operation, and pave
the way towards fast and practical quantum computation, opening the door for
solving sophisticated problems with only a few qubits.
