Realizing quantum speed limit in open system with a PT -symmetric trapped-ion qubit

Abstract Faster quantum gate operation time is one of the key issues in quantum information processing. It has a lower bound in a closed quantum system, so called quantum speed limit (QSL). But this limit could be significantly decreased in an open system, resulting in novel quantum computation schemes. Here we have experimentally studied the QSL in a non-Hermitian parity time symmetric (PT -symmetric) quantum system with a dissipative trapped-ion qubit. The QSL decreases with the increase of dissipation intensity, which is significantly smaller than that of closed system. The non-Hermitian QSL exhibits chiral dependence on the evolution path, for which we propose the non-Hermitian Bloch sphere and construct its corresponding SU(2) Lie group to explain it. Furthermore, the QSL with the anti-parity-time-symmetric system has been verified in our experiments. These results enable a wellcontrolled knob for speeding up quantum gate operation, paving the way towards faster quantum computation in an open system.