Universal single-qubit non-adiabatic holonomic quantum gates in optomechanical systems

Vahid Azimi Mousolou, C. M. Canali, Erik Sjöqvist

Shi Hu, Wen‐Xue Cui, Qi Guo +3 more

Shan‐Shan Chen, Hao Zhang, Xue‐Ke Song +3 more

Abstract The nonadiabatic holonomic quantum computation has attracted much attention in recent years because of its fastness and robustness. Here, the first scheme to realize theoretically universal single‐qubit gates on an optomechanical system working with nonadiabatic geometric phases is proposed. These quantum gates are robust to the control errors and parameter fluctuations. They can be used to achieve efficiently both quantum state transfer and entanglement generation between two optical modes via the intermediate action of a mechanical mode, showing that they are useful in robust quantum information processing.

Chunfang Sun, Gangcheng Wang, Chunfeng Wu +4 more

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of (N - 2)/N. The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.

Zhikun Han, Yuqian Dong, Bao-Jie Liu +14 more

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.

Vladimir S. Malinovsky, S. Rudin