Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion

Abstract

For circuit-based quantum computation, experimental implementation of universal set of quantum logic gates with high-fidelity and strong robustness is essential and central. Quantum gates induced by geometric phases, which depend only on global properties of the evolution paths, have built-in noise-resilience features. Here, we propose and experimentally demonstrate nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped 171 Yb + ion based on four-level systems with resonant drives. We confirm the implementation with measured gate fidelity through both quantum process tomography and randomized benchmarking methods. Meanwhile, we find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies. Compared with previous implementations on three-level systems, our experiment share both the advantage of fast nonadiabatic evolution and the merit of robustness against systematic errors, and thus retains the main advantage of geometric phases. Therefore, our experiment confirms a promising method for fast and robust holonomic quantum computation.

Composite Short-path Nonadiabatic Holonomic Quantum Gates

“…Another method of getting faster holonomic quantum gates is achieved via shortening the evolution path [40,41]. Besides the gate-time consideration, the pulse shaping technique is also applied in NHQC schemes [42][43][44][45][46] with experimental demonstrations [47][48][49][50][51][52], mainly to strength the gate-robustness.…”

“…Interestingly, the population of excited state will decrease with the increase of the composite pulse sequence in our S-NHQC, and thus improves both the gate fidelity and robustness. This is distinct from the conventional NHQC schemes [42][43][44][45][46][47][48][49][50][51][52] with dynamical decoupling pulse [55] and pulse shaping, where the gate robustness is obtained at the cost of decreasing the gate-fidelity. In addition, we compare our CS-NHQC scheme with the conventional dynamical scheme, and our scheme performs better in certain parameters ranges.…”

Ultrafast Holonomic Quantum Gates

“…Recently, the research in this field is extended to investigate and implement the nonadiabatic holonomic quantum computation (NHQC) [21,22] based on the non-Abelian geometric phase, as it is faster than the adiabatic case and can naturally be used to construct universal quantum gates. At present, the better robust performance of geometric quantum computation has been theoretically investigated [20,[23][24][25][26][27] and some of them have already been experimentally demonstrated [28][29][30][31][32].…”

Noncyclic nonadiabatic holonomic quantum gates via shortcuts to adiabaticity

“…As the first stage, the conventional encoding methods have been proposed [12,[34][35][36][37][38][39][40][41][42][43][44], which require more resources of physical qubits. Then, other quantum control techniques are introduced in cooperating with NHQC, such as the composite scheme or dynamical decoupling strategy [45][46][47], the delib- * zyxue83@163.com erately optimal pulse control technique [48][49][50][51][52][53][54][55], and complex pulses target to shorten the gate-time [56][57][58][59][60], etc. However, these kinds of enhancement of gate robustness either need deliberate control of experimental pulse or greatly lengthen the gate-time.…”