# Experimental realization of non-Abelian non-adiabatic geometric gates

@article{Abdumalikov2013ExperimentalRO, title={Experimental realization of non-Abelian non-adiabatic geometric gates}, author={Abdufarrukh A. Abdumalikov and Johannes M. Fink and Kristinn J{\'u}l{\'i}usson and Marek Pechal and Simon A. Berger and Andreas Wallraff and Stefan Filipp}, journal={Nature}, year={2013}, volume={496}, pages={482-485} }

The geometric aspects of quantum mechanics are emphasized most prominently by the concept of geometric phases, which are acquired whenever a quantum system evolves along a path in Hilbert space, that is, the space of quantum states of the system. The geometric phase is determined only by the shape of this path and is, in its simplest form, a real number. However, if the system has degenerate energy levels, then matrix-valued geometric state transformations, known as non-Abelian holonomies—the… Expand

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The experiment shows that all-geometric and potentially robust quantum computation can be realized with solid-state spin quantum bits, making use of recent advances in the coherent control of this system. Expand

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This work proposes and experimentally demonstrate that HQC via shortcut to adiabaticity can be constructed with only three energy levels, using a superconducting qubit in a scalable architecture and can be extended to construct two-qubit holonomic entangling gates, leading to a universal set of STAHQC gates. Expand

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Non-Abelian geometric phase in laser-coupled ultracold strontium atoms is shown by using a tripod scheme and it is revealed how the gauge field imprinted on the atoms impact their internal state dynamics. Expand

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Geometric phases are only dependent on evolution paths but independent of evolution details so that they possess some intrinsic noise-resilience features. Based on different geometric phases, various… Expand

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- 2019

The phase factor plays a vital role in modern quantum physics. Especially, geometric phases induced in quantum evolutions have the built-in noise-resilient character, and thus found comprehensive… Expand

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- 2018

Non-Abelian and non-adiabatic variants of Berry's geometric phase have been pivotal in the recent advances in fault tolerant quantum computation gates, while Berry's phase itself is at the heart of… Expand

Experimental realization of noncyclic geometric gates with shortcut to adiabaticity in a superconducting circuit

- Physics
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- 2021

Possessing the noise-resilience feature, geometric phases have become important in robust quantum computation. Gates based on the Abelian and non-Abelian geometric phases have been experimentally… Expand

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