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arXiv:2210.03326

Experimental Implementation of Noncyclic and Nonadiabatic Geometric Quantum Gates in a Superconducting Circuit

Zhuang Ma, Jianwen Xu, Tao Chen, Yu Zhang, Wen Zheng, Lan Dong, Zheng‐Yuan Xue, Xinsheng Tan, Yang Yu

Published Oct 7, 2022• 0 citations
arXivHTMLPDF

Abstract

Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, which greatly shortens the gate time. And also, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency error and qubit frequency shift-induced error, compared to the conventional dynamical gates, by using the randomized benchmarking method. Moreover, this scheme can be utilized to construct two-qubit geometric operations, while the generation of the maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.

DOI
10.48550/arxiv.2210.03326

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Quantum gates based on geometric phases possess intrinsic noise-resilience features and therefore attract much attention. However, the implementations of previous geometric quantum computation typically require a long pulse time of gates. As a result, their experimental control inevitably suffers from the cumulative disturbances of systematic errors due to excessive time consumption. Here, we experimentally implement a set of noncyclic and nonadiabatic geometric quantum gates in a superconducting circuit, which greatly shortens the gate time. And also, we experimentally verify that our universal single-qubit geometric gates are more robust to both the Rabi frequency error and qubit frequency shift-induced error, compared to the conventional dynamical gates, by using the randomized benchmarking method. Moreover, this scheme can be utilized to construct two-qubit geometric operations, while the generation of the maximally entangled Bell states is demonstrated. Therefore, our results provide a promising routine to achieve fast, high-fidelity, and error-resilient quantum gates in superconducting quantum circuits.
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Using geometric phases to realize noise-resilient quantum computing is an important method to enhance the control fidelity. In this work, we experimentally realize a universal nonadiabatic geometric quantum gate set in a superconducting qubit chain. We characterize the realized single- and two-qubit geometric gates with both quantum process tomography and randomized benchmarking methods. The measured average fidelities for the single-qubit rotation gates and two-qubit controlled-Z gate are 0.9977(1) and 0.977(9), respectively. Besides, we also experimentally demonstrate the noise-resilient feature of the realized single-qubit geometric gates by comparing their performance with the conventional dynamical gates with different types of errors in the control field. Thus, our experiment proves a way to achieve high-fidelity geometric quantum gates for robust quantum computation.
Nonadiabatic geometric quantum computation (NGQC) has attracted a lot of attention for noise-resilient quantum control. However, previous implementations of NGQC require long evolution paths that make them more vulnerable to incoherent errors than their dynamical counterparts. In this work, we experimentally realize a universal short-path nonadiabatic geometric gate set (SP NGQC) with a 2-times shorter evolution path on a superconducting quantum processor. Characterizing with both quantum process tomography and randomized benchmarking methods, we report an average single-qubit gate fidelity of $99.86\mathrm{%}$ and a two-qubit gate fidelity of $97.9\mathrm{%}$. Additionally, we demonstrate superior robustness of single-qubit SP NGQC gate to Rabi frequency error in some certain parameter space by comparing their performance to those of the dynamical gates and the former NGQC gates.
Recently, nonadiabatic geometric quantum computation has received much attention due to its fast manipulation and intrinsic error-resilience characteristics. However, to obtain universal geometric quantum control, only limited and special evolution paths have been proposed, which usually require longer gate-time and more operational steps, and thus lead to lower quality of the implemented quantum gates. Here, we present an effective scheme to find the shortest geometric path under conventional conditions of geometric quantum computation, where high-fidelity and robust geometric gates can be realized by only single-loop evolution, and the gate performances are better than the corresponding dynamical ones. Furthermore, we can optimize the pulse shapes in our scheme to further shorten the gate-time, which is determined by how fast the path is traveled. In addition, we also present its physical implementation on superconducting circuits, consisting of capacitively coupled transmon qubits, where fidelities of geometric single- and two-qubit gates can be higher than 99.95% and 99.80% within the current state-of-the-art experimental technologies, respectively. These results indicate that our scheme is promising for large-scale fault-tolerant quantum computation.
Nonadiabatic geometric quantum computation is dedicated to the realization of high-fidelity and robust quantum gates, which is the necessity of fault-tolerant quantum computation. However, it is limited by cyclic and mutative evolution path, which usually requires longer gate-time and abrupt pulse control, and thus weaken the gate performance. Here, we propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolutions, which effectively shorten the gate duration, and universal quantum gates can be realized in one step without path mutation. Our numerical simulation shows that, comparing with the conventional dynamical gates, the constructed geometric gates have stronger resistant not only to noise but also to decoherence effect. In addition, our scheme can also be implemented on a superconducting circuit platform, with the fidelities of single-qubit and two-qubit gates higher than 99.97%\%% and 99.84%\%%, respectively. Therefore, our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.
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 demonstrated in different physical systems. However, previous proposals require cyclic evolution with a constant operation time even for small rotation angles, which set a limit to the gate operation time. Here, we experimentally realize noncyclic geometric gates, where the cyclic condition is removed and the operation time is proportional to the rotation angle. With the adiabatic process sped up by shortcut to adiabaticity, the fidelities of a noncyclic geometric gate characterized by randomized benchmarking are above 99.5%. Comparing with the dynamic scheme, we demonstrate the robustness of our gate against control instability in the experiment. Moreover, our results indicate that the noncyclic geometric gate with a smaller rotation angle corresponds to a shorter evolution time and higher fidelity. As small rotation angles are essential in the quantum algorithm, the superiority of noncyclic geometric gates makes them promising candidates in fast and robust quantum computation.