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arXiv:1811.06252 · New Journal of Physics

Single-shot realization of nonadiabatic holonomic gates with a superconducting Xmon qutrit

Zhenxing Zhang, P Z Zhao, Tenghui Wang, Liang Xiang, Zhilong Jia, Peng Duan, D M Tong, Yi Yin, Guoping Guo

Published Jul 1, 2019• 44 citations
arXivHTMLPDF

Abstract

Abstract Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors and high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with a superconducting transmon qutrit. However, it requires two noncommuting gates to complete an arbitrary one-qubit gate, doubling the exposure time of the gate to error sources and thus leaving the gate vulnerable to environment-induced decoherence. Single-shot protocol has been subsequently proposed to realize an arbitrary one-qubit nonadiabatic holonomic gate. In this paper, a single-shot protocol of nonadiabatic holonomic gates is experimentally demonstrated by using a superconducting Xmon qutrit, with all the single-qubit Clifford gates carried out by a single-shot implementation. Characterized by quantum process tomography and randomized benchmarking, the single-shot gates reach a fidelity exceeding 99%.

DOI
10.1088/1367-2630/ab2e26

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Abstract Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors and high-speed realization. The original protocol of nonadiabatic holonomic one-qubit gates has been experimentally demonstrated with a superconducting transmon qutrit. However, it requires two noncommuting gates to complete an arbitrary one-qubit gate, doubling the exposure time of the gate to error sources and thus leaving the gate vulnerable to environment-induced decoherence. Single-shot protocol has been subsequently proposed to realize an arbitrary one-qubit nonadiabatic holonomic gate. In this paper, a single-shot protocol of nonadiabatic holonomic gates is experimentally demonstrated by using a superconducting Xmon qutrit, with all the single-qubit Clifford gates carried out by a single-shot implementation. Characterized by quantum process tomography and randomized benchmarking, the single-shot gates reach a fidelity exceeding 99%.
Nonadiabatic holonomic quantum computation in decoherence-free subspaces has attracted increasing attention recently, as it allows for high-speed implementation and combines both the robustness of holonomic gates and the coherence stabilization of decoherence-free subspaces. Since the first protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, a number of schemes for its physical implementation have been put forward. However, all previous schemes require two noncommuting gates to realize an arbitrary one-qubit gate, which doubles the exposure time of gates to error sources as well as the resource expenditure. In this paper, we propose an alternative protocol for nonadiabatic holonomic quantum computation in decoherence-free subspaces, in which an arbitrary one-qubit gate in decoherence-free subspaces is realized by a single-shot implementation. The present protocol not only maintains the merits of the original protocol but also avoids the extra work of combining two gates to implement an arbitrary one-qubit gate and thereby reduces the exposure time to various error sources.
Nonadiabatic holonomic quantum computation has received increasing attention due to its robustness against control errors. However, all the previous schemes have to use at least two sequentially implemented gates to realize a general one-qubit gate. In this paper we put forward a scheme by which one can directly realize an arbitrary holonomic one-qubit gate with a single-shot implementation, avoiding the extra work of combining two gates into one. Based on a three-level model driven by laser pulses, we show that any single-qubit holonomic gate can be realized by varying the detuning, amplitude, and phase of lasers. Our scheme is compatible with previously proposed nonadiabatic holonomic two-qubit gates, combining with which the arbitrary holonomic one-qubit gates can play universal nonadiabatic holonomic quantum computation. We also investigate the effects of some unavoidable realistic errors on our scheme.
Control errors and decoherence are two main obstacles for realization of quantum computation. Nonadiabatic holonomic quantum computation in decoherence-free subspaces can protect quantum gates from both control errors and decoherence, and, therefore, it has received increasing attention. The original protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces needs two loops in the Grassmann manifold to generate an arbitrary nonadiabatic holonomic one-qubit gate. In this paper, we proposed a protocol of nonadiabatic holonomic quantum computation in decoherence-free subspaces, where an arbitrary one-qubit gate is generated by only a single loop in the Grassmann manifold and an entangling two-qubit gate assisted by two single-qubit gates can be used to construct a two-qubit controlled unitary gate. In addition, the encoding of our protocol for nonadiabatic holonomic gates requires a lower number of physical qubits compared with previous schemes. Our scheme not only maintains the merits of the original protocol but it also avoids the extra work of combining two gates to realize an arbitrary one-qubit gate.
Geometric phases are noise resilient, and thus provide a robust way towards high-fidelity quantum manipulation. Here we experimentally demonstrate arbitrary nonadiabatic holonomic single-qubit quantum gates for both a superconducting transmon qubit and a microwave cavity in a single-loop way. In both cases, an auxiliary state is utilized, and two resonant microwave drives are simultaneously applied with well-controlled but varying amplitudes and phases for the arbitrariness of the gate. The resulting gates on the transmon qubit achieve a fidelity of 0.996 characterized by randomized benchmarking and the ones on the cavity show an averaged fidelity of 0.978 based on a full quantum process tomography. In principle, a nontrivial two-qubit holonomic gate between the qubit and the cavity can also be realized based on our presented experimental scheme. Our experiment thus paves the way towards practical nonadiabatic holonomic quantum manipulation with both qubits and cavities in a superconducting circuit.
Nonadiabatic holonomic gates provide a promising way to realize high-fidelity quantum gates because of their robustness and high-speed implementation. Compared with quantum computation that consists of many nonadiabatic holonomic one-qubit and two-qubit gates, the nonadiabatic holonomic multiqubit gate, which can reduce the number of quantum gates, is more efficient to construct simpler and faster complicated quantum computation. We propose the simplest scheme to realize nonadiabatic holonomic three-qubit controlled gates. On the one hand, the parameters we set to realize the three-qubit controlled gates are all time independent, which makes it easy to control and operate the quantum systems. On the other hand, our scheme avoids the combination of the elementary gates and realizes the three-qubit controlled gates only by one-shot implementation.
For circuit-based quantum computation, experimental implementation of a 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 171Yb+ 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, our experiments share both the advantages of fast nonadiabatic evolution and robustness against systematic errors. Therefore, our experiments confirm a promising method for fast and robust holonomic quantum computation.