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The Japan Society of Applied Physics

The fidelity measurement of holonomic quantum gates by ramdomized benchmarking

Kazuyasu Matsuda, Kodai Nagata, Shiro Tamiya, Kouyou Kuramitani, Yuhei Sekiguchi, Hideo Kosaka

Published Jul 10, 2018• 0 citations
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Among existing approaches to holonomic quantum computing, the adiabatic holonomic quantum gates (HQGs) suffer errors due to decoherence, while the non-adiabatic HQGs either require additional Hilbert spaces or are difficult to scale. Here, we report a systematic, scalable approach based on dynamical invariants to realize HQGs without using additional Hilbert spaces. While presenting the theoretical framework of our approach, we design and experimentally evaluate single-qubit and two-qubits HQGs for the nuclear magnetic resonance system. The single-qubit gates acquire average fidelity 0.9972 by randomized benchmarking, and the controlled-NOT gate acquires fidelity 0.9782 by quantum process tomography. Our approach is also platform-independent, and thus may open a way to large-scale holonomic quantum computation.
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.
Non-Abelian geometric phases acquired in cyclic quantum evolution can be utilized as natural resources for constructing robust holonomic gates for quantum-information processing. Recently, an extensible holonomic quantum computation (HQC) was proposed and demonstrated in a recent superconducting experiment [Yan et al., Phys. Rev. Lett. 122, 080501 (2019)]. However, for the weakly anharmonic system, this HQC was given of low gate fidelity due to leakage to states outside of the computational subspace. Here, we propose a scheme to construct nonadiabatic holonomic gates via a dynamical invariant using resonant interaction of three-level superconducting quantum systems. Furthermore, the proposed scheme can be compatible with optimal control technology for maximizing the gate fidelity against leakage error. For benchmarking, we provide a thorough analysis on the performance of our scheme under experimental conditions, which shows that the gate error can be reduced by as much as 91.7% compared with the conventional HQC. Moreover, the leakage rates can be reduced to the ${10}^{\ensuremath{-}3}$ level by numerically choosing a suitable control parameter. Therefore, our scheme provides a promising way towards fault-tolerant quantum computation in a weakly anharmonic solid-state system.