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arXiv:2105.05481 · Physical Review Research

Fast high-fidelity geometric quantum control with quantum brachistochrones

Yang Dong, Ce Feng, Y. H. Zheng, Xiang-Dong Chen, Guang‐Can Guo, Fang‐Wen Sun

Published Dec 13, 2021• 22 citations
arXivHTMLPDF

Abstract

We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over $99.2%$ on the spin state of the nitrogen-vacancy center are realized with average durations shortened by $21.5%$ compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds $96.5%$ on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.

DOI
10.1103/physrevresearch.3.043177

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We experimentally demonstrate fast and high-fidelity geometric control of a quantum system with the brachistochrone method on hybrid spin registers in diamond. Based on the time-optimal universal geometric control, single geometric gates with fidelities over 99.299.2%99.2 on the spin state of the nitrogen-vacancy center are realized with average durations shortened by 21.521.5%21.5 compared with the conventional geometric method. The fidelity of the fast geometric two-qubit gate exceeds 96.596.5%96.5 on the hybrid spin registers. With the fast and high-fidelity universal set of geometric gates available, we implement a quantum entanglement-enhanced phase estimation algorithm and demonstrate the Heisenberg quantum limit of phase estimation at room temperature. Hence our results show that high-fidelity quantum control based on a fast geometric route will be a versatile tool for broad applications of quantum information processing in practice.
Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.
Abstract Geometric phases and holonomies are a promising resource for the realization of high-fidelity quantum operations in noisy devices, due to their intrinsic fault-tolerance against parametric noise. However, for a long time their practical use in quantum computing was limited to proof of principle demonstrations. This was partly due to the need for adiabatic time evolution or the requirement of complex, high-dimensional state spaces and a large number of driving field parameters to achieve universal quantum gates employing holonomies. In 2016 Liang et al. proposed universal, superadiabatic, geometric quantum gates exploiting transitionless quantum driving, thereby offering fast and universal quantum gate performance on a simple two-level system. Here, we report on the experimental implementation of a set of non-commuting single-qubit superadiabatic, geometric quantum gates on the electron spin of the nitrogen-vacancy center in diamond under ambient conditions. This provides a promising and powerful tool for large-scale quantum computing under realistic, noisy experimental conditions.
Hybrid systems of electron and nuclear spins are a fundamental building block for scalable quantum information processing. Here we propose a fast and high-fidelity control scheme based on geometric Landau-Zener-St\"uckelberg-Majorana interferometry, using a nitrogen-vacancy center in diamond as an example. When this hybrid spin multilevel system is driven through avoided crossings, geometric phases accumulate in each spin subspace and manifest as interference patterns in the dynamics of the whole system. We systematically study the effects of various decoherence mechanisms and fluctuations of control parameters on this geometric phase process. We also consider the application of quantum memory, where electron spins are used as a processing qubit and nuclear spins are used as a storage qubit. This scheme can achieve a transfer fidelity of 0.985 and a total storage fidelity of 0.96. These results pave the way for geometric coherent manipulations on a variety of hybrid quantum platforms.
A negatively charged nitrogen-vacancy (NV) center in diamond has been recognized as a good solid-state qubit. A system consisting of the electronic spin of the NV center and hyperfine-coupled nitrogen and additionally nearby carbon nuclear spins can form a quantum register of several qubits for quantum information processing or as a node in a quantum repeater. Several impressive experiments on the hybrid electron and nuclear spin register have been reported, but fidelities achieved so far are not yet at or below the thresholds required for fault-tolerant quantum computation (FTQC). Using quantum optimal control theory based on the Krotov method, we show here that fast and high-fidelity single-qubit and two-qubit gates in the universal quantum gate set for FTQC, taking into account the effects of the leakage state, nearby noise qubits, and distant bath spins, can be achieved with errors less than those required by the threshold theorem of FTQC.
High-fidelity two-logical-qubit gates are essential for realizing fault-tolerant quantum computation with bosonic codes, yet experimentally reported fidelities have rarely exceeded 90\%. Here, we propose a geometric phase engineering approach for implementing controlled-phase gates for binomially encoded logical qubits. This method leverages the structural simplicity of geometric drives to reduce the numerical optimization dimensionality while fully incorporating system nonlinearities, enabling fast and high-fidelity logical operations. As an example, we experimentally demonstrate a process fidelity of 97.4$\pm$0.8\% for a controlled-Z gate between two binomial codes, surpassing all previously reported two-logical-qubit gates in bosonic codes. This work demonstrates that geometric phase engineering provides an effective and experimentally feasible route to fast, high-fidelity logical operations in bosonic quantum processors.
Experimental realization of a universal set of quantum logic gates with high fidelity is critical to quantum-information processing, which is always challenging due to the inevitable interaction between the quantum system and environment. Geometric quantum computation is noise immune, and thus, offers a robust way to enhance control fidelity. Here, we experimentally implement the recently proposed extensible nonadiabatic holonomic quantum computation with solid spins in diamond at room temperature, which maintains both flexibility and resilience against decoherence and system-control errors. Compared with the previous geometric method, the fidelities of a universal set of holonomic single-qubit and two-qubit quantum logic gates are improved in experiments. Therefore, this work makes a step towards high-fidelity quantum-information processing based on extensible nonadiabatic holonomic quantum computation in realistic systems.