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arXiv:2309.16470 · Physical Review A

Machine-learning-inspired quantum optimal control of nonadiabatic geometric quantum computation via reverse engineering

Meng-Yun Mao, Zheng Cheng, Yan Xia, Andrzej M. Oleś, Wen‐Long You

Published Sep 27, 2023• 9 citations
arXivHTMLPDF

Abstract

Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity $(>99.99%)$ phase gates, such as the $\ensuremath{\pi}/8$ gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.

DOI
10.1103/physreva.108.032616

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Quantum control plays an irreplaceable role in practical use of quantum computers. However, some challenges have to be overcome to find more suitable and diverse control parameters. We propose a promising and generalizable average-fidelity-based machine-learning-inspired method to optimize the control parameters, in which a neural network with periodic feature enhancement is used as an ansatz. In the implementation of a single-qubit gate by cat-state nonadiabatic geometric quantum computation via reverse engineering, compared with the control parameters in the simple form of a trigonometric function, our approach can yield significantly higher-fidelity (>99.99(>99.99%)(>99.99 phase gates, such as the \ensuremathπ/8\ensuremath{\pi}/8\ensuremathπ/8 gate (t gate). Single-qubit gates are robust against systematic noise, additive white Gaussian noise, and decoherence. We numerically demonstrate that the neural network possesses the ability to expand the model space. With the help of our optimization, we provide a feasible way to implement cascaded multiqubit gates with high quality in a bosonic system. Therefore, the machine-learning-inspired method may be feasible in quantum optimal control of nonadiabatic geometric quantum computation.
Adaptive quantum computing control is important for the stability and efficiency of quantum systems, especially in the presence of dynamic environmental noise and hardware fluctuations. We present a unified strategy for machine learning (ML) techniques to improve adaptive quantum control in two main directions: optimization speed and out-of-sample error. Here, we propose a hybrid learning method combining reinforcement learning (RL), deep neural networks (DNNs), and quantum-inspired models to actively and adaptively update quantum gate parameters and error mitigation strategies on the fly. Embedding of quantum noise models directly into the learning allows the system to predict and correct for decoherence, gate errors and measurement inaccuracy before they affect computational fidelity. Using extensive simulations as well as experimental validation on noisy intermediate-scale quantum (NISQ) processors, our improved ML model achieves a substantially higher fidelity and robustness compared to standard model-free and static control approaches. We introduce a novel feedback-loop mechanism based on online learning algorithms enabling the system to adjust for changing noise profiles and hardware drift without retraining. The optimization part uses metaheuristic methods to quickly converge to control parameters that perform well, and the error prevention mechanism features anomaly detection and prediction correction layers to minimize the effects of cumulative decoherence. The results demonstrate that our adaptive control framework can be used to not only speed up the convergence in training quantum algorithms, but also sustain the performance of gates against error at a variety of error rates with the reduction of the real-time impact of the error up to 35 %. This work highlights the promise of machine learningaugmented quantum control for improving reliability and scalability in quantum computing and serves as a stepping stone for future incorporation with fault-tolerant designs.
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Implementing fast and high-fidelity quantum operations using open-loop quantum optimal control relies on having an accurate model of the quantum dynamics. Any deviations between this model and the complete dynamics of the device, such as the presence of spurious modes or pulse distortions, can degrade the performance of optimal controls in practice. Here, we propose an experimentally simple approach to realize optimal quantum controls tailored to the device parameters and environment while specifically characterizing this quantum system. Concretely, we use physics-inspired machine learning to infer an accurate model of the dynamics from experimentally available data and then optimize our experimental controls on this trained model. We show the power and feasibility of this approach by optimizing arbitrary single-qubit operations on a superconducting transmon qubit, using detailed numerical simulations. We demonstrate that this framework produces an accurate description of the device dynamics under arbitrary controls, together with the precise pulses achieving arbitrary single-qubit gates with a high fidelity of about 99.99%.
Quantum gates, which are the essential building blocks of quantum computers, are very fragile. Thus, to realize robust quantum gates with high fidelity is the ultimate goal of quantum manipulation. Here, we propose a nonadiabatic geometric quantum computation scheme on superconducting circuits to engineer arbitrary quantum gates, which share both the robust merit of geometric phases and the capacity to combine with optimal control technique to further enhance the gate robustness. Specifically, in our proposal, arbitrary geometric single-qubit gates can be realized on a transmon qubit, by a resonant microwave field driving, with both the amplitude and phase of the driving being time-dependent. Meanwhile, nontrivial two-qubit geometric gates can be implemented by two capacitively coupled transmon qubits, with one of the transmon qubits’ frequency being modulated to obtain effective resonant coupling between them. Therefore, our scheme provides a promising step towards fault-tolerant solid-state quantum computation.
Geometric phases are used to construct quantum gates since it naturally resists local noises, acting as the modularized units of geometric quantum computing. Meanwhile, fast nonadiabatic geometric gates are required for reducing the information loss induced by decoherence. Here, we propose a digital simulation of nonadiabatic geometric quantum gates in terms of shortcuts to adiabaticity (STA). More specifically, we combine the invariant-based inverse engineering with optimal control theory for designing the fast and robust Abelian geometric gates against systematic error, in the context of two-level qubit systems. We exemplify X and T gates, in which the fidelities and robustness are evaluated by simulations in ideal quantum circuits. Our results can also be extended to constructing two-qubit gates, for example, a controlled-PHASE gate, which shares the equivalent effective Hamiltonian with rotation around the Z-axis of a single qubit. These STA-inspired nonadiabatic geometric gates can realize quantum error correction physically, leading to fault-tolerant quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era.
In this paper, a flexible and effective scheme is proposed to realize nonadiabatic geometric quantum gates with the invariant based reverse engineering and the nonadiabatic holonomic quantum computation (NHQC+\mathrm{NHQC}+NHQC+) presented in recent work [B.-J. Liu et al., Phys. Rev. Lett. 123, 100501 (2019)] for extensible geometric quantum computation. The scheme provides variabilities for most of control parameters, and can build up multiple evolution paths with different geometric phases acquired in a cycling evolution. As the computational basis can be covered by the evolution paths, the realization of the nonadiabatic geometric quantum computation is possible without auxiliary levels. Moreover, multiple types of nonadiabatic geometric quantum gates can also be easily constructed by only adjusting boundary conditions of control parameters with the method. To show the applications of the scheme, we discuss the implementations of nonadiabatic geometric quantum gates of spin qubits in a double-quantum-dot system with numerical simulations. The results indicate that the scheme possesses robustness against the errors and noise. Therefore, the scheme may offer some interesting perspectives for the realization of the nonadiabatic geometric quantum computation.