量子学习中量子数据驱动的动态跃迁

IF 8.3 1区 物理与天体物理 Q1 PHYSICS, APPLIED
Bingzhi Zhang, Junyu Liu, Liang Jiang, Quntao Zhuang
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引用次数: 0

摘要

量子神经网络是在特定成本函数下优化的参数化量子电路,为在量子信息处理中实现近期量子优势提供了一种范式。理解QNN训练动态对于优化其性能至关重要。然而,量子数据在分类和回归等监督学习训练中的作用仍不清楚。我们揭示了一种量子数据驱动的动态过渡,其中目标值和数据决定了训练的收敛性。通过对动力学方程不动点的解析分类,我们揭示了一个综合的“相图”,它具有起源于多个余维分岔的七种不同的动力学。微扰分析同时确定指数和多项式收敛类。我们提供了一个非微扰理论来解释广义受限Haar系综的跃迁。在IBM量子器件上进行了数值模拟和实验,验证了分析结果。我们的研究结果为构建代价函数以加速QNN训练中的收敛提供了指导。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Quantum-data-driven dynamical transition in quantum learning

Quantum-data-driven dynamical transition in quantum learning

Quantum neural networks, parameterized quantum circuits optimized under a specific cost function, provide a paradigm for achieving near-term quantum advantage in quantum information processing. Understanding QNN training dynamics is crucial for optimizing their performance. However, the role of quantum data in training for supervised learning such as classification and regression remains unclear. We reveal a quantum-data-driven dynamical transition where the target values and data determine the convergence of the training. Through analytical classification over the fixed points of the dynamical equation, we reveal a comprehensive ‘phase diagram’ featuring seven distinct dynamics originating from a bifurcation with multiple codimension. Perturbative analyses identify both exponential and polynomial convergence classes. We provide a non-perturbative theory to explain the transition via generalized restricted Haar ensemble. The analytical results are confirmed with numerical simulations and experimentation on IBM quantum devices. Our findings provide guidance on constructing the cost function to accelerate convergence in QNN training.

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来源期刊
npj Quantum Information
npj Quantum Information Computer Science-Computer Science (miscellaneous)
CiteScore
13.70
自引率
3.90%
发文量
130
审稿时长
29 weeks
期刊介绍: The scope of npj Quantum Information spans across all relevant disciplines, fields, approaches and levels and so considers outstanding work ranging from fundamental research to applications and technologies.
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