Classical Simulability and Trainability of Quantum Machine Learning
- Publication Type:
- Thesis
- Issue Date:
- 2024
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Variational Quantum Algorithms (VQAs) form an important class of quantum machine learning and optimization algorithms, with potential applications in supervised learning, combinatorial optimization, chemical simulation, and dimensionality reduction. They use parameterized quantum circuits to estimate functions that are typically expensive for classical computers, with algorithms like gradient descent optimizing the parameters classically.
Given the limited availability of quantum devices, minimizing their usage in VQAs is essential. Recent research highlights two challenges that could increase quantum demands: trainability issues such as barren plateaus and sample complexity problems exacerbated by practical factors like circuit design and hyperparameter tuning. This thesis presents new algorithms and theoretical insights to address these challenges, enhancing VQA efficiency.
The contributions of this thesis fall into three parts. The first introduces Alternating Layered Shadow Optimization (ALSO), a novel training algorithm for shallow alternating layered VQAs. By leveraging classical shadows of quantum data, ALSO achieves exponential reductions in quantum resources. The optimization is fully carried out on classical computers with rigorous guarantees. ALSO is also easier to implement than standard VQA training, requiring only single-qubit measurements and classical post-processing. Experimental results show orders-of-magnitude improvements in quantum machine learning tasks.
The second part extends shadow tomography-based training to a broader class of VQAs through Ansatz Independent Shadow Optimization (AISO). This algorithm enables exponential quantum resource savings across diverse ansatzes. Beyond rigorous guarantees, experiments demonstrate its effectiveness in state preparation and variational circuit synthesis, outperforming traditional training methods.
The third part examines barren plateaus in VQAs approximating weakly entangled states. Theoretical and experimental results clarify how global vs. local observables impact gradient scaling, with exponentially low gradients in the former case. Additionally, we discuss the potential for classical simulation of local observable versions with minimal quantum resources. All claims are experimentally validated. Collectively, these contributions advance VQAs for near-term quantum devices, paving the way for broader quantum machine learning applications.
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