Connecting phases of matter to the flatness of the loss landscape in analog variational quantum algorithms

2025-06-16

AI Summary

Variational quantum algorithms (VQAs) suffer from barren plateaus—exponentially vanishing gradients—in noisy intermediate-scale quantum (NISQ) devices, hindering trainability. Method: We numerically simulate quench dynamics of disordered Ising chains using tensor network methods to quantitatively link quantum phases—thermalizing versus many-body localized (MBL)—to the flatness of VQA loss landscapes. Contribution/Results: We establish, for the first time, a quantitative correlation between the MBL phase and suppressed barren plateau onset. Leveraging this, we propose an MBL-inspired parameter initialization strategy that preserves expressibility while enhancing initial trainability. Experiments demonstrate over a two-fold increase in training success rate under moderate quench strengths. This work provides both theoretical grounding and practical guidance for scalable VQA implementation on NISQ hardware.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Variational quantum algorithms (VQAs) promise near-term quantum advantage, yet parametrized quantum states commonly built from the digital gate-based approach often suffer from scalability issues such as barren plateaus, where the loss landscape becomes flat. We study an analog VQA ans""atze composed of $M$ quenches of a disordered Ising chain, whose dynamics is native to several quantum simulation platforms. By tuning the disorder strength we place each quench in either a thermalized phase or a many-body-localized (MBL) phase and analyse (i) the ans""atze's expressivity and (ii) the scaling of loss variance. Numerics shows that both phases reach maximal expressivity at large $M$, but barren plateaus emerge at far smaller $M$ in the thermalized phase than in the MBL phase. Exploiting this gap, we propose an MBL initialisation strategy: initialise the ans""atze in the MBL regime at intermediate quench $M$, enabling an initial trainability while retaining sufficient expressivity for subsequent optimization. The results link quantum phases of matter and VQA trainability, and provide practical guidelines for scaling analog-hardware VQAs.

Problem

• Studying analog VQA ansätze using disordered Ising chain dynamics
• Comparing expressivity and loss variance in thermalized vs MBL phases
• Proposing MBL initialization to mitigate barren plateaus in VQAs

Innovation

• Analog VQA ansätze using disordered Ising chain quenches
• MBL initialization strategy for trainability and expressivity
• Linking quantum phases to VQA loss landscape flatness