Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
By Martín Larocca, Piotr Czarnik, Gopikrishnan Muraleedharan, Patrick J. Coles, M. Cerezo. Quantum, 2021
300 citations recorded by the source corpus.
Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the degree of controllability of the system, and hence can be diagnosed through the dynamical Lie algebra g obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. Our work establishes a link between the existence of barren plateaus and the scaling of the dimension of g.
Subfields: Artificial Intelligence
View Paper: https://www.semanticscholar.org/paper/2d0fb5150a6333a9746e4ed5dbba228dba4abbc0
How researchers see this paper
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In Artificial Intelligence
- M. Cerezo
- Patrick J. Coles
- Lukasz Cincio
- Hsin-Yuan Huang
- Guillaume Verdon
- Thomas Schulte-Herbrüggen
- Ronnie Kosloff
- Simone Montangero
Citations in the corpus
- Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe (2022, background): “Insight from QOCT on overcoming barren plateaus may help overcome convergence problems in quantum machine learning [97, 292] or in variational quantum algorithms [361].”
- Challenges and opportunities in quantum machine learning (2022, background): “[96] Martin Larocca, Piotr Czarnik, Kunal Sharma, Gopikrishnan Muraleedharan, Patrick J.”
- Barren plateaus in variational quantum computing (2024, unknown): “16, it was noted that tools from quantum optimal control, such as the study of the PQC’s dynamical Lie algebra, can be used to diagnose BPs. Nowadays, some tools developed in variational quantum computing have started to see use in optimal control schemes 250–254 , and the extent of this…”