ArticleNature communications2024
Characterizing barren plateaus in quantum ansätze with the adjoint representation.
Article in Nature communications, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 8 papers.
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Who cites it
8 citing papers in PubMed.
- Counterdiabatic ADAPT-VQE for Molecular Simulation.Journal of chemical theory and computation · 2026Article
- A repetitive amplitude encoding method for enhancing the mapping ability of quantum neural networks.Scientific reports · 2025Article
- Does provable absence of barren plateaus imply classical simulability?Nature communications · 2025Review
- Non-variational quantum random access optimization with alternating operator ansatz.Scientific reports · 2025Article
- Towards large-scale quantum optimization solvers with few qubits.Nature communications · 2025Article
- A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits.Nature communications · 2024Article
- Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver.Journal of chemical theory and computation · 2024Article
- Classification of dynamical Lie algebras of 2-local spin systems on linear, circular and fully connected topologies.NPJ quantum information · 2024Article
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Abstract
Variational quantum algorithms, a popular heuristic for near-term quantum computers, utilize parameterized quantum circuits which naturally express Lie groups. It has been postulated that many properties of variational quantum algorithms can be understood by studying their corresponding groups, chief among them the presence of vanishing gradients or barren plateaus, but a theoretical derivation has been lacking. Using tools from the representation theory of compact Lie groups, we formulate a theory of barren plateaus for parameterized quantum circuits whose observables lie in their dynamical Lie algebra, covering a large variety of commonly used ansätze such as the Hamiltonian Variational Ansatz, Quantum Alternating Operator Ansatz, and many equivariant quantum neural networks. Our theory provides, for the first time, the ability to compute the exact variance of the gradient of the cost function of the quantum compound ansatz, under mixing conditions that we prove are commonplace.
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