ArticleNature communications2024
A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits.
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 9 papers.
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9 citing papers in PubMed.
- Counterdiabatic ADAPT-VQE for Molecular Simulation.Journal of chemical theory and computation · 2026Article
- CohAlign: Predicting the first-order noise susceptibility of gradients in equivariant quantum neural networks.PloS one · 2026Article
- Surrogate optimization of variational quantum circuits.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Does provable absence of barren plateaus imply classical simulability?Nature communications · 2025Review
- Towards large-scale quantum optimization solvers with few qubits.Nature communications · 2025Article
- Variational quantum generative modeling by sampling expectation values of tunable observables.NPJ quantum information · 2025Article
- Characterizing barren plateaus in quantum ansätze with the adjoint representation.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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7 authors.
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Abstract
Variational quantum computing schemes train a loss function by sending an initial state through a parametrized quantum circuit, and measuring the expectation value of some operator. Despite their promise, the trainability of these algorithms is hindered by barren plateaus (BPs) induced by the expressiveness of the circuit, the entanglement of the input data, the locality of the observable, or the presence of noise. Up to this point, these sources of BPs have been regarded as independent. In this work, we present a general Lie algebraic theory that provides an exact expression for the variance of the loss function of sufficiently deep parametrized quantum circuits, even in the presence of certain noise models. Our results allow us to understand under one framework all aforementioned sources of BPs. This theoretical leap resolves a standing conjecture about a connection between loss concentration and the dimension of the Lie algebra of the circuit's generators.
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