A Lie algebraic theory of barren plateaus for deep parameterized quantum circuits

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.…

• NS
  National Science Foundation

  Awards: 1818914, 2325080, DE-AC05-76RLO1830
• UD
  U.S. Department of Energy

  Awards: DE-AC05, DE-AC05-76RLO1830
• B
  Battelle

  Awards: DE-AC05-76RLO1830, DE-AC05
• LA
  Los Alamos National Laboratory

  Awards: 20230049DR, 20230527ECR
• PN
  Pacific Northwest National Laboratory

  Award: DE-AC05-76RLO1830