Math Picture Language Seminar: Training landscapes for parameterized quantum circuits
MATHEMATICAL PICTURE LANGUAGE, SEMINARS
Patrick Coles - Los Alamos National Laboratory
Parameterized quantum circuits (PQCs) are the leading proposal for near-term quantum computing, with applications including electronic structure, dynamical simulation, and solving linear systems. However, there has recently been major progress in understanding the training landscapes for PQCs, and the results paint a concerning picture. Exponentially vanishing gradients, known as barren plateaus, have been shown to occur for various situations, including circuits that are either deep or noisy or that generate much entanglement. This can lead to exponential resource scaling for algorithms based on PQCs. On the flip side, some architectures for PQCs have been proven to be immune to barren plateaus. Moreover, the dynamical Lie algebra for a PQC has been connected to presence or absence of barren plateaus, leading to an algebraic theory for the trainability of PQCs. This theory could allow us to engineer favorable training landscapes for PQCs. In this talk, I will overview our theoretical understanding of PQCs training landscapes and how we might engineer them to achieve scalability for near-term quantum computing.