Exponentially many initializations to avoid barren plateaus
For researchers in quantum machine learning, this work reveals that the common view of initialization as a simple cure for barren plateaus is insufficient, highlighting a new complexity in the optimization landscape.
The paper shows that avoiding barren plateaus in variational quantum algorithms via smart initializations is not unique; there exist exponentially many inequivalent initialization strategies that avoid concentration, but this trades the exponential concentration problem for the challenge of selecting the right trainable pocket among many options.
Barren plateaus are stated as an average-case phenomenon: pick an ansatz, initialize it naively, and concentration follows. This has led to the common view that a potential cure for barren plateaus is simply to initialize the parameters more carefully. Here we show that the situation is subtler. We introduce a first-moment framework that gives a simple operator-level diagnostic for when an initialization may escape the fully concentrated barren-plateau fixed point, and for comparing the biases induced by different initialization strategies. Our framework recovers several known initialization schemes such as identity and Gaussian initialization, but also shows that barren-plateau avoidance is highly non-unique. Indeed, many shifted, biased, and non-symmetric parameter distributions can avoid concentration, and these choices need not be equivalent. In fact, our results show that one can generate exponentially many families of inequivalent initialization strategies. Then, our numerics indicate that different first-moment-distinct initializations can lead to different attained minima, suggesting that avoiding barren plateaus via smart initializations can trade the exponential concentration problem for the challenge of selecting the right trainable pocket amongst many options.