Barren Plateaus
Overview
Barren plateaus are optimization landscapes in variational quantum circuits where gradient signals become exponentially small as systems grow, making parameter updates ineffective under finite measurement budgets. Theory connects them to random, highly expressive circuits and concentration of measure, while practical work studies gradient variance, Fisher information, and Lie-algebra structure in VQE, QAOA, and quantum-learning tasks. Mitigation approaches include local costs and readouts, symmetry- or subspace-preserving ansätze, controlled circuit growth, and informed initialization; other work learns update rules or changes objectives to amplify usable signals. The central tension is that expressivity and entanglement can improve representation while suppressing gradients, but shallow and structured circuits can have different, sometimes rugged rather than barren, landscapes—and a diagnostic alone does not establish easier end-to-end optimization.
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