Speaker
Description
PQC-based policies are promising candidates for quantum reinforcement learning, but their trainability can be limited by barren plateaus. We analyze Born-rule quantum policies beyond local 2-design assumptions by deriving tight policy-variance and gradient bounds for practical PQC architectures. For action probabilities defined by projectors onto Hilbert-space subspaces, we prove that, under uniform parameter initialization and standard angle/basis encodings, the policy and gradient variances decompose into independent contributions from the basis elements of each action subspace. Consequently, a policy avoids exponential concentration whenever at least one basis element contains a Pauli component with a logarithmic backwards light-cone.
This provides a constructive design principle for trainable mixed-locality quantum policies: local terms enable non-vanishing gradients at initialization, while increasingly global terms can contribute later during optimization. We apply the theory to recursive parity-based action decoding, showing that larger action spaces introduce local variance contributions absent in the two-action parity case. Numerical experiments confirm polynomial variance scaling for several circuits composed of single-qubit rotation gates plus Clifford. Further simulations in probability maximization, CartPole, and a 20-action contextual bandit show that mixed-locality policies with richer locality structure improve convergence and policy performance.
| Topic | Quantum variational circuits and their applications |
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| Additional Topic | Theoretical foundations of quantum learning |