LC-Implicit-QAOA: Active-Workspace-Capped Exact Objective-and-Gradient Evaluation for Training over Bounded QUBO Light Cones

QAOA training requires repeated evaluation of the objective function and its gradients. Traditional simulators maintain the global quantum state, which grows exponentially with the number of qubits (2^n), making them infeasible for large-scale optimization. This paper addresses the bottleneck of exact evaluation by asking whether one can compute these values by focusing only on the local causal cones of the cost terms, rather than the entire global state.

The author introduces LC-Implicit-QAOA, a framework that decomposes the global objective into a sum of local expectations. Each term in the QUBO objective is restricted to its causal cone—the set of qubits that influence that specific term after p layers of the QAOA circuit. The framework profiles these cones before execution to determine memory requirements. It then uses a "fit-or-reject" contract: if a requested evaluation exceeds a pre-specified workspace budget, the system rejects the request before allocating memory. The implementation uses reverse-mode adjoint differentiation to compute gradients efficiently without needing to store the global state or a global cost table.

• Numerical Accuracy: The method achieves high numerical precision, with a worst relative gradient error of 1.56 x 10^-13 compared to a dense global-state adjoint, confirming the algebraic correctness of the decomposition.
• Memory Efficiency: By using a profiled batching and checkpointing strategy, the system successfully keeps memory usage within declared budgets. In tests, measured evaluator memory remained below 80% of the allocated budget.
• Performance: On a 3-regular graph with 512 qubits at depth p=2, the adjoint evaluation reached the target endpoint in 101 objective-equivalent calls and 189 seconds, significantly outperforming central finite differences, which required 909 calls and 1,565 seconds.