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

2026-08-06

AI Summary

This work addresses the memory and computational bottlenecks in Quantum Approximate Optimization Algorithm (QAOA) training, where exact evaluation of the objective function and its gradients remains challenging even under bounded QUBO light cones. The authors propose an implicit evaluation strategy that integrates causal light-cone pruning, adjoint differentiation, and dynamic workspace allocation. By pre-analyzing light-cone structures and induced edge counts, the method jointly optimizes micro-batch sizes and checkpoint scheduling, thereby avoiding explicit construction of global quantum states and cost tables while rejecting infeasible requests under strict memory constraints. On a 512-node 3-regular graph with circuit depth \( p=2 \), the approach reduces gradient oracle calls by nearly 9× compared to central finite differences, cutting runtime from 1565 seconds to 189 seconds while consistently staying within the prescribed memory budget, significantly enhancing scalability and efficiency.

Abstract

QAOA training repeatedly queries an objective and all shared gradients, making exact evaluation a feasibility bottleneck even when QUBO terms have bounded causal cones. Building on established causal-cone restriction and adjoint differentiation, LC-Implicit-QAOA profiles cone structure and induced-edge counts before local-amplitude and named-workspace allocation, then jointly selects equal-size microbatches and checkpoint schedules under a named active-evaluator workspace budget. "Implicit" means omitting both global state and global cost table, not implicit differentiation; infeasible requests are rejected before those allocations. An independently implemented complex128/float64 dense adjoint agrees with LC over 1,800 graph-angle comparisons, with a worst relative gradient error of 1.56 x 10^-13. LC completes all 104 target requests in a p=2 bounded-cone grid; under a prespecified n <= 24 validation cap, the matched state-plus-cost reference is executed for 28 requests and deliberately not run on 76. Across 80 budgeted requests, measured allocated evaluator memory stays within budget, reaching at most 0.797 of it. On 3-regular n=512, p=2, the adjoint reaches the same finite-budget endpoint in 101 objective-equivalent calls and 189 s, versus 909 calls and 1,565 s for central differences. LC targets fixed-depth one- and two-local diagonal QUBO costs with a transverse-field mixer; it provides neither global states, sampling, nor a hardware-independent fastest-backend rule.

Problem

• QAOA
• QUBO
• causal cone
• gradient evaluation
• memory budget

Innovation

• QAOA
• causal cone
• implicit evaluation
• adjoint differentiation
• memory-constrained optimization