Microservice-based applications are characterized by stochastic latencies arising from long-tail execution patterns and heterogeneous resource constraints across computational nodes. To address this challenge, we first formulate the problem using Quadratic Unconstrained Binary Optimization (QUBO), which aligns the problem with emerging quantum-optimization paradigms. Building upon this, we propose Q-GARS (Quantum-Guided Adaptive Robust Scheduling), a hybrid framework that integrates the QUBO model with Simulated Quantum Annealing (SQA) based combinatorial search and online rescheduling mechanisms, enabling global microservice rank generation and real-time robust adjustment. We treat the SQA-produced rank as a soft prior, and update a closed-loop trust weight to adaptively switch and mix between this prior and a robust proportional-fairness allocator, maintaining robustness under prediction failures and runtime disturbances. Simulation results demonstrate that Q-GARS achieves an average weighted completion time improvement of 2.1\% relative to a greedy baseline of the remaining shortest processing-time (SRPT), with performance gains reaching up to 16.8\% in heavy-tailed latency. The adaptive mechanism reduces tail latency under high-variance conditions. In addition, Q-GARS achieves a mean node resource utilization rate of 0.817, which is 1.1 percentage points above the robust baseline (0.806).