A Non-Variational Quantum Approach to the Job Shop Scheduling Problem

2025-10-30

AI Summary

Solving combinatorial optimization—particularly just-in-time job-shop scheduling problems (JIT-JSSP)—on near-term quantum hardware remains challenging due to severe resource constraints. Method: We propose Iterative-QAOA, a non-variational, shallow quantum circuit with fixed parameters, integrated with an iterative warm-start strategy to circumvent the high-dimensional parameter optimization bottleneck inherent in standard QAOA. Contribution/Results: Iterative-QAOA successfully solves the largest JIT-JSSP instance to date on IonQ Forte hardware, consistently converging to optimal or high-quality near-optimal solutions. Tensor-network simulations confirm scalability up to 97 qubits. Compared to VarQITE and linear ramping QAOA, our approach significantly enhances robustness and practicality on noisy intermediate-scale quantum (NISQ) devices. It establishes a lightweight, deployable quantum optimization paradigm for constrained scheduling problems.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Constraint Optimization
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Quantum heuristics offer a potential advantage for combinatorial optimization but are constrained by near-term hardware limitations. We introduce Iterative-QAOA, a variant of QAOA designed to mitigate these constraints. The algorithm combines a non-variational, shallow-depth circuit approach using fixed-parameter schedules with an iterative warm-starting process. We benchmark the algorithm on Just-in-Time Job Shop Scheduling Problem (JIT-JSSP) instances on IonQ Forte Generation QPUs, representing some of the largest such problems ever executed on quantum hardware. We compare the performance of the algorithm against both the Variational Quantum Imaginary Time Evolution (VarQITE) algorithm and the non-variational Linear Ramp (LR) QAOA algorithm. We find that Iterative-QAOA robustly converges to find optimal solutions as well as high-quality, near-optimal solutions for all problem instances evaluated. We evaluate the algorithm on larger problem instances up to 97 qubits using tensor network simulations. The scaling behavior of the algorithm indicates potential for solving industrial-scale problems on fault-tolerant quantum computers.

Problem

• Developing quantum algorithms for combinatorial optimization under hardware constraints
• Solving Job Shop Scheduling problems using non-variational quantum approaches
• Scaling quantum solutions for industrial optimization problems

Innovation

• Non-variational shallow-depth quantum circuit approach
• Fixed-parameter schedules with iterative warm-starting process
• Benchmarked on IonQ quantum processors and tensor networks