Research Engineer – Optimization

About QpiAI At QpiAI, we are leading the effort to discover optimal AI and Quantum systems in Life sciences, Healthcare, Transportation, Finance, Industrial, and Space technologies. QpiAI is building a full- stack Enterprise Quantum Computers. QpiAI Quantum hardware team is responsible for designing and characterisation of Quantum Processor, Cryogenic Quantum Control Circuits, RF Control Hardware, and QpiAI ASGP. About the Role We are building high-performance optimization infrastructure for real-world decision-making problems across logistics, manufacturing, and emerging tech domains. We are looking for a mathematically inclined, algorithmically sharp engineer who thrives at the intersection of theory and systems — someone who can translate abstract optimization problems into efficient, production-ready solvers. Key Responsibilities Design and implement fast, scalable solvers for complex optimization problems across discrete and continuous domains. Develop constraint modeling frameworks and metaheuristic algorithms grounded in strong mathematical principles. Evaluate solution quality, convergence behavior, and performance benchmarks across diverse instances and datasets. Work with system engineers to integrate your solver modules into larger optimization stacks and real-time decision systems. Explore and adapt techniques from mathematical programming, stochastic methods, and quantum-inspired approaches. What We're Looking For Strong foundation in mathematics : linear algebra, combinatorics, graph theory, numerical methods, convex and discrete optimization. Algorithmic and systems thinking : should be able to write fast, memory-efficient code and optimize for performance bottlenecks. Exceptional programming skills in Python and C++ (or Rust/Julia); low-level optimizations and profiler-driven development are a plus. Experience with algorithm design for constraint systems, heuristics, and metaheuristics. Hands-on coding profile : A high rating on platforms like Leetcode, Codeforces, or Hackerrank is a strong signal. Product thinking : capable of modular, reusable, and extensible solver design; understands how solvers scale in production systems. Exposure to quantum computing or hybrid quantum-classical paradigms is a plus. Good to Have Familiarity with model encoding techniques and constraint representations. Benchmarking experience on large-scale combinatorial datasets. Participation in mathematical modeling competitions (e.g., INMO, COMAP, Kaggle competitions involving optimization). Interested candidates can attempt the below mentioned Screening problems and share your submission file to As part of the submission, we require a zip file containing all associated code and a PDF of a report summarizing the approach for each problem and the findings obtained. Optimization Research Engineer - Screening Problems Problem 1: Max-Cut Optimization (Easy) Problem Statement: Given an undirected weighted graph, partition the vertices into two disjoint subsets such that the sum of edge weights between the subsets is maximized. Dataset: Use the GSET dataset from Stanford ( Benchmark your results against the Toshiba Digital Annealer results published on GSET instances. Deliverables: 1. Formulate the Max-Cut problem as a QUBO model. 2. Implement a solver (Python, D-Wave, or simulated annealing). 3. Demonstrate results on small and medium GSET graphs. 4. Benchmark solver results against published Toshiba solver results. Interpretation and Explanation: - Explain how Max-Cut maps to QUBO structure. - Discuss scalability limits and computational trade-offs. Solution Methodology Research: - Compare classical, heuristic, and quantum-inspired techniques. - Evaluate solver performance with respect to accuracy and computational time. Problem 2: Vehicle Routing with Time Windows (Medium) Problem Statement: A logistics company must deliver goods from a single depot to multiple customers. Each customer has a delivery time window, and each vehicle has a limited capacity. The goal is to minimize total travel distance while satisfying delivery constraints. Dataset Requirement: You must generate your own dataset with the following fields: - Customer ID - Coordinates (x, y) - Demand (units) - Time Window Start - Time Window End - Service Time - Vehicle Capacity - Depot Coordinates Deliverables: 1. Formulate the Vehicle Routing Problem with Time Windows (VRPTW) as a MILP. 2. Implement a solver using OR-Tools, Pyomo, or a custom heuristic method. 3. Generate synthetic datasets and demonstrate solution performance. 4. Provide a visual representation of optimized routes. Interpretation and Explanation: - Describe the trade-off between total distance and time window constraints. - Explain how constraints like capacity and delivery windows are modeled. Solution Methodology Research: - Compare MILP vs. heuristic formulations. - Discuss scalability and solver performance for varying problem sizes. Problem 3: Design and Benchmark a MILP Solver (Hard) Problem Statement: Design and implement a custom Mixed Integer Linear Programming (MILP) solver from scratch. The solver should handle general linear constraints, integer variables, and support branch-and-bound logic. Benchmark your solver on standard datasets. Benchmark Datasets: Use public datasets such as TSPLIB and CVRPLIB for benchmarking. Compare your solver's performance with commercial solvers such as Gurobi, CPLEX, or HiGHS in terms of runtime, optimality gap, and scalability. Deliverables: 1. Design and implement a modular MILP solver (Python or C++ preferred). 2. Document solver architecture, algorithms, and implementation details. 3. Benchmark solver on TSPLIB/CVRPLIB datasets. 4. Produce a technical report detailing performance, comparisons, and insights. Interpretation and Explanation: - Discuss your solver design choices (branching, cutting planes, presolve strategies). - Explain trade-offs between solver efficiency, generality, and accuracy. Solution Methodology Research: - Review state-of-the-art MILP solver architectures and compare with your implementation. - Suggest future improvements such as hybrid heuristics or parallelization. Why Join Us You’ll work closely with a team that understands optimization not just as a mathematical challenge, but as a product engineering problem. If you're excited about building fast solvers, pushing boundaries in hybrid or hardware-accelerated optimization, and solving problems at scale, we’d love to hear from you.