Research Engineer – Optimization

About QpiAIAt 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 QuantumProcessor, Cryogenic Quantum Control Circuits, RF Control Hardware, and QpiAI ASGP.About the RoleWe 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 krithika.r@qpiai.tech.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 ProblemsProblem 1: Max-Cut Optimization (Easy)Problem Statement:Given an undirected weighted graph, partition the vertices into two disjoint subsets such that thesum of edge weights between the subsets is maximized.Dataset:Use the GSET dataset from Stanford (http://web.stanford.edu/~yyye/yyye/Gset/). Benchmark yourresults 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 customerhas a delivery time window, and each vehicle has a limited capacity. The goal is to minimize totaltravel 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 CoordinatesDeliverables: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. Thesolver should handle general linear constraints, integer variables, and support branch-and-boundlogic. Benchmark your solver on standard datasets.Benchmark Datasets:Use public datasets such as TSPLIB and CVRPLIB for benchmarking. Compare your solver'sperformance 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 UsYou’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.