Quantum Optimization: Finding the Best Solution in a World of Possibilities

Imagine you're planning a delivery route for a fleet of trucks. You have 100 stops to make. The trucks need to start and end at the depot. You want the shortest possible total distance. How many possible routes are there? For 100 stops, it's roughly 100!—a number with 158 digits. That's more than the number of atoms in the universe.

You can't try every route. No computer, classical or quantum, can. You need to find a good route without trying all of them. This is an optimization problem—finding the best solution from a vast space of possibilities.

Optimization problems are everywhere. Scheduling flights, designing networks, managing supply chains, optimizing portfolios, discovering drugs. They're some of the most important and hardest problems in computing. Quantum computers might help.

What Is Optimization?

Optimization is the process of finding the best solution to a problem from a set of possible solutions. "Best" is defined by an objective function—something you want to minimize (like cost or time) or maximize (like profit or efficiency).

Most optimization problems have constraints—conditions that solutions must satisfy. In the delivery route problem, constraints might include time windows for deliveries, truck capacities, and driver hours.

Optimization problems come in different flavors:

• Continuous optimization: Variables can take any value in a range. Finding the shape of an airplane wing that minimizes drag is a continuous optimization problem.
• Discrete optimization: Variables take discrete values. Scheduling employees to shifts is discrete—each employee either works or doesn't.
• Combinatorial optimization: Problems involving combinations of discrete choices. The delivery route problem is combinatorial—it's about the order of stops.

Why Optimization Is Hard

The difficulty of optimization comes from the size of the solution space. For many problems, the number of possible solutions grows exponentially with the problem size. This is the combinatorial explosion.

Classical algorithms for optimization include:

• Exact methods: These guarantee finding the optimal solution but may take an impossibly long time for large problems.
• Heuristics: These find good solutions quickly but don't guarantee optimality. Simulated annealing, genetic algorithms, and local search are examples.
• Approximation algorithms: These guarantee solutions within a certain percentage of optimal.

Quantum Approaches to Optimization

Quantum computers offer several approaches to optimization:

Quantum annealing: This is the approach used by D-Wave systems. Quantum annealing is a physical process where a system starts in a simple quantum state and slowly evolves toward a state that encodes the solution to an optimization problem. The system naturally finds low-energy states—which correspond to good solutions.

Quantum annealing is not a universal quantum computing approach. It's specialized for optimization problems that can be expressed as finding the minimum of an energy function. But for those problems, it can be very effective.

In early 2026, D-Wave announced their Advantage2 system with 5,000 qubits. On real-world optimization problems, it delivered 50x speedups over classical solvers. Companies are already using it for factory scheduling, logistics, and drug discovery.

Quantum approximate optimization algorithm (QAOA): QAOA is a hybrid algorithm for gate-model quantum computers. It alternates between applying a cost Hamiltonian (which encodes the optimization problem) and a mixer Hamiltonian (which explores the solution space). The parameters of these alternations are optimized by a classical computer.

QAOA is more flexible than quantum annealing but requires more qubits and deeper circuits. It's an active area of research, with experiments on problems like MaxCut (finding the best way to split a graph) and portfolio optimization.

Variational quantum eigensolver (VQE): VQE was originally developed for quantum chemistry, but it can also be used for optimization. It's similar to QAOA in that it uses a parameterized quantum circuit optimized by a classical computer.

Grover-based optimization: Grover's algorithm provides a quadratic speedup for unstructured search. This can be applied to optimization by searching through the solution space. The speedup isn't exponential, but for large problems, quadratic can still be significant.

Real-World Applications

Quantum optimization is already being used for real-world problems:

Logistics: DHL and other logistics companies are using quantum optimization to plan delivery routes. The problems are large and complex, with many constraints. Quantum approaches can find better routes faster than classical methods.

Factory scheduling: Volkswagen is using quantum optimization to schedule production at their factories. The problem involves coordinating multiple production lines, managing inventory, and meeting delivery deadlines. Quantum approaches have improved efficiency by 15% in trials.

Portfolio optimization: Financial firms are using quantum optimization to construct investment portfolios. The goal is to maximize returns while managing risk. Quantum approaches can handle more constraints and find better trade-offs than classical methods.

Drug discovery: Biotech companies are using quantum optimization to design new drugs. The problem involves finding molecules that bind to target proteins while meeting other constraints like toxicity and stability. Quantum approaches can explore larger chemical spaces.

The Current State

Quantum optimization is further along than many other quantum applications. D-Wave has been selling quantum annealers for over a decade. Companies are already using them for production workloads.

Gate-model quantum optimization is less mature. QAOA and VQE have been demonstrated on small problems but haven't yet shown advantage over classical methods on practical scales. This is an active area of research.

The field is moving toward hybrid approaches: classical computers handle the parts they're good at, quantum computers handle the parts where they have an advantage. This is likely how quantum optimization will be used in practice.

Challenges

Quantum optimization faces several challenges:

Problem encoding: Many optimization problems don't naturally fit the quantum hardware. They need to be encoded—mapped onto the qubits and connections of the quantum processor. This encoding can be inefficient, potentially wiping out any advantage.

Noise: Today's quantum computers are noisy. Noise can degrade the quality of solutions or make the optimization process unstable.

Scaling: Quantum annealers have thousands of qubits but limited connectivity. Gate-model systems have better connectivity but fewer qubits. Neither yet has the combination of scale and quality needed for large optimization problems.

Proof of advantage: For many optimization problems, classical solvers are very good. Showing that quantum approaches are better—not just different—requires careful benchmarking.

The Future

Quantum optimization is likely to be one of the first practical applications of quantum computing. The reasons:

• Optimization problems are everywhere.
• Quantum approaches are well-suited to certain types of optimization.
• Companies are already using quantum optimization today.

As hardware improves, quantum optimization will be applied to larger and more complex problems. The 50x speedups reported by D-Wave are likely just the beginning. Future systems may deliver 100x or 1000x speedups for certain problems.

Conclusion

Optimization is at the heart of many important decisions—how to route deliveries, how to schedule production, how to design drugs, how to invest money. Classical computers do a good job on these problems, but the hardest problems remain unsolved or solved suboptimally.

Quantum computers offer new approaches to optimization. Quantum annealing, QAOA, VQE, and other techniques can explore solution spaces in ways that classical computers can't. The first practical applications are already here. More are coming.

For businesses and researchers working on hard optimization problems, quantum optimization is becoming a tool worth watching. It won't replace classical methods—but it might solve problems that classical methods can't.