Combinatorial optimisation (CO) is the class of problems that seek the best solution from a finite but exponentially large set of discrete configurations — scheduling, routing, portfolio selection, protein folding, chip placement, and logistics are canonical instances. What makes them hard is that exhaustive search is infeasible at scale, and for NP-hard problems (travelling salesman, max-cut, graph colouring) no polynomial-time exact algorithm is known.
Classical solvers fall into two families: exact methods (branch-and-bound, integer linear programming via CPLEX or Gurobi) that find provably optimal solutions but scale poorly, and heuristics (simulated annealing, genetic algorithms, tabu search) that find near-optimal solutions in practical time. The gap between the two is the core engineering tradeoff.
The deep-tech investment angle is the claim that physics-native hardware — systems that physically encode a CO problem in an energy landscape and let the physics find the minimum — can deliver large advantages in energy efficiency and time-to-solution for specific problem classes. The principal substrates being developed are: Quantum Annealing (superconducting flux qubits mapping problem to Ising Hamiltonian), Stochastic / Ising Machines (CMOS or FPGA Ising emulators running probabilistic bit-flip dynamics), Coherent Ising Machine (optical parametric oscillators or photonic networks), and photonic-compute accelerators.
The unresolved question for investment is whether the advantage is at the hardware substrate level (defensible moat) or at the application-mapping software layer, where a well-tuned classical solver still competes.
Frontier
- For which problem classes and instance sizes do physics-native solvers (Ising machines, quantum annealers, photonic CO accelerators) consistently beat best-in-class classical heuristics without cherry-picking benchmarks?
- Is the investable wedge the hardware substrate, the problem-mapping software layer, or the vertical application (logistics, drug discovery, financial portfolio, chip design)?
- As LLM-based combinatorial solvers (using reinforcement learning on graph-structured problems) mature, does physics-native CO retain a defensible energy or latency moat?