Hospital
The hospital's problem is not that it cannot treat people. It is that it cannot move them. Bed occupancy above the 85% safe threshold every year since 2010, and up to one in three beds holding a patient who is medically fit to leave, means that the acute system's scarcest resource is discharge, not clinical capacity. Everything else on this page is downstream of that.
Problems, sorted honestly
Bed and discharge flow
CombinatorialMatching patients who no longer meet the criteria to reside against community and social-care placements over a rolling horizon.
- Classical baseline
- MILP assignment models and discrete-event simulation of patient flow; discharge-to-assess as the operational model.
- Quantum relevance today
- The flagship problem for this project. Clean QUBO form, exact classical optimum available at small instance sizes for benchmarking. Treated in full on its own page.
Elective and theatre scheduling
CombinatorialSequencing lists across theatres and surgeons subject to session length, kit availability, staffing and priority class, against an elective backlog.
- Classical baseline
- MILP and constraint programming, widely deployed. Commercial theatre-scheduling products exist and work.
- Quantum relevance today
- Structurally a QUBO but classically well served. A quantum method would need to beat a tuned CP solver on a realistic instance, which no published result does.
Diagnostic pathway sequencing
CombinatorialOrdering tests across community diagnostic centres and acute imaging to minimise time-to-diagnosis under scanner capacity.
- Classical baseline
- Scheduling heuristics and simulation; capacity, not sequencing, is usually binding.
- Quantum relevance today
- Low. Worth stating because the 10 Year Health Plan expands community diagnostics substantially.
Single national formulary and ward stock
CombinatorialAllocating stock across wards and sites under a national formulary, with shelf life, storage constraints and demand variability.
- Classical baseline
- Inventory theory and stochastic programming; automated dispensing systems already optimise at cabinet level.
- Quantum relevance today
- Low today. The formulary change is a policy simplification that reduces the combinatorial size of the problem, not increases it.
Molecular electronic structure
CombinatorialGround-state and excited-state energies for molecules relevant to drug action and materials.
- Classical baseline
- CCSD(T) and DMRG remain the reference for the molecule sizes anyone can currently run on quantum hardware.
- Quantum relevance today
- The one place on this page where quantum hardware has a credible long-run advantage, and the furthest from the ward. Demonstrated here on ethylene and H2.
Sources
- NHS hospital beds data analysis (BMA, January 2025)
- Fit for the Future: 10 Year Health Plan for England (DHSC, July 2025)