GP surgery
General practice absorbs the demand the rest of the system generates and the demand prevention failed to stop. Most of what hurts here is capacity and workforce, which no solver fixes. A minority of it is genuinely combinatorial. This page separates the two, because conflating them is how quantum computing earns its reputation for irrelevance.
Problems, sorted honestly
Same-day access and the 8am scramble
StatisticalDemand arrives in a spike at 08:00 against a fixed daily capacity, and is triaged into same-day, routine, and redirect streams. Online consultation tools flatten the arrival curve but do not change the integral.
- Classical baseline
- Queueing theory and discrete-event simulation, both mature and already used in practice-level capacity planning. Total-triage models are an operational change, not an algorithmic one.
- Quantum relevance today
- None. This is a demand-versus-capacity problem with a well-understood classical treatment. Listing it here is a boundary marker.
Appointment and clinic capacity allocation
CombinatorialAssigning appointment slots across clinicians, session types, and continuity requirements over a rolling week, subject to skill mix and contractual limits.
- Classical baseline
- Mixed-integer programming. Instances at practice scale solve to optimality in seconds with an off-the-shelf solver.
- Quantum relevance today
- The structure is a QUBO, so it is expressible — but the instances are small and classical solvers are exact. No crossover in sight.
Risk stratification and case finding (Core20PLUS5)
CombinatorialIdentifying undiagnosed hypertension, uncontrolled diabetes or missed severe-mental-illness health checks across a registered list, then selecting whom to invite under a fixed review capacity.
- Classical baseline
- Population-health-management dashboards and risk scores already deployed across ICBs; selection is usually greedy on predicted yield.
- Quantum relevance today
- Interesting only for the constrained-selection layer, where the Core20 fairness floor turns greedy selection into a genuinely constrained problem. The prediction layer stays classical.
Social prescribing referral routing
CombinatorialMatching patients to link workers and community assets with limited places, travel constraints, and patient preference.
- Classical baseline
- Bipartite matching — Hungarian algorithm, or min-cost flow. Polynomial time, exact.
- Quantum relevance today
- Exactly solvable classically. The interest is in the constrained variant with coverage floors, which is the same shape as the discharge problem at lower stakes.
Prescribing and deprescribing in multimorbidity
Not a solver problemSelecting a medication regimen that respects interactions, renal function, anticholinergic burden and patient preference — and knowing what to stop.
- Classical baseline
- STOPP/START, structured medication reviews, decision-support rule engines in the clinical system.
- Quantum relevance today
- Not an optimisation bottleneck. The molecular layer beneath it — how a drug binds — is where quantum chemistry lives, and that sits years upstream of the consultation.