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Problem Comparison

All quantum problems with real Azure Quantum Resource Estimator data. Click column headers to sort.

Physical Qubits by Problem

AlgorithmStageRuntime
Catalysis SimulationQPEStage C423.1k3527—6558010.6s
Climate ModelingHHLArchived58.9k234028182.9ms
Database SearchGroverArchived61.1k18—18—507.5μs
Drug DiscoveryQPEStage C423.1k3527—328445.1s
Error CorrectionQECStage C1.7k18———7.3μs
FactorizationShorStage C60.7k259591.0ms
High-Frequency TradingSamplingArchived51.3k12—25547.4μs
Hubbard ModelQPEStage C595.0k4027—8194810.7s
Linear SolversHHLArchived86.6k23285611416.9ms
Materials DiscoveryQPEStage C754.7k3554—16389627.2s
Nuclear PhysicsQPEStage C667.0k3527—13105221.2s
PhotovoltaicsQuantum WalkStage C47.2k12—20101.8ms
Post-Quantum CryptographyGroverArchived26.1k12—2—66.2μs
Protein FoldingQAOAArchived60.9k15——9732.5μs
QAE Risk AnalysisQAE/IQAEArchived369.4k4015106873713843.1ms
QAOA MaxCutQAOAArchived53.6k12——6498.8μs
Quantum ChromodynamicsTrotterStage C54.6k9——9716.5μs
Quantum Machine LearningSwap TestArchived86.9k18—210603.8μs
Quantum OptimizationQAOAArchived63.8k15——10805.0μs
Space Mission PlanningQAOAArchived70.3k15——14953.8μs

Key Observations

  • Qubit range: 1.7k (Error Correction) to 754.7k (Materials Discovery), a 432x spread.
  • Magic states set the cost: every T gate, Toffoli and arbitrary-angle rotation is paid for with magic states (a rotation is synthesized from T states, a Toffoli consumes a CCZ state), so T factories take 60-94% of the physical qubits in these estimates, whatever the explicit T-gate count.
  • Largest non-Clifford counts: 163,896 rotations (Materials Discovery); 10,687 Toffolis (QAE Risk Analysis); 54 T gates (Materials Discovery).
  • What was estimated: the toy instances themselves, compiled for fault tolerance with the Quantum Resource Estimator (qdk.qre) on 50 ns gates at a 10⁻³ error rate with a surface code; these are not utility-scale versions of the problems.