HADOF
Industrial Scale Applications on Today’s QPUs
The Hamiltonian Auto-Decomposition Optimisation Framework splits optimisation problems far larger than any quantum processor into circuits that fit on it, then recombines the answers. It has already assembled a bacterial genome on IBM hardware.
Real problems are hundreds of times bigger than the chip
A state-of-the-art IBM Heron processor has 156 qubits. Industrial optimisation problems run to tens of thousands of variables.
variables in our largest run, a fully dense QUBO
pairwise couplings in that problem
qubits available on the IBM device
Solve a few qubits at a time, share what each piece learns
- DecomposeSplit the QUBO into small groups of variables that each fit in one circuit.
- Solve on the QPURun each group as a small circuit. Every other variable enters through its current probability, so each piece sees the rest of the problem.
- Share and repeatUpdate the probabilities from the measured samples and sweep again. The circuit size never grows with the problem.
- RecombineAssemble thousands of full candidate solutions and keep the best. Any sampler plugs in: QAOA, quantum annealing, SA, FALQON.
Small circuits hold their quality where full circuits collapse
best quality at 50 variables on ibm_kingston: HADOF vs full-circuit QAOA
less wall-clock time running HADOF across four IBM QPUs, at comparable quality
of simulated annealing’s quality at 500 variables, using 5-qubit sub-circuits (ECAI 2025)
Quantum genome assembly of the P. aeruginosa bacterial chromosome
Exploiting today’s quantum computers for real optimisation workloads: real nanopore reads, a standard assembly pipeline, and the hard ordering step solved by HADOF on ibm_torino.
From 5-qubit circuits to 150-qubit circuits
Our newest version fills almost the whole chip in every circuit. That took a fully dense 45,000-variable QUBO onto ibm_aachen in 300 circuits.
| Random dense QUBO | 22,350 vars | 45,000 vars |
|---|---|---|
| QAOA-HADOF on ibm_aachen quality vs full SA | 52.6% | 49.1% |
| SA-HADOF, same groups quality vs full SA | 98.5% | 98.8% |
| SA-HADOF speed-up vs full SA | 7.9× | 8.6× |
| QPU execution time | ~35 min | 73 min |
| Time in the IBM queue | ~6.4 h | ~74.6 h |
If your problem is a QUBO, HADOF can run it on hardware too small for it
Genome assembly
Ordering DNA reads into a chromosome, end to end on ibm_torino.
Dense random QUBOs
The hardest general case: every variable coupled to every other.
Routing and logistics
Vehicle routing and travelling-salesman tours share assembly’s maths.
Scheduling
Shifts, jobs and machine time with conflicts as penalties.
Portfolio optimisation
Asset selection under risk and budget penalties.
Network design and partitioning
Max-cut, clustering and graph partitioning.
Feature selection
Choosing informative, non-redundant inputs for machine learning.
Outbreak and cancer genomics
Faster assembly and many near-optimal candidates for variant analysis.
Bring us a problem that doesn’t fit your QPU
- Quantum genome assembly of a complete bacterial chromosome from real sequencing data on NISQ hardwareSankar, Miliotis & Caton · 2026
- Towards High Performance Quantum computing (HPQ): parallelisation of HADOFSankar, Miliotis & Caton · arXiv:2604.27836 (2026)
- Scalable quantum optimisation using HADOFSankar, Miliotis & Caton · AIQxQIA @ ECAI 2025, CEUR-WS vol. 4153