Quantum readiness: classical, quantum-inspired and hybrid approaches compared

By Muhammad Haziq Faris, Co-founderTopic QuantumPublished Read 6 min
Contents
Most of the value is in how the problem is framed, long before any solver runs.

“Quantum-ready” should not mean buying into a prediction. It should mean understanding a problem well enough to test different methods fairly, with real constraints, a strong baseline and measurable outcomes.

This article explains the formulations behind most quantum optimisation work, the difference between classical, quantum-inspired and hybrid approaches, and how to compare them without fooling yourself. It is a companion to quantum computing in Malaysia: where should a business begin?

An illustrative problem

Take an illustrative scheduling problem. A workshop has jobs to run on a set of machines. Each job must go to exactly one machine, some jobs cannot share a machine, each machine has limited hours, and the aim is to finish everything as early and as evenly as possible. Change one assignment and others have to move. Problems like this, along with routing, allocation and timetabling, are combinatorial: the number of possible assignments grows explosively with size.

Many methods could tackle it: exact mixed-integer programming, constraint programming, purpose-built heuristics, and quantum-inspired or quantum formulations. Which is right depends on the problem, its size, how quickly an answer is needed and how good it has to be.

What QUBO and Ising models are

Quadratic unconstrained binary optimisation (QUBO) writes a problem as a set of yes-or-no decision variables x1 to xn, each 0 or 1, and an objective made only of single and pairwise terms: minimise the sum of Qijxixj over all pairs i, j. In the scheduling example, xjm = 1 might mean “job j runs on machine m”.

The Ising model is the same idea in the language of physics. Each variable is a spin si that is either −1 or +1, with a field hi on each spin and a coupling Jij between pairs, and the aim is the arrangement with the lowest energy. Substituting xi = (1 + si) / 2 turns one form into the other. Quantum annealers are built to find low-energy states of exactly this kind of model, which is why it appears so often in quantum optimisation.

Constraints become penalties

“Unconstrained” is the catch. Real problems have constraints, and a QUBO has no direct way to state them, so they are added to the objective as penalties. “Each job runs on exactly one machine” becomes P × (xj1 + xj2 + … − 1)2, which is zero when exactly one of the variables is 1 and positive otherwise.

The penalty weight P is a design choice. Too small, and the solver returns cheap schedules that break the rules. Too large, and the penalties swamp the real objective and make the landscape harder to search. Inequalities, such as limited machine hours, need extra slack variables, and whole-number quantities need several binary variables each, so a modest real problem can become a large QUBO.

None of this needs quantum hardware. A QUBO is a mathematical form, and it can be solved, or approximately solved, on an ordinary computer. Calling a formulation “quantum” does not mean quantum hardware was used, and it does not make the result faster or better.

Classical, quantum-inspired, quantum and hybrid

Classical methods run on ordinary hardware. Exact solvers, such as mixed-integer programming with branch and bound, or constraint programming, can prove how good a solution is. Heuristics, such as local search, tabu search, simulated annealing and genetic algorithms, find good solutions quickly without that proof. For many industrial problems a well-tuned classical solver is the benchmark to beat.

Quantum-inspired methods also run on classical hardware, but borrow ideas from quantum physics or quantum algorithms. In optimisation the most common are solvers that work directly on QUBO or Ising models: simulated annealing, parallel tempering, simulated bifurcation and purpose-built digital annealer chips, alongside tensor-network methods. The term is used loosely, and also covers classical algorithms derived by studying quantum ones. These methods can be very effective on problems that suit the QUBO form. They are still classical computing.

Quantum methods run on quantum hardware. Quantum annealers search directly for low-energy states of an Ising model. On gate-based machines, the quantum approximate optimisation algorithm (QAOA) is the best-known approach to the same kind of problem. Both are limited today by the number and quality of qubits, by how well the problem's connections map onto the hardware, and by noise.

Hybrid methods combine the two. A classical optimiser may tune the parameters of a quantum circuit in a loop, as in QAOA and the variational quantum eigensolver (VQE). Or a classical solver may split a large problem into pieces and send some of them to quantum hardware. Most practical quantum optimisation today is hybrid, and the classical part often does much of the work.

How to compare them fairly

A disciplined evaluation runs the same instances through each route and scores every route the same way.

How to compare classical, quantum-inspired and hybrid methods fairly One problem runs through three routes. A strong classical baseline: an exact solver and a tuned heuristic. A QUBO or Ising formulation solved by a quantum-inspired solver on classical hardware. The same formulation on a quantum or hybrid approach, only when meaningful. All three are scored the same way, on feasibility, solution quality, time to target, total cost and reproducibility, and a person makes a written stop or go decision. If classical wins, ship the classical solution. One problemillustrative scheduling Classical baselineexact solver · tuned heuristic QUBO / Isingpenalties Quantum-inspiredon classical hardware QUBO / Isingpenalties Quantum or hybridonly when meaningful Same scorecardfeasibilitysolution qualitytime to targettotal costreproducibility Stop or goa writtendecision How to compare classical, quantum-inspired and hybrid methods fairly One problem runs through three routes. A strong classical baseline: an exact solver and a tuned heuristic. A QUBO or Ising formulation solved by a quantum-inspired solver on classical hardware. The same formulation on a quantum or hybrid approach, only when meaningful. All three are scored the same way, on feasibility, solution quality, time to target, total cost and reproducibility, and a person makes a written stop or go decision. If classical wins, ship the classical solution. One problemillustrative scheduling Classical baselineexact solver · tuned heuristic QUBO / Isingpenalties Quantum-inspiredon classical hardware QUBO / Isingpenalties Quantum or hybridonly when meaningful Same scorecardfeasibilitysolution qualitytime to targettotal costreproducibility Stop or goa written decision

ReadoutOne problem, three routes, the same scorecard. Hover or tap a part to read it.

How to compare classical, quantum-inspired and hybrid methods fairly. The scheduling problem is illustrative; this is a method, not a REKA project result.
  1. A strong classical baseline first: the best available exact solver with a time limit, and a well-tuned heuristic. Not a naive one.
  2. A quantum-inspired solver on the QUBO formulation, if the problem suits it.
  3. A quantum or hybrid approach only when hardware access, problem size, noise and the algorithm make the experiment meaningful.

Then report, for each route:

  • Feasibility: how often the answer satisfies every constraint.
  • Solution quality: the gap to the best known solution, or to a proven bound.
  • Time to target: how long it takes to reach a given quality, including formulation and data preparation, not only solver time.
  • Total cost: compute, hardware access and engineering effort.
  • Reproducibility: results across repeated runs and random seeds, with solver versions and settings recorded.
  • Limitations: what was not tested, and the instance sizes for which the result holds.

End with a written stop or go decision, with the evidence behind it. Avoid cherry-picked instances, weak baselines and claims of advantage that nobody else can repeat. If classical wins, which is common today, ship the classical solution.

What readiness means for a business

For most businesses in Malaysia and the wider region, the near-term value is not quantum hardware. It is better problem formulation, stronger classical optimisation, and people inside the organisation who can judge future quantum claims for themselves. When better hardware arrives, an organisation that has already framed its problems, built its baselines and kept its data in order will be able to test it quickly.

Security runs on a separate track. Preparing for post-quantum cryptography means taking an inventory of where cryptography is used and planning a migration to the new standards, as covered in where should a business begin?

How REKA approaches it

The method on our Quantum Lab page is the one described here: find the real optimisation problem, formulate its objectives and constraints as a QUBO or Ising model where that suits, solve with quantum-inspired and, where meaningful, quantum solvers, validate against the best classical method, and stop if classical wins. Whether quantum-inspired methods can outperform classical solvers on the routing, allocation and scheduling problems in our domains is an open research question in the Lab, recorded as experiment EXP-06.

This is a methodology and a potential offering, not a case study. We have not published a client project that uses it, and we do not claim a quantum advantage.

Further reading

References

  • Lucas, A. (2014). Ising formulations of many NP problems. Frontiers in Physics, 2, 5. doi:10.3389/fphy.2014.00005
  • Glover, F., Kochenberger, G. and Du, Y. (2019). Quantum Bridge Analytics I: a tutorial on formulating and using QUBO models. 4OR, 17, 335–371. doi:10.1007/s10288-019-00424-y
  • Farhi, E., Goldstone, J. and Gutmann, S. (2014). A Quantum Approximate Optimization Algorithm. arXiv:1411.4028. arxiv.org/abs/1411.4028

Questions people ask

What is a QUBO?

Quadratic unconstrained binary optimisation writes a problem as a set of yes-or-no decision variables, each 0 or 1, and an objective made only of single and pairwise terms.

How do you compare quantum and classical solvers fairly?

Run the same instances through each route and score every route the same way, against a classical baseline.

Does a business need quantum hardware to benefit?

For most businesses in Malaysia and the wider region, the near-term value is not quantum hardware.

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