QAOA vs MILP for Portfolio Knapsack OptimizationQuantum Heuristics Against Classical Baselines
Benchmark a 5-asset, 11-qubit QAOA run against MILP.
Compare Quantum Search with an Exact Classical Baseline
Comparison Setup
Portfolio knapsack optimization asks which assets to select when each candidate has value, weight, and explicit capacity constraints. The source use case describes a feasible constrained-QAOA proof of concept on a 5-asset instance using 11 qubits on a simulator.
MILP and heuristics remain strong baselines for constrained selection. The QAOA variant uses a Quantum Walk Mixer to explore feasible selections while preserving the constrained structure of the problem, then compares objective value, feasibility, and seed stability against the classical references.
- • Does the 11-qubit QAOA run return feasible selections under the same budget or risk caps?
- • Is the objective comparable to MILP and heuristics on the same 5-asset instance?
- • Are results stable across seeds, schedules, and documented configuration?
Why compare them
- MILP gives a strong classical reference for constrained portfolio selection.
- QAOA with a Quantum Walk Mixer keeps the search inside a constraint-aware subspace.
- Running both methods on the same objective and constraints makes feasibility and objective gaps visible.
Limits to keep explicit
- QAOA is a heuristic and does not replace exact classical optimization for all instances.
- Performance depends on the encoding, mixer design, depth, schedule, and device noise.
- Small simulator benchmarks are useful for methodology, but not a production guarantee.
Comparison Outputs
The source material reports a feasible constrained-QAOA simulator run whose objective is comparable to MILP and heuristics on the same instance.
Classical baseline
MILP
Quantum method
Constrained QAOA
PoC instance
5 assets
Quantum resources
11 qubits
Who should use this comparison
Use it when you need a defensible QAOA benchmark against MILP, backed by the concrete PoC setup from the source material.
5 assets
PoC portfolio instance
11 qubits
Simulator setup
MILP
Exact classical baseline
Feasible
Constraint-aware QAOA run
Optimization teams
For teams that need a classical reference before evaluating a quantum heuristic.
Portfolio researchers
For researchers testing knapsack-style asset selection under strict budget or risk caps.
R&D leads
For teams deciding whether constrained QAOA is worth deeper simulator or hardware experiments.
How it works
One formulation, two solvers, one reproducible benchmark.
Define Problem
Set the 5-asset instance, values, weights, budget or risk caps, and the shared objective
Run MILP
Solve the classical baseline and record feasibility, objective value, and constraints
Run QAOA
Use constrained QAOA with a Quantum Walk Mixer in an 11-qubit simulator setup
Compare
Measure feasibility, objective gap, seed stability, and configuration sensitivity
Export
Download the methods, assumptions, code, and reproducible benchmark report
Related pages
Algorithms, applied use cases and benchmarks connected to this page
Finance
Quantum Portfolio Optimization: QAOA, HHL and Annealing
Compare quantum portfolio optimization: QAOA with quantum walk mixers, HHL mean-variance allocation, and quantum annealing for cardinality-constrained QUBOs.
Algorithms
QAOA for QUBO and Ising Optimization
Explore the Quantum Approximate Optimization Algorithm for QUBO and Ising problems with reproducible benchmarks, parameter schedules, and hardware notes.
Comparisons
Quantum Annealing vs QAOA for QUBO Problems
Compare quantum annealing with QAOA on QUBO/Ising optimization: hardware, constraints, scaling, and two real portfolio-optimization benchmarks.
Algorithms
Quantum Annealing for QUBO and Ising Problems
Map combinatorial optimization problems to QUBO and Ising form and benchmark quantum annealing with reproducible runs, baselines, and hardware notes.
Benchmark QAOA Against MILP
Run the 5-asset, 11-qubit constrained QAOA benchmark and compare feasibility and objective quality against MILP and heuristics.
Try your first case for free