Portfolio Optimization as KnapsackQAOA with Quantum Walk Mixer
Select assets under strict budget and risk capacity.
Select Assets Under Tight Budget and Risk Caps
Goal and Method Overview
The goal is to select a set of assets maximizing utility, or return, under a strict budget or risk capacity. Each asset carries a value and a weight, and the problem is framed as a knapsack instance.
The source material argues that real portfolios contain multiple hard constraints and that knapsack-style modeling captures tight budget and risk caps directly, while MILP, ILP, and heuristics remain strong baselines for constrained selection.
The quantum angle is to encode the knapsack as constrained QAOA with a Quantum Walk Mixer so the optimization stays within the feasible subspace.
- • End-to-end knapsack-form portfolio selection on a simulator, with budget or risk capacity and optional group caps.
- • Metrics for feasible rate, objective value, per-constraint violations, and seed-controlled reproducibility.
- • Downloadable report with methods, assumptions, and references, plus ready-to-run Python code.
How We Solve It
- Collect per-asset value and weight inputs, plus global capacity and any optional group caps.
- Encode binary variables in a constraint-preserving subspace, with a QAOA cost that penalizes violations.
- Use a Quantum Walk Mixer to explore the feasible subspace with shallow schedules and depth for stability.
- Run constrained QAOA and classical MILP or heuristics, then report objective value, feasibility, and seed stability.
- Deliver fixed seeds, environment notes, assumptions, and references for reproducibility.
Runs use public or client-provided price and risk estimates. The report documents windows, capacity settings, and any normalization applied to values and weights.
Strengths
- Quantum Walk Mixer keeps the search within a constraint-preserving subspace during optimization.
- The workflow compares constrained QAOA against MILP and heuristics on the same instance.
- Documented parameter schedules, seeds, and config support full reruns.
Weaknesses & Risks
- The source material describes this as a research-grade pipeline rather than a production-ready one.
- Hardware-readiness depends on problem size and device noise.
- Supporting multiple capacities requires additional constraints and penalty terms in the encoding.
What to Expect
PoC snapshot: a feasible constrained-QAOA run on a 5-asset instance using 11 qubits on a simulator.
Instance
5 assets
Qubits
11
Execution
Simulator
Key Outcomes
Feasibility
Feasible constrained-QAOA
Objective
Comparable to MILP and heuristics
Schedules
Parameter schedules logged
Reproducibility
Mixer depth logged
Who it's for
This landing is aimed at teams evaluating constrained portfolio selection under explicit capacity limits and reproducible mixer design.
Quant PMs and research quants
For teams working with tight budgets and caps in portfolio selection.
Optimization teams
For groups evaluating constrained QAOA as an alternative or complement to classical solvers.
Academic and industry R&D
For teams exploring mixer-design trade-offs in constrained optimization.
How it works
Constrained QAOA with a Quantum Walk Mixer, benchmarked against classical baselines
Data & Capacity
Collect per-asset value and weight inputs, plus global capacity and optional group caps
Encoding
Build binary variables in a constraint-preserving subspace and encode penalties for violations
Mixer Design
Run QAOA with a Quantum Walk Mixer using shallow schedules and depth for stability
Evaluation
Compare constrained QAOA against MILP and heuristics on objective value, feasibility, and seed stability
Outputs
Deliver fixed seeds, environment notes, assumptions, references, code, and report
Try Superpositions Studio
Run knapsack-form portfolio selection on a simulator, review feasibility and objective metrics, and download the report and code.
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