MarkoScaleCompare

Comparison

Classical vs Quantum-inspired

Two different approaches to the same portfolio optimization problem.

Quantum-inspired

QUBO + SA

Formulation Type
Lagrangian Objective
Method
QUBO (Quadratic Unconstrained Binary Optimization)
Solver / Sampler
Simulated Annealing (Heuristic Search) (neal)
Objective
Minimize energy function
Model (Energy)
$$F(x)=q\cdot\operatorname{Risk}(x)-\operatorname{Return}(x)+A\left(\sum_{i=1}^{n}x_i-k\right)^2$$

Classical

MILP + CBC

Formulation Type
Epsilon-Constraint
Method
Mixed-Integer Linear Programming (MILP)
Solver
CBC (COIN-OR Branch and Cut)
Objective
Maximize expected return
Model
$$\max_x\;\frac{\mu^{\mathsf T}x}{k}$$

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