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Chapter XXI Max Cut
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  1. 61 — The maximum cut
  2. 62 — Local search in Julia
  3. 63 — Spin glasses and portfolio risk
63

Spin glasses and portfolio risk

Max Cut is the Ising model wearing a graph-theory hat. It runs everything from condensed-matter simulations to portfolio risk balancing.

In condensed-matter physics, the Ising spin glass is the ground state of a system of interacting magnetic spins — exactly Max Cut on the interaction graph. This problem motivated the development of simulated annealing (Kirkpatrick et al., 1983), which is now standard in optimization. In finance, mean-variance portfolio rebalancing under cardinality constraints reduces to a quadratic problem isomorphic to Max Cut; QC Ware and 1QBit have shipped Max-Cut-based portfolio optimizers. VLSI design uses Max Cut for layer assignment (assign each net to one of two metal layers, minimize via crossings). And quantum computing companies (Rigetti, IonQ, IBM Quantum) benchmark their hardware on Max Cut via QAOA — the canonical NISQ-era quantum optimization workload.

In plain terms

In a magnet, atoms can spin up or down, and atoms with opposite spins are happier together. Finding the most-stable arrangement (the most "happy pairs") is Max Cut. The same math runs in quantum-computing benchmarks and portfolio-balancing software.

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