Quantum-Accelerated Portfolio Rebalancing for Multi-Custodian Wealth Platforms: A Cost-Benefit Framework

Abstract

Wealth management is marred by systemic fragmentation. Investors today distribute assets across multiple custodians, each running its own ledger, its own tax lot system, and its own compliance engine, yet portfolio rebalancing tools still treat every account as if it exists in isolation. The result is predictable: missed tax opportunities, duplicated risk exposure, and wash-sale violations that span custodial boundaries; no single system is watching. The article introduces the Multi-Custodian Hybrid Optimization Theory (MCHOT), a framework that treats the entire household as a single optimization target rather than a collection of disconnected accounts. The global rebalancing task is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, encoding budget constraints, portfolio covariance, expected returns, tax-lot granularity, and cross-custodian compliance penalties into one energy minimization objective. A Hybrid Quantum-Classical (HQC) pipeline then solves this objective using the Quantum Approximate Optimization Algorithm (QAOA), followed by a deterministic compliance-repair stage before any order is routed. Beyond the technical architecture, MCHOT establishes a practical economic rationale for hybrid quantum deployment, identifying the exact portfolio size and custodian density at which quantum coordination becomes financially justified. The proposed approach highlights how quantum-powered global coordination can minimize combinatorial fragmentation while adhering to rigorous regulatory requirements. The implications reach beyond computation: this framework reframes rebalancing as a household-wide coordination discipline with long-term consequences for scalable, tax-aware wealth management.