Hierarchical Portfolio Optimization via Clustering and Quantum Processing
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Solution Overview
Problem
Current quantum computers with limited qubits struggle to optimize large asset portfolios due to integer constraints and odd-lot asset trading, making it difficult to solve mixed binary optimization problems efficiently.
Innovation Solution
A hybrid classical-quantum algorithm that uses Hierarchical clustering to decompose the portfolio optimization problem into smaller sub-problems, which are then solved using a quantum processor with binary/mixed-integer mean-variance optimization, allowing for recursive capital allocation and transmission of sub-clusters for quantum processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If quantum computers are used to optimize large asset portfolios, then optimization accuracy is improved, but the limited number of qubits makes it impossible to process large portfolios directly
Solution Approach 1:
The patent applies segmentation by dividing the large portfolio optimization problem into multiple smaller sub-problems through hierarchical clustering. The portfolio is clustered into groups where each group contains a manageable number of assets that can be processed by the limited qubits available. This allows the quantum computer to solve multiple smaller optimization problems sequentially, ultimately achieving optimization of the entire large portfolio despite qubit limitations.
2Productivity
If hierarchical clustering is used to decompose the portfolio, then the problem size fits quantum processor capabilities, but the system complexity increases due to multiple processing components
Solution Approach 1:
The patent merges classical computing components (portfolio analysis, hierarchical clustering, capital allocation) with quantum computing components (binary/mixed-integer optimization) into a hybrid system. This integration allows the system to leverage the strengths of both classical and quantum computing - classical systems handle data preparation and problem decomposition, while quantum systems provide accelerated optimization for specific sub-problems, achieving high productivity despite increased system complexity.
3Reliability
If integer constraints and odd-lot asset trading are enforced, then investment realism is improved, but the optimization problem becomes more difficult to solve
Solution Approach 1:
The patent addresses integer constraints and odd-lot trading requirements by formulating the optimization problem as a binary/mixed-integer program. This parameter change transforms the continuous optimization problem into a discrete one, where asset allocations are constrained to integer values representing actual tradable units. The hybrid quantum-classical algorithm is specifically designed to handle these discrete constraints, maintaining investment realism while finding optimal solutions despite increased optimization complexity.
Data Source
AI summary
Systems and methods that address an optimized method to handle portfolio constraints such as integer budget constraints and solve portfolio optimization problems that map both to mixed binary and quadratic binary optimization problems. A digital processor is used to create a hierarchical clustering; this clustering is leveraged to allocate capital to sub-clusters of the hierarchy. Once the sub-clusters are sufficiently small, a quantum processor is used to solve the portfolio optimization problem. Thus, the innovation employs clustering to reduce an optimization problem to sub-problems that are sufficiently small enough to be solved using a quantum computer given available qubits.