Large-scale Portfolio Optimization Using Pauli Correlation Encoding Achieves Efficient Exploration of Complex Solution Spaces with Gate-based Quantum Systems

Portfolio optimisation, a fundamental process in finance, traditionally employs classical techniques to balance investment risk and potential returns. Vicente P. Soloviev and Michal Krompiec, from Fujitsu Research of Europe Ltd., present a new approach that harnesses the power of quantum computing to tackle this complex problem. Their work demonstrates how a gate-based quantum computer can address realistic portfolio optimisation scenarios by cleverly assigning multiple financial variables to each qubit, overcoming limitations that previously restricted quantum applications in this field. The team successfully applies this method to a problem involving over 250 variables, modelling a real stock market by dividing it into groups of closely related assets, and this improved scalability promises to unlock new opportunities for more sophisticated and effective financial modelling.

Graph Partitioning for Quantum Portfolio Optimisation

This research details a new approach to portfolio optimisation, combining graph theory and quantum computing to address limitations in existing quantum methods. The team tackled the challenge of scaling quantum algorithms for portfolio construction by representing the stock market as a graph and iteratively dividing it into groups of correlated assets. They then selected representative assets from each group and used a Parameterized Circuit Ansatz to optimise the portfolio, successfully handling larger portfolios, up to 250 assets, than many previous quantum approaches, with promising computational performance. The key contributions of this work include a graph-based portfolio construction method, a strategy for selecting representative assets, and the application of a Parameterized Circuit Ansatz for quantum optimisation.

This approach improves scalability by reducing the complexity of encoding the optimisation problem onto a quantum computer, demonstrating the ability to solve instances with over 200 assets in approximately one hour using a statevector simulator, achieving a higher Sharpe ratio compared to baseline methods, indicating superior risk-adjusted performance. The methodology involves modelling the stock market as a graph where assets are nodes and correlations, measured using the Pearson correlation coefficient, define the edges. The graph is then iteratively divided into two groups of correlated assets, and a representative asset is selected from each group. These representative assets serve as input to a quantum optimisation algorithm based on the Parameterized Circuit Ansatz. The quantum circuits are simulated using a statevector simulator, and performance is evaluated using metrics such as Sharpe ratio and runtime.

Pauli Encoding for Portfolio Optimization Problems

Scientists have developed a new methodology for portfolio optimisation using a gate-based variational quantum algorithm and a recently developed qubit encoding technique. This allows them to address a complex financial problem involving over 250 variables, overcoming a significant limitation of previous methods. The innovative Pauli Correlation Encoding allows each qubit to encode multiple variables, significantly reducing the quantum resource requirements. The team implemented a variational quantum algorithm, carefully designed to explore the complex solution space and identify optimal portfolio configurations.

They benchmarked the algorithm’s performance against both a classical optimiser and QAOA for smaller instances, providing a comprehensive evaluation of its capabilities. To validate the approach, they addressed a portfolio optimisation problem with over 250 variables, a substantial increase in scale compared to previous gate-based quantum implementations, demonstrating the feasibility of applying gate-based quantum algorithms to realistic financial scenarios. This methodology expands the scope of quantum portfolio optimisation and offers a pathway to overcome current hardware constraints, enabling the exploration of increasingly complex financial models.

Quantum Portfolio Optimization with Pauli Encoding

This work presents a novel application of gate-based quantum computing to a real-world portfolio optimisation problem, successfully addressing a problem involving over 250 variables representing stock assets. The team constructed a market graph representing the stock market, treating assets as nodes and relationships between them as edges. They then applied their encoding scheme, achieving a substantial reduction in the number of qubits required to represent the problem.

Experiments involved benchmarking the performance of this approach against both Quantum Approximate Optimisation Algorithm (QAOA) for smaller instances and a classical optimiser for larger instances, utilising an iterative bipartition strategy. Results demonstrate the effectiveness of the method in solving complex portfolio optimisation problems. The research shows that the number of qubits scales favourably with the number of variables, particularly when employing a cubic order encoding. The team utilised the Hardware Efficient Ansatz circuit, requiring a number of layers determined by the problem size and encoding parameters, avoiding the depth limitations often encountered in other quantum variational algorithms.

Quantum Portfolio Optimization Scales to Real Markets

This work demonstrates a new approach to portfolio optimisation, successfully applying a gate-based quantum computer to a problem involving over 250 variables representing a real stock market. Researchers achieved this by assigning multiple variables per qubit, overcoming a significant limitation of previous quantum methods. The team iteratively partitioned the market into sub-portfolios of highly correlated assets, improving the scalability of the quantum solution. The results show that this method effectively balances risk and return, a key goal of portfolio optimisation, and provides a viable path towards enhanced financial applications.

Benchmarking against both classical optimisers and other quantum approaches, such as QAOA, confirms the potential of this technique, particularly for large-scale problems. The authors note that further research could explore the impact of different partitioning strategies and investigate the performance of the method with varying levels of market correlation. Future work may also focus on incorporating more realistic constraints and transaction costs into the model to further refine its practical applicability.