Quantum Portfolio Optimization: Binary encoding of discrete variables for QAOA with hard constraint
| Autor: | Chen, Bingren, Wu, Hanqing, Yuan, Haomu, Wu, Lei, Li, Xin |
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| Rok vydání: | 2023 |
| Předmět: | |
| DOI: | 10.48550/arxiv.2304.06915 |
| Popis: | In this paper, we propose a new quantum approximate optimization algorithm (QAOA) with binary encoding to address portfolio optimization under hard constraints. Portfolio optimization involves selecting the optimal combination of assets to achieve a balance of profit and risk based on historical returns. As a quantum algorithm, QAOA has the potential to outperform classical algorithms in solving combinatorial optimization problems. However, its application to portfolio optimization is restricted due to the high number of qubits required in its encoding (Hodson encoding or Domain-wall encoding) to represent a narrow range of shares. To overcome this limitation, we use quasi-binary encoding to represent integer shares and construct a mixing operator for this purpose. The number of qubits used to represent each asset does not exceed $2\log_2(D+1)$ when the sum constraint of the combinatorial optimization problem is $D$. Our optimization model is more complex, with range constraints added to the sum constraint. We have also developed an iterative method to improve the accuracy without increasing the number of qubits through multiple experiments. Numerical experiments show that by simulating 18-qubit systems seven times, we can improve the precision to above 0.01, and the approximation ratio can reach 0.99998. Comment: 18 pages, 7 figures, 5 tables |
| Databáze: | OpenAIRE |
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