Quantum variational PDE solver with machine learning

• DOI: 10.48550/arxiv.2109.09216
• Publication Date: 2021-01-01
• Authors: Jaewoo Joo; H. Moon
• Keywords: Solver; Quantum system

To solve nonlinear partial differential equations (PDEs) is one of the most common but important tasks in not only basic sciences also many practical industries. We here propose a quantum variational (QuVa) PDE solver with aid machine learning (ML) schemes to synergise two emerging technologies mathematically hard problems. The core processing this calculate efficiently expectation value specially designed operators. For large system, we obtain data from measurements few control qubits avoid exponential cost whole system and optimise pathway find possible solution sets desired PDEs using ML techniques. As an example, different types second-order DEs are examined randomly chosen samples regression method implemented chase best candidates functions another trial samples. demonstrated that three-qubit successfully follows pattern analytical solutions three high fidelity since given by necessary condition exact DEs. Thus, believe final candidate extracted QuVa support techniques algorithm could be beneficial search for complex mathematical problems as well good ansatzs eigenstates systems (e.g., chemistry).