A Hybrid Quantum Solver for the Lorenz System
Author Information
Author(s): Fathi Hafshejani, Gaur Daya, Dasgupta Arundhati, Benkoczi Robert, Gosala Narasimha Reddy, Iorio Alfredo
Primary Institution: Department of Mathematics and Computer Science, University of Lethbridge
Hypothesis
Can a hybrid classical-quantum method improve the numerical solutions of the Lorenz system?
Conclusion
The VQLS method can effectively compute solutions comparable to classical methods for the Lorenz system.
Supporting Evidence
- The VQLS method requires significantly fewer qubits compared to other quantum algorithms.
- Simulation results demonstrate that the VQLS method effectively computes solutions comparable to classical methods.
- The method is easily extended to solve other similar nonlinear differential equations.
- Short-depth circuits can be implemented in NISQ computers, making the VQLS method practical.
Takeaway
This study shows that using a mix of classical and quantum computing can help solve complex math problems like the Lorenz system, which is important for understanding chaotic systems.
Methodology
The study uses a hybrid classical-quantum method, specifically the Variational Quantum Linear Solver (VQLS), to solve the Lorenz system by discretizing it with the forward Euler method.
Limitations
The method relies on classical optimization, requires exact preparation of initial states, and is sensitive to noise in quantum computation.
Digital Object Identifier (DOI)
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