# Towards Mixed Quantum-Classical Dynamics on Quantum Computers

**Authors:** Daniel Bultrini, Oriol Vendrell  
**arXiv:** [2303.11375](https://arxiv.org/abs/2303.11375)  
**Date:** 2023-03-20  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2303.11375v1/

## Key points

- Authors Daniel Bultrini and Oriol Vendrell explore mixed quantum-classical dynamics for understanding complex systems
- Mixed quantum-classical dynamics involves linking a quantum subsystem with a classical subsystem for a more comprehensive understanding
- Introduction of a modular algorithm for general mixed quantum-classical dynamics to address the gap in this area
- Testing the algorithm on a modified Shin-Metiu model through Ehrenfest propagation shows effectiveness for short-time evolutions and accurate qualitative results during longer-time evolutions
- Research highlights the potential of mixed quantum-classical dynamics in tackling complex systems and emphasizes the need for innovative algorithms bridging quantum and classical approaches

## Summary

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In their paper titled "Towards Mixed Quantum-Classical Dynamics on Quantum Computers," authors Daniel Bultrini and Oriol Vendrell explore the use of mixed quantum-classical dynamics as a method to understand complex systems beyond traditional computational boundaries. This approach involves linking the intricacies of a quantum subsystem with a classical subsystem, providing a more comprehensive understanding than using quantum mechanics alone. While there are various techniques available for full quantum mechanical evolution on quantum computers, the realm of mixed quantum-classical dynamics remains relatively uncharted. To address this gap, the authors introduce a modular algorithm designed for general mixed quantum-classical dynamics. They test its efficacy by applying it to a modified Shin-Metiu model in first quantization through Ehrenfest propagation. The results show that the Time-Dependent Variational Time Propagation algorithm is highly effective for short-time evolutions and continues to provide accurate qualitative results even during longer-time evolutions. This research sheds light on the potential of mixed quantum-classical dynamics in tackling complex systems and highlights the importance of developing innovative algorithms that can bridge the gap between quantum and classical approaches. The findings presented in this study pave the way for further exploration and utilization of mixed quantum-classical dynamics on quantum computers, offering new insights into understanding intricate systems beyond traditional computational boundaries.