# Convergence of Digitized-Counterdiabatic QAOA: circuit depth versus free parameters

**Authors:** Mara Vizzuso, Gianluca Passarelli, Giovanni Cantele, Procolo Lucignano  
**arXiv:** [2307.14079](https://arxiv.org/abs/2307.14079)  
**Date:** 2023-07-26  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2307.14079v4/

## Key points

- Authors explore the use of Digitized-Counterdiabatic (CD) approach in Quantum Approximate Optimization Algorithm (QAOA)
- Method inspired by Trotterized counterdiabatic driving in continuous-time quantum annealing
- Focus on weighted and unweighted one-dimensional MaxCut problem
- Investigate two variations of QAOA with first and second-order CD corrections
- Higher-order CD corrections lead to faster convergence towards exact solutions by increasing complexity of variational cost function
- Total number of free parameters needed for better results remains consistent across different QAOA variants
- Study highlights effectiveness of incorporating CD corrections within QAOA frameworks for optimizing solutions to computational problems

## Summary

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In their paper titled "Convergence of Digitized-Counterdiabatic QAOA: circuit depth versus free parameters," authors Mara Vizzuso, Gianluca Passarelli, Giovanni Cantele, and Procolo Lucignano explore the use of the Digitized-Counterdiabatic (CD) approach in Quantum Approximate Optimization Algorithm (QAOA). This method draws inspiration from Trotterized counterdiabatic driving in continuous-time quantum annealing to improve the convergence of QAOA towards optimal solutions for optimization problems. The researchers focus on the well-known weighted and unweighted one-dimensional MaxCut problem and investigate two variations of QAOA that incorporate first and second-order CD corrections. Their findings reveal that higher-order CD corrections can lead to faster convergence towards exact solutions by increasing the complexity of the variational cost function. Interestingly, despite this improved convergence capability, the total number of free parameters needed to achieve better results remains consistent across different QAOA variants. This study sheds light on the effectiveness of incorporating CD corrections within QAOA frameworks for optimizing solutions to challenging computational problems. It provides valuable insights into leveraging advanced quantum computing techniques to streamline optimization processes and enhance algorithmic efficiency in various applications.