# Implementation of quantum imaginary-time evolution method on NISQ devices: Nonlocal approximation

**Authors:** Hirofumi Nishi, Taichi Kosugi, Yu-ichiro Matsushita  
**arXiv:** [2005.12715](https://arxiv.org/abs/2005.12715)  
**Date:** 2020-05-26  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2005.12715v1/

## Key points

- The quantum computing field recognizes the efficiency of the imaginary-time evolution method for determining ground states of quantum many-body systems on classical computers.
- Challenges arise in implementing this method on NISQ devices due to deep circuit depth and complexity.
- A recent study introduces the quantum imaginary-time evolution method (QITE) with a focus on nonlocal approximation techniques to address these challenges.
- Two key approximation methods, extended LA (eLA) and nonlocal approximation (NLA), significantly reduce circuit depth compared to traditional approaches.
- eLA and NLA were validated through solving max-cut problems in various graph structures, showing improved efficiency while maintaining accuracy.
- A "compression" technique was developed to reduce circuit complexity during imaginary-time steps within QITE, reducing error accumulation and computational overhead.

## Summary

The quantum computing field has long recognized the efficiency of the imaginary-time evolution method in determining ground states of quantum many-body systems on classical computers. However, with the emergence of quantum computing technologies like NISQ devices, implementing this method poses challenges due to deep circuit depth and complexity. To address these issues, a recent study introduces a novel approach known as the quantum imaginary-time evolution method (QITE) with a focus on nonlocal approximation techniques. By deviating from traditional locality conditions, researchers were able to significantly reduce circuit depth using two key approximation methods: extended LA (eLA) and nonlocal approximation (NLA). These methods were validated through solving max-cut problems in both unweighted 3-regular graphs and weighted fully connected graphs. Results showed that eLA and NLA required fewer circuit depths while maintaining accuracy compared to conventional LA approach. Additionally, a "compression" technique was developed to reduce circuit complexity during imaginary-time steps within QITE, further mitigating error accumulation and reducing computational overhead. Overall, these advancements pave the way for more efficient utilization of quantum computing resources in tackling complex many-body quantum problems with improved accuracy and reduced computational overhead.