# Super-resolution of Green's functions on noisy quantum computers

**Authors:** Diogo Cruz, Duarte Magano  
**arXiv:** [2210.04919](https://arxiv.org/abs/2210.04919)  
**Date:** 2022-10-10  
**Summary page:** https://www.summarizepaper.com/en/paper/2210.04919v1/

## Key points

- Quantum computers have shown promise in simulating complex quantum systems beyond classical computers' capabilities.
- Super-resolution techniques like Atomic Norm Minimization can overcome the limitation posed by decoherence errors of near-term quantum processors.
- Diogo Cruz and Duarte Magano demonstrate how Atomic Norm Minimization can recover the spectral function of an impurity model from measurements of its Green's function on an IBM quantum computer.
- The use of Atomic Norm Minimization reduces reconstruction error by one order of magnitude compared to standard signal processing methods.
- Super-resolution methods can facilitate the simulation of large and previously unexplored quantum systems, potentially establishing a quantum advantage in the future.
- Efficient Hamiltonian evolution routines are highlighted as useful for simulating Green's functions of classically-intractable quantum systems, but decoherence errors pose limits on spectrum resolution due to prohibitive large evolution times.
- Super-resolution techniques such as Atomic Norm Minimization can significantly reduce circuit depth requirements for accurate spectrum reconstruction.
- These findings could pave the way for new breakthroughs in various fields such as materials science, chemistry, and physics.

## Summary

In recent years, quantum computers have shown great promise in simulating complex quantum systems that are beyond the capabilities of classical computers. One approach to overcome the limitation posed by decoherence errors of near-term quantum processors is to use super-resolution techniques such as Atomic Norm Minimization, which can significantly reduce the minimum circuit depth required for accurate spectrum reconstruction. In this work by Diogo Cruz and Duarte Magano, they demonstrate how Atomic Norm Minimization can be used to recover the spectral function of an impurity model from measurements of its Green's function on an IBM quantum computer. The authors show that using Atomic Norm Minimization reduces the reconstruction error by one order of magnitude compared to more standard signal processing methods. This result suggests that super-resolution methods can facilitate the simulation of large and previously unexplored quantum systems and may constitute a useful non-variational tool to establish a quantum advantage in a nearer future. The study highlights the potential of efficient Hamiltonian evolution routines in simulating Green's functions of classically-intractable quantum systems. However, decoherence errors pose limits on spectrum resolution due to prohibitive large evolution times. The authors' findings suggest that super-resolution techniques such as Atomic Norm Minimization can significantly reduce circuit depth requirements for accurate spectrum reconstruction. Overall, this work provides valuable insights into how super-resolution methods can enhance our understanding and simulation capabilities of complex quantum systems using near-term quantum processors. These findings could pave the way for new breakthroughs in various fields such as materials science, chemistry, and physics.