# Digital-analog quantum algorithm for the quantum Fourier transform

## TL;DR

This paper introduces a digital-analog quantum algorithm for the quantum Fourier transform, demonstrating improved fidelity in noisy quantum environments, which could enhance quantum computing capabilities in the NISQ era.

## Contribution

The paper presents a novel digital-analog quantum algorithm for the quantum Fourier transform, combining digital and analog methods to improve performance under noise.

## Key findings

- Fidelity of quantum Fourier transform improves with the hybrid approach.
- The method is effective for increasing qubit numbers in noisy conditions.
- Hybrid digital-analog protocols are promising for quantum supremacy in NISQ devices.

## Abstract

Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the evolution of classical computation, an alternative paradigm merging the flexibility of digital quantum computation with the robustness of analog quantum simulation has emerged. This universal paradigm is known as digital-analog quantum computing. Here, we introduce an efficient digital-analog quantum algorithm to compute the quantum Fourier transform, a subroutine widely employed in several relevant quantum algorithms. We show that, under reasonable assumptions about noise models, the fidelity of the quantum Fourier transformation improves considerably using this approach when the number of qubits involved grows. This suggests that, in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid protocols combining digital and analog quantum computing could be a sensible approach to reach useful quantum supremacy.