# Effective quantum state reconstruction using compressive sensing in NMR quantum computing

## TL;DR

This paper introduces a compressive sensing-based method for quantum state reconstruction in NMR that reduces measurement requirements and improves efficiency for multi-qubit systems.

## Contribution

It presents a novel NMR quantum state reconstruction technique using actual experimental data, enhancing efficiency and accuracy over traditional methods.

## Key findings

- Successfully reconstructed 2, 3, 4 qubit states with fewer measurements
- Method is easy to implement and scales well with system size
- Achieved high accuracy and efficiency in practical NMR experiments

## Abstract

The number of measurements required to reconstruct the states of quantum systems increases exponentially with the quantum system dimensions, which makes the state reconstruction of high-qubit quantum systems have a great challenge in physical quantum computing experiments. Compressive sensing (CS) has been verified as a effective technique in the reconstruction of quantum state, however, it is still unknown that if CS can reconstruct quantum states given the less data measured by nuclear magnetic resonance (NMR). In this paper, we propose an effective NMR quantum state reconstruction method based on CS. Different from the conventional CS-based quantum state reconstruction, our method uses the actual observation data from NMR experiments rather than the data measured by the Pauli operators. We implement measurements on quantum states in practical NMR computing experiments and reconstruct states of 2,3,4 qubits using fewer number of measurements, respectively. The proposed method is easy to implement and performs more efficiently with the increase of the system dimension size. The performance reveals both efficiency and accuracy, which provides an alternative for the quantum state reconstruction in practical NMR.