# Optimal experiment design for quantum state tomography

## TL;DR

This paper introduces an integer programming approach to optimize measurement settings in quantum state tomography, reducing the number of measurements needed and simplifying experimental procedures.

## Contribution

The authors develop a novel integer programming method to identify minimal measurement sets for quantum state tomography, improving efficiency over previous greedy strategies.

## Key findings

- Significantly fewer measurement settings are required using the proposed method.
- The approach is effective in practical NMR quantum systems.
- It simplifies measurement schemes, reducing experimental effort.

## Abstract

Quantum state tomography is an indispensable but costly part of many quantum experiments. Typically, it requires measurements to be carried in a number of different settings on a fixed experimental setup. The collected data is often informationally overcomplete, with the amount of information redundancy depending on the particular set of measurement settings chosen. This raises a question about how should one optimally take data so that the number of measurement settings necessary can be reduced. Here, we cast this problem in terms of integer programming. For a given experimental setup, standard integer programming algorithms allow us to find the minimum set of readout operations that can realize a target tomographic task. We apply the method to certain basic and practical state tomographic problems in nuclear magnetic resonance experimental systems. The results show that, considerably less readout operations can be found using our technique than it was by using the previous greedy search strategy. Therefore, our method could be helpful for simplifying measurement schemes so as to minimize the experimental effort.