Pure State Tomography with Fourier Transformation

TL;DR

This paper introduces two adaptive quantum state tomography protocols for pure multi-qubit states using Fourier transformation, requiring fewer measurements and demonstrating feasibility on IBM quantum hardware.

Contribution

It proposes novel adaptive protocols that reduce measurement complexity for pure state tomography and validates them through experiments and simulations.

Findings

Protocols require only two or three observables.

Number of measurement outcomes is reduced compared to existing methods.

Experimental validation on IBM 5-qubit quantum computer confirms feasibility.

Abstract

Extracting information from quantum devices has long been a crucial problem in the field of quantum mechanics. By performing elaborate measurements, quantum state tomography, an important and fundamental tool in quantum science and technology, can be used to determine unknown quantum states completely. In this study, we explore methods to determine multi-qubit pure quantum states uniquely and directly. Two adaptive protocols are proposed, with their respective quantum circuits. Herein, two or three observables are sufficient, while the number of measurement outcomes is either the same as or fewer than those in existing methods. Additionally, experiments on the IBM 5-qubit quantum computer, as well as numerical investigations, demonstrate the feasibility of the proposed protocols.