Three-qubit W state tomography via full and marginal state reconstructions on ibm_osaka

TL;DR

This paper introduces an efficient three-qubit W state tomography method requiring fewer measurements, demonstrated on IBM's quantum processor, and shows that subsystem tomography can outperform full state tomography in fidelity.

Contribution

The authors develop a reduced-measurement tomography scheme for three-qubit states and experimentally validate it on IBM's quantum hardware, demonstrating practical advantages over conventional methods.

Findings

Reduced measurement settings for three-qubit tomography (17 instead of 63)

Subsystem tomography yields higher fidelity estimates than full tomography

Experimental validation on IBM's ibm_osaka quantum processor

Abstract

We present a three-qubit quantum state tomography scheme requiring a set of 17 measurement settings, significantly reducing the experimental overhead compared to the conventional 63 Pauli measurement settings. Using IBM's 127-qubit open-access quantum processor ibm osaka, we prepare the three-qubit W state and employ our tomography scheme to reconstruct it. Additionally, we implement a two-qubit tomography protocol, involving 7 measurement settings, on ibm osaka to reconstruct two of the two-qubit marginals of the W state. This serves as a {\em proof-of-principle} demonstration of the well-known theoretical result that any two of the two-qubit reduced density matrices can uniquely determine most of the whole three-qubit pure states. We show that the fidelity of the W-state reconstructed from its two-qubit subsystems is consistently larger than that obtained from the full three-qubit tomography, highlighting the practical advantage of the subsystem-based tomography approach.