Partial and complete qubit estimation using a single observable: optimization and quantum simulation

TL;DR

This paper explores optimizing quantum state estimation for a single spin component and all components using unitary evolution, evaluates performance via qTTF, and proposes scalable circuit designs for IBM quantum devices.

Contribution

It introduces optimized unitary models for qubit estimation, evaluates their performance with qTTF, and develops scalable circuits to improve quantum tomography on IBM hardware.

Findings

Maximum entangling power yields minimum qTTF for one-parameter model

Single-spin component estimation was successful on IBM quantum hardware

Proposed scalable circuit design enhances qubit state tomography

Abstract

Quantum state estimation is an important task of many quantum information protocols. We consider two families of unitary evolution operators, one with a one-parameter and the other with a two-parameter, which enable the estimation of a single spin component and all spin components, respectively, of a two-level quantum system. To evaluate the tomographic performance, we use the quantum tomographic transfer function (qTTF), which is calculated as the average over all pure states of the trace of the inverse of the Fisher information matrix. Our goal is to optimize the qTTF for both estimation models. We find that the minimum qTTF for the one-parameter model is achieved when the entangling power of the corresponding unitary operator is at its maximum. The models were implemented on an IBM quantum processing unit, and while the estimation of a single-spin component was successful, the whole spin estimation displayed relatively large errors due to the depth of the associated circuit. To address this issue, we propose a new scalable circuit design that improves qubit state tomography when run on an IBM quantum processing unit.