Single Qubit State Estimation on NISQ Devices with Limited Resources and SIC-POVMs

TL;DR

This paper proposes a method for estimating a qubit's quantum state on NISQ devices using symmetric, informationally complete measurements without direct measurement, optimizing resource use on noisy quantum hardware.

Contribution

It introduces a parameterized measurement model for qubit state estimation optimized via the quantum tomographic transfer function, suitable for resource-limited NISQ devices.

Findings

The measurement set is symmetric and informationally complete.

Resource requirements are reduced when direct measurements are permitted.

The method is successfully tested on Finnish and IBM quantum computers.

Abstract

Current quantum computers have the potential to overcome classical computational methods, however, the capability of the algorithms that can be executed on noisy intermediate-scale quantum devices is limited due to hardware imperfections. Estimating the state of a qubit is often needed in different quantum protocols, due to the lack of direct measurements. In this paper, we consider the problem of estimating the quantum state of a qubit in a quantum processing unit without conducting direct measurements of it. We consider a parameterized measurement model to estimate the quantum state, represented as a quantum circuit, which is optimized using the quantum tomographic transfer function. We implement and test the circuit using the quantum computer of the Technical Research Centre of Finland as well as an IBM quantum computer. We demonstrate that the set of positive operator-valued measurements used for the estimation is symmetric and informationally complete. Moreover, the resources needed for qubit estimation are reduced when direct measurements are allowed, keeping the symmetric property of the measurements.