Optimal Single Qubit Tomography: Realization of Locally Optimal Measurements on a Quantum Computer

TL;DR

This paper develops and implements locally optimal measurement strategies for single qubit tomography on a quantum computer, achieving near-theoretical limits and demonstrating robustness with simulations.

Contribution

It introduces a method for optimal qubit measurement based on quantum metrology and demonstrates its practical implementation on a superconducting quantum computer.

Findings

Achieved low error measurements saturating the Nagaoka--Hayashi bound.

Validated robustness of the method through simulations with varying prior knowledge.

Demonstrated practical realization of optimal measurements on current quantum hardware.

Abstract

Quantum bits, or qubits, are the fundamental building blocks of present quantum computers. Hence, it is important to be able to characterize the state of a qubit as accurately as possible. By evaluating the qubit characterization problem from the viewpoint of quantum metrology, we are able to find optimal measurements under the assumption of good prior knowledge. We implement these measurements on a superconducting quantum computer. Our experiment produces sufficiently low error to allow the saturation of the theoretical limits, given by the Nagaoka--Hayashi bound. We also present simulations of adaptive measurement schemes utilizing the proposed method. The results of the simulations show the robustness of the method in characterizing arbitrary qubit states with different amounts of prior knowledge.