Practical implementation of mutually unbiased bases using quantum circuits

TL;DR

This paper presents a practical method for generating mutually unbiased bases using simple quantum circuits, facilitating scalable quantum state tomography for multi-qubit systems.

Contribution

It introduces an efficient cyclic generation method for mutually unbiased bases using basic gates, applicable to three and four qubits with different entanglement structures.

Findings

Complete sets of mutually unbiased bases for three and four qubits demonstrated.

Quantum circuits for various entanglement classes analyzed.

Method reduces complexity of quantum state reconstruction.

Abstract

The number of measurements necessary to perform the quantum state reconstruction of a system of qubits grows exponentially with the number of constituents, creating a major obstacle for the design of scalable tomographic schemes. We work out a simple and efficient method based on cyclic generation of mutually unbiased bases. The basic generator requires only Hadamard and controlled-phase gates, which are available in most practical realizations of these systems. We show how complete sets of mutually unbiased bases with different entanglement structures can be realized for three and four qubits. We also analyze the quantum circuits implementing the various entanglement classes.