Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities

TL;DR

This paper explores how four-level superconducting circuits can function as two-qubit systems, enabling specific quantum operations, state preparation, and testing entropic inequalities, advancing quantum information processing capabilities.

Contribution

It introduces a method to implement two-qubit gates and prepare entangled states in four-level superconducting circuits, facilitating entropic inequality verification.

Findings

Implementation of iSWAP and Hadamard gates via pulse sequences

Preparation of pure entangled states with controlled reduced density matrices

Verification of Shannon and Rényi entropy inequalities in noncomposite systems

Abstract

We theoretically study operations with a four-level superconducting circuit as a two-qubit system. Using a mapping on a two-qubit system, we show how to implement iSWAP gates and Hadamard gates through pulses on transitions between particular pairs of energy levels. Our approach allows one to prepare pure two-qubit entangled states with desired form of reduced density matrices of the same purity and, in particular, arbitrary identical reduced states of qubits. We propose using schemes for the Hadamard gate and two-qubit entangled states with identical reduced density matrices in order to verify $\log{N}$ inequalities for Shannon and R\'enyi entropies for the considered noncomposite quantum system.