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

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 Rényi entropies for the considered noncomposite quantum system.

7 pages, 3 figures; published version

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• Decomposing the generalized Toffoli gate with qutrits
• Dynamical Lamb Effect in a Tunable Superconducting Qubit-Cavity System
• New entropic inequalities for qubit and unimodal Gaussian states
• Information processing using three-qubit and qubit-qutrit encodings of noncomposite quantum systems
• High cooperativity coupling to nuclear spins on a circuit QED architecture
• Probability representation of photon states and tomography
• The Partition Formalism and New Entropic-Information Inequalities for Real Numbers on an Example of Clebsch-Gordan Coefficients