Phys. Rev. A, 2015, Volume 91, Issue 4, 42312, 7 pp.
Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities
E. O. Kiktenkoab, A. K. Fedorovac, O. V. Man'kod, V. I. Man'kod
a Bauman Moscow State Technical University, Moscow 105005, Russia
b Geoelectromagnetic Research Center of Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, Troitsk, Moscow Region 142190, Russia
c Russian Quantum Center, Skolkovo, Moscow 143025, Russia
d P. N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia
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.
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