This work aims to describe the method of analytical calculation of an orthonormalized basis of states of the Josephson flux quantum bits (qubits) using a two-level approximation under the condition that the potential energy of the system is a combination of two potential wells separated by a tunnel barrier. For illustration, the calculation results in the case of the well-known three- and four-junction flux qubits, as well as promising silent qubits, are presented.
85.25.Dq Superconducting quantum interference devices
03.67.Lx Quantum computation architectures and implementations
03.65.Yz Decoherence; open systems; quantum statistical methods
$^1$Department of Atomic Physics, Plasma Physics and Microelectronics, Faculty of physics, Lomonosov Moscow State University
$^2$Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University
$^3$Moscow Technical University of Communications and Informatics