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Figure 3.3: Simulation of Mock-Qubit – a) Eigenstates: Lowest 30 eigenstates of
example qubit potential: V (δ) = δ 2 −8 cos(δ +1). b) Transition matrix: Absolute
value of transition matrix elements |T nm |.
to the deep minimum. Just like in the harmonic oscillator case, transitions
between non-neighboring states are very hard to achieve (T nm ≈ 0 for n <
m − 1 or n > m + 1). In contrast to the harmonic oscillator, the diagonal
elements here are not zero. This allows for phase changes, i.e. Z-rotations,
of the states (see Section 3.3.1).
• The center region corresponds to transitions between states that are alternatingly
confined to the shallow or the deep minimum. The fact that the
states’ confinement alternates perfectly between the minima is a result of
the exact potential chosen and does not hold in general.
In this region
the dominating transitions are also between neighboring states in the same
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