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It has recently been shown that a parametrically driven oscillator with Kerr nonlinearity yields a Schr\"odinger cat state via quantum adiabatic evolution through its bifurcation point and a network of such nonlinear oscillators can be used for solving combinatorial optimization problems by bifurcation-based adiabatic quantum computation [H.
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M. Rehák, P. Neilinger, M. Grajcar, G. Oelsner, U. Hübner, E. Il’ichev, and H.-G. Meyer, Parametric amplification by coupled flux qubits, Appl. Phys. Lett. 104
2014
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A coherent state | α ⟩ |\alpha\rangle is defined as an eigenstate of the annihilation (lowering) operator, a a , of the harmonic oscillator: a | α ⟩ = α | α ⟩ a|\alpha\rangle=\alpha|\alpha\rangle . Since the inner product of two coherent states | α ⟩ |\alpha\rangle and | β ⟩ |\beta\rangle is given by ⟨ α | β ⟩ = exp [ − | α − β | 2 / 2 + i Im ( α ∗ β ) ] \langle\alpha|\beta\rangle=\exp[-|\alpha-\beta|^{2}/2+i\mbox{Im}(\alpha^{*}\beta)] , two coherent states with largely different amplitudes are approximately orthogonal. And even and odd cat states are defined as | α ⟩ + | − α ⟩ |\alpha\rangle+|-\alpha\rangle and | α ⟩ − | − α ⟩ |\alpha\rangle-|-\alpha\rangle , respectively, where the normalization factors have been omitted
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