  We propose an approach that enables to use it for construction of rotations
of coherent states, in particular, it gives a possibility to construct Hadamard
gate for the coherent states. Our approach is based on representation of
arbitrary one-mode pure state in free-travelling fields, in particular
superposition of coherent states (SCSs), in terms of displaced number states
with arbitrary amplitude of displacement. Studied optical scheme is based on
alternation of photon additions and displacement operators (in general case,
photon additions and displacements are required) with seed coherent state to
generate both even and odd displaced squeezed SCSs (DSSCSs) regardless of
number of used photon additions. It is shown the studied optical scheme is
sensitive to seed coherent state provided that other parameters are invariable.
Output states approximate with high fidelity either even squeezed SCS or odd
SCS shifted relative each other by some value. It enables to construct local
rotation operator for coherent states, in particular, Hadamard gate being
mainframe element for quantum computation with coherent states. The effects
deteriorating quality of output states are considered.
