  Multiphoton femtosecond coherent control of is used for implementing
innovative photo-induced analog coherent computation that generally might be a
basis for future "smart hardware". The specific implemented computational task
the classification of an unknown sequence into one of the three groups: (i) a
constant sequence that is composed of identical numbers, (ii) a sequence that
is antisymmetric around a given point, or (iii) neither. The input sequence is
encoded into the spectral phases of a broadband femtosecond pulse and the
computational task is being carried out by the multiphoton nonlinear response
of the irradiated physical system. Here, it is the simultaneous coherent two-
and three-photon absorption in atomic sodium (Na). The corresponding
computational resources are the manifold of initial-to-final multiphoton
excitation pathways photo-induced by the broad spectrum of the irradiating
femtosecond pulse. The answer is obtained by measuring only two observables,
which are two state-populations excited via the two- and three-photon
absorption processes. Hence, the computational task is accomplished in a
constant number of operations irrespective of the sequence length. As such, the
presented scheme, where the femtosecond pulse serves as a query and the
irradiated physical system serves as an oracle, provides a sufficient gain in
the computational complexity.
