The connection between the boson sampling problem in a linear optical interferometer with single photon sources and the computation of matrix permanents has recently brought a strong interest for quantum computing applications. In this work we explore the physics of N-order interference in terms of N-order correlation functions in a generic linear optical interferometer with both Fock states sources and thermal sources. We will show how also in this case the connection of such a problem with matrix permanents play a fundamental role.
In a recent experiment, we have shown how optical interference can be exploited in order to perform computations
and in particular factoring large integers. This has lead us to the developing of a novel analogue algorithm which
allows the factorization of several large integers in a single run. This work represents a step stone towards the
developing of novel physical networks able to implement quantum digital algorithms other than Shor’s algorithm.
We describe the main ideas leading to this new line of research referring to future publications for a detailed
We present a novel factorization algorithm which can be computed using an analogue computer based on a
polychromatic source with a given wavelength bandwidth, a multi-path interferometer and a spectrometer. The
core of this algorithm stands on the measurement of the periodicity of a "factoring" function given by an
exponential sum at continuous argument by recording a sequence of interferograms associated with suitable
units of displacement in the inteferometer. A remarking rescaling property of such interferograms allows, in
principle, the prime number decomposition of several large integers. The information about factors is encoded
in the location of the inteferogram maxima.
We exploit the remarkable phenomena of interference in physics together with aspects of number theory in
order to factorize large numbers. In particular, the introduction of continuous truncated exponential sums
(CTES) allows us to develop a new algorithm for factoring several large numbers by a single measurement of
the periodicity of a CTES interferogram. Such an interferogram can be obtained by measuring the interference
pattern produced by polychromatic light interacting with an interferometer with variable optical paths.
We will describe a new factorization algorithm based on the reproduction of continuous exponential sums, using
the interference pattern produced by polychromatic light interacting with an interferometer with variable optical
paths. We will describe two possible interferometers: a generalized symmetric Michelson interferometer and a
liquid crystal grating. Such an algorithm allows, for the first time, to find all the factors of a number N in a
single run without precalculating the ratio N/l, where l are all the possible trial factors. It also allows to solve
the problem of ghost factors and to factorize different numbers using the same output interference pattern.
The so called NOON states are the main ingredient of many quantum optic schemes. The reliability of NOON-state
production protocols thus plays an important role in view of practical applications. In realistic situations,
the reliability of NOON-state sources strongly depends on the non-unitary photodetection efficiency of the single
photon detectors involved in the protocol. We discuss and compare the reliability of NOON-state schemes
based on both single-photon detection and non detection. Our result may be of great interest for practical
implementation of NOON-state schemes.