  Quantum walks provide simple models of various fundamental processes. It is
pivotal to know when the dynamics underlying a walk lead to quantum advantages
just by examining its statistics. A walk with many indistinguishable particles
and measurements of non-classical multi-particle correlations is likely to
reveal the quantum nature. The number of elements $O(n)$ in a setup realizing
walks grows with their length or spread $n$. We introduce the concept of a
quantum leap, a process which can be achieved with fewer or complementary
resources and which in a single step simulates another long process. The
process and its leap are described by the same Hamiltonian but, the latter
parametrizes the evolution with a tunable parameter of a setup. In the case of
walks, a leap immediately gives a probability distribution which results only
after many steps. This may be appealing for simulation of processes which are
lengthy or require dynamical control. We discuss a leap based on the
multi-particle Hong--Ou--Mandel interference, an inherently quantum phenomenon.
It reproduces a quantum walk enabling perfect state transfer through spin
chains. It requires a beam splitter, two detectors and $n$ particles to mimic a
walk on a chain of size $O(n)$, for time fixed by beam-splitter's reflectivity.
Our results apply to a broad class of systems where the HOM-like effects can be
observed, and may constitute a new approach to simulation of complex
Hamiltonians with passive interferometers.
