  Simulation of quantum systems promises to deliver physical and chemical
predictions for the frontiers of technology. Unfortunately, the exact
representation of these systems is plagued by the exponential growth of
dimension with the number of particles, or colloquially, the curse of
dimensionality. The success of approximation methods has hinged on the relative
simplicity of physical systems with respect to the exponentially complex worst
case. Exploiting this relative simplicity has required detailed knowledge of
the physical system under study. In this work, we introduce a general and
efficient black box method for many-body quantum systems that utilizes
technology from compressed sensing to find the most compact wavefunction
possible without detailed knowledge of the system. It is a Multicomponent
Adaptive Greedy Iterative Compression (MAGIC) scheme. No knowledge is assumed
in the structure of the problem other than correct particle statistics. This
method can be applied to many quantum systems such as spins, qubits,
oscillators, or electronic systems. As an application, we use this technique to
compute ground state electronic wavefunctions of hydrogen fluoride and recover
98% of the basis set correlation energy or equivalently 99.996% of the total
energy with $50$ configurations out of a possible $10^7$. Building from this
compactness, we introduce the idea of nuclear union configuration interaction
for improving the description of reaction coordinates and use it to study the
dissociation of hydrogen fluoride and the helium dimer.
