  Adiabatic quantum computing has recently been used to factor 56153 [Dattani &
Bryans, arXiv:1411.6758] at room temperature, which is orders of magnitude
larger than any number attempted yet using Shor's algorithm (circuit-based
quantum computation). However, this number is still vastly smaller than RSA-768
which is the largest number factored thus far on a classical computer. We
address a major issue arising in the scaling of adiabatic quantum factorization
to much larger numbers. Namely, the existence of many 4-qubit, 3-qubit and
2-qubit interactions in the Hamiltonians. We showcase our method on various
examples, one of which shows that we can remove 94% of the 4-qubit interactions
and 83% of the 3-qubit interactions in the factorization of a 25-digit number
with almost no effort, without adding any auxiliary qubits. Our method is not
limited to quantum factoring. Its importance extends to the wider field of
discrete optimization. Any CSP (constraint-satisfiability problem),
psuedo-boolean optimization problem, or QUBO (quadratic unconstrained Boolean
optimization) problem can in principle benefit from the "deduction-reduction"
method which we introduce in this paper. We provide an open source code which
takes in a Hamiltonian (or a discrete discrete function which needs to be
optimized), and returns a Hamiltonian that has the same unique ground state(s),
no new auxiliary variables, and as few multi-qubit (multi-variable) terms as
possible with deduc-reduc.
