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Adiabatic quantum computing has recently been used to factor 56153 [Dattani &Bryans, arXiv:1411.6758] at room temperature, which is orders of magnitudelarger than any number attempted yet using Shor's algorithm (circuit-basedquantum computation). However, this number is still vastly smaller than RSA-768which is the largest number factored thus far on a classical computer. Weaddress a major issue arising in the scaling of adiabatic quantum factorizationto much larger numbers. Namely, the existence of many 4-qubit, 3-qubit and2-qubit interactions in the Hamiltonians. We showcase our method on variousexamples, one of which shows that we can remove 94% of the 4-qubit interactionsand 83% of the 3-qubit interactions in the factorization of a 25-digit numberwith almost no effort, without adding any auxiliary qubits. Our method is notlimited to quantum factoring. Its importance extends to the wider field ofdiscrete optimization. Any CSP (constraint-satisfiability problem),psuedo-boolean optimization problem, or QUBO (quadratic unconstrained Booleanoptimization) problem can in principle benefit from the "deduction-reduction"method which we introduce in this paper. We provide an open source code whichtakes in a Hamiltonian (or a discrete discrete function which needs to beoptimized), and returns a Hamiltonian that has the same unique ground state(s),no new auxiliary variables, and as few multi-qubit (multi-variable) terms aspossible with deduc-reduc.

Reducing multi-qubit interactions in adiabatic quantum computation  without adding auxiliary qubits. Part 1: The "deduc-reduc" method and its  application to quantum factorization of numbers