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

Abstract: 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.