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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 magnitude larger than any number attempted yet using Shors 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.
Quantum annealing has recently been used to determine the Ramsey numbers R(m,2) for 3 < m < 9 and R(3,3) [Bian et al. (2013) PRL 111, 130505]. This was greatly celebrated as the largest experimental implementation of an adiabatic evolution algorithm
We introduce two methods for speeding up adiabatic quantum computations by increasing the energy between the ground and first excited states. Our methods are even more general. They can be used to shift a Hamiltonians density of states away from the
In previous implementations of adiabatic quantum algorithms using spin systems, the average Hamiltonian method with Trotters formula was conventionally adopted to generate an effective instantaneous Hamiltonian that simulates an adiabatic passage. Ho
We propose an adiabatic quantum algorithm capable of factorizing numbers, using fewer qubits than Shors algorithm. We implement the algorithm in an NMR quantum information processor and experimentally factorize the number 21. Numerical simulations in
We construct mode-selective effective models describing the interaction of N quantum emitters (QEs) with the localised surface plasmon polaritons (LSPs) supported by a spherical metal nanoparticle (MNP) in an arbitrary geometric arrangement of the QE