One research paper could help make the algorithms that used on DWave’s adiabatic quantum annealing system faster.
We present the results of a numerical study, with 20 qubits, of the performance of the Quantum Adiabatic Algorithm on randomly generated instances of MAX 2-SAT with a unique assignment that maximizes the number of satis ed clauses. The probability of obtaining this assignment at the end of the quantum evolution measures the success of the algorithm. Here we report three strategies which consistently increase the success probability for the hardest instances in our ensemble: decreasing the overall evolution time, initializing the system in excited states, and adding a random local Hamiltonian to the middle of the evolution
Dwave implements the Ising model. A researcher has created Ising formulations of many NP problems.
Andrew Lucas, Harvard, provides Ising formulations for many NP-complete and NP-hard problems, including all of Karp’s 21 NP-complete problems. This collects and extends mappings to the Ising model from partitioning, covering and satisfiability. In each case, the required number of spins is at most cubic in the size of the problem. This work may be useful in designing adiabatic quantum optimization algorithms.
The primary purpose of this paper is to pres ent constructions of Ising Hamiltonians for problems where finding a choice of Hamiltonian is a bit subtle; for pedagogical purposes, we will also provide a review of some of the simple maps from partitioningand satisfiability to an Ising spin glass. In particular, we will describe how “all of the famous NP problems” can be written down as Ising models with a polynomial number of spins which scales no faster than N^3.
For most of this paper, we will find it no more difficult to solve the NP-hard optimization problem vs. the NP-complete decision problem, and as such we will usually focus on the optimization problems. The techniques employed in this paper, which are rare elsewhere in the quantum computation literature, are primarily of a few flavors, which roughly correspond to the tackling the following issues: minimax optimization problems, problems with inequalities as constraints (for example, n ≥ 1, as opposed to n = 1), and problems which ask global questions about graphs. The methods we use to phrase these problems as Ising glasses generalize very naturally
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