Embedding p-body interacting models onto the 2-body networks implemented on commercial quantum annealers is a relevant issue. For highly interacting models, requiring a number of ancilla qubits, that can be sizable and make unfeasible (if not impossible) to simulate such systems. In this manuscript, we propose an alternative to minor embedding, developing a new approximate procedure based on genetic algorithms, allowing to decouple the p-body in terms of 2-body interactions. A set of preliminary numerical experiments demonstrates the feasibility of our approach for the ferromagnetic p-spin model, and pave the way towards the application of evolutionary strategies to more complex quantum models.Keywords Adiabatic quantum computation · quantum annealing · p-spin model · genetic algorithms · graph embedding 1 IntroductionFinding the solution of NP-hard problems requires a time-to-solution increasing exponentially as a function of the system size [1]. NP-hard tasks can be studied with adiabatic quantum computation [2, 3], a heuristic tool for finding the optimal solution to this kind of problems. The D-Wave quantum machines [4] can perform finite-time adiabatic quantum computation, or quantum annealing. The superconducting architecture of D-Wave processors is built on the Chimera graph [5,6], a sparsely connected graph that can host N ≤ 2048 qubits, with at most 2-body G. A. and A. V. supervised the research activities related to evolutionary computation. P. R. H. and G. P. designed and implemented the genetic algorithm, and performed numerical simulations and data analysis. P. L. and V. C. supervised the project. All authors contributed to the preparation of the present manuscript. We consider a system of N qubits. The two logical states in the computational basis of qubit i can be equivalently labeled as |σ i , with σ i = ±1, or |x i , with x i = 0, 1. The two choices are related by σ i = 1 − 2x i . In the following, we will use the x i representation, unless stated otherwise. We denote by σ k i , with k = x, y, z, the Pauli matrices acting on the ith qubit. Moreover, we work in natural units and fix = 1.
A crucial step in the race towards quantum advantage is optimizing quantum annealing using ad-hoc annealing schedules. Motivated by recent progress in the field, we propose to employ long-short term memory (LSTM) neural networks to automate the search for optimal annealing schedules for random Ising models on regular graphs. By training our network using locally-adiabatic annealing paths, we are able to predict optimal annealing schedules for unseen instances and even larger graphs than those used for training. 
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