An evolutionary strategy for finding effective quantum 2-body Hamiltonians of p -body interacting systems
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SHORT COMMUNICATION
An evolutionary strategy for finding effective quantum 2-body Hamiltonians of p -body interacting systems G. Acampora1 · V. Cataudella1,2,3 · P. R. Hegde1 · P. Lucignano1 · G. Passarelli1,2
· A. Vitiello1
Received: 3 June 2019 / Accepted: 6 November 2019 © Springer Nature Switzerland AG 2019
Abstract 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 paves 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 Introduction Finding the solution of NP-hard problems requires a timeto-solution increasing exponentially as a function of the system size (Cook 1971). NP-hard tasks can be studied with adiabatic quantum computation (Farhi et al. 2000; Albash and Lidar 2018), a heuristic tool for finding the optimal solution to this kind of problems. The D-Wave quantum machines (Harris et al. 2011) can perform finitetime adiabatic quantum computation, or quantum annealing. The superconducting architecture of D-Wave processors is built on the Chimera graph (Choi 2008; 2011), a sparsely connected graph that can host N ≤ 2048 qubits, with at most 2-body interactions. However, many interesting problems, including the ferromagnetic p-spin model (Derrida 1981; Gross and Mezard 1984; Bapst and Semerjian 2012), can be mapped on fully connected qubit systems with p-body interactions (p ≥ 2). In order to G. Passarelli
[email protected] 1
Dipartimento di Fisica “E. Pancini”, Universit`a di Napoli Federico II, Complesso di Monte S. Angelo, via Cinthia, 80126 Naples, Italy
2
CNR-SPIN, c/o Complesso di Monte S. Angelo, via Cinthia - 80126 Naples, Italy
3
Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Naples, 80126, Italy
exploit the available quantum hardware, these problems have to be mapped to effective Hamiltonians (Lucas 2014), containing at most 2-body interactions. This necessarily implies the introduction of auxiliary degrees of freedom, or ancillae (Biamonte 2008). The major challenge in this problem is to find the free parameters in the 2-body Hamiltonian, corresponding to the p-body one, such that the two Hamiltonians share the same spectral properties (Brell et al. 2011). In this paper, we show that genetic algorithms can be a powerful tool to optimize the free parameters in the effective 2-body model, focusing on the ferromagnetic p-spin system. Genetic algorithms are stochastic met
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