Quantum annealing search of Ising spin glass ground state(s) with tunable transverse and longitudinal fields

Abstract

Here we first discuss briefly the quantum annealing technique. We then study the quantum annealing of Sherrington-Kirkpatrick spin glass model with the tuning of both transverse and longitudinal fields. Both the fields are time-dependent and vanish adiabatically at the same time, starting from high values. We solve, for rather small systems, the time-dependent Schrodinger equation of the total Hamiltonian by employing a numerical technique. At the end of annealing we obtain the final state having high overlap with the exact ground state(s) of classical spin glass system (obtained independently).

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing

“…We believe, the numerical results reported here for the quantum SK model establishes the nature of the earlier conjectured [5] ergodicity in the model and its role in quantum annealing [6,7,16] of the SK model. It is also possible that the crossover region shrinks as N → ∞.…”

Multivariable optimization: Quantum annealing and computation

“…We discusss two applications of QA (see e.g., [28,14] for details). First we review the performance of QA annealing for the Sherrington-Kirkpatrick (SK) spin glass model.…”

“…First we review the performance of QA annealing for the Sherrington-Kirkpatrick (SK) spin glass model. The classical SK model [2] is known to contain highly rugged energy landscape and QA seems to work here satisfactory [28]. Next we focus on the QA of kinetically constrained system (KCS).…”

“…The basic point behind the criticisms had been that the incoherent mixture of the tunnelling waves coming from different energy barriers, may lead to localization of the wave functions while penetrating energy barriers, as the phases of the transmitted waves are completely random. However several recent theoretical and experimental studies (see e.g., [9,10,11,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32]) seem to have cleared almost all such doubts. Recently the technological implementation of QA to develop an analog quantum computer has been mastered successfully by the D-wave systems [18].…”

Caracterização da evolução adiabática em cadeias de spin

“…Para compreender eles, permitamos escrever uma função de custo Ep Ý Ñ x q que deseja-se optimizar como uma soma linear e quadrática de variáveis binárias x i (39,40), Fonte: RAJAK; CHAKRABARTI. (41) CQA essa dinâmica está vinculada tradicionalmente à relação entre a variação temporal do Hamiltoniano total e o gap entre o estado fundamental e excitado, a qual deve ser muito pequena, e é fundamentada pelo teorema adiabático, tal que o sucesso dessa técnica dependerá se é satisfeita a condição de adiabaticidade imposta por dito teorema. Portanto, permitamos entrar em detalhes nesse teorema essencial para o entendimento da CQA.…”