@misc{10481/97010,
year = {2024},
month = {10},
url = {https://hdl.handle.net/10481/97010},
abstract = {We present extensive simulations of a quantum version of the Hopfield neural network to explore
its emergent behavior. The system is a network of N qubits oscillating at a given Ω frequency and
which are coupled via Lindblad jump operators built with local fields hi depending on some given
stored patterns. Our simulations show the emergence of pattern-antipattern oscillations of the
overlaps with the stored patterns similar (for large Ω and small temperature) to those reported
within a recent mean-field description of such a system, and which are originated deterministically
by the quantum term including si
x qubit operators. However, in simulations we observe that such
oscillations are stochastic due to the interplay between noise and the inherent metastability of the
pattern attractors induced by quantum oscillations, and then are damped in finite systems when
one averages over many quantum trajectories. In addition, we report the system behavior for large
number of stored patterns at the lowest temperature we can reach in simulations (namely
T = 0.005 TC). Our study reveals that for small-size systems the quantum term of the Hamiltonian
has a negative effect on storage capacity, decreasing the overlap with the starting memory pattern
for increased values of Ω and number of stored patterns. However, it also impedes the system to be
trapped for long time in mixtures and spin-glass states. Interestingly, the system also presents a
range of Ω values for which, although the initial pattern is destabilized due to quantum
oscillations, other patterns can be retrieved and remain stable even for many stored patterns,
implying a quantum-dependent nonlinear relationship between the recall process and the number
of stored patterns.},
organization = {Project PID2021-128970OA-I00 funded by MCIN/AEI/ 10.13039/
501100011033},
organization = {“ERDF A way of making Europe”, by the “European Union”, the Ministry of Economic
Affairs and Digital Transformation of the Spanish Government through the QUANTUM ENIA project call -
Quantum Spain project},
organization = {European Union through the Recovery, Transformation and Resilience
Plan - NextGenerationEU within the framework of the Digital Spain 2026 Agenda and FEDER/Junta de
Andalucía program A.FQM.752.UGR20},
organization = {Consejería de Transformación Económica, Industria,
Conocimiento y Universidades, Spain, Junta de Andalucía, Spain},
organization = {European Regional Development
Funds, Ref. P20_00173},
organization = {Project of I+D+i, Spain Ref. PID2020-113681GBI00,
financed by MICIN/AEI/10.13039/501100011033, Spain},
publisher = {IOP science},
keywords = {neural networks},
keywords = {Hopfield},
keywords = {quantum neural networks},
title = {Dissipative quantum Hopfield network: a numerical analysis},
doi = {10.1088/1367-2630/ad5e15},
author = {Torres, Joaquín J and Manzano Diosdado, Daniel},
}