We introduce quantum-enhanced memetic tabu search (QE-MTS), a non-variational hybrid algorithm that achieves state-of-the-art scaling for the low-autocorrelation binary sequence (LABS) problem. By seeding the classical MTS with high-quality initial states from digitized counterdiabatic quantum optimization (DCQO), our method suppresses the empirical time-to-solution scaling to $\mathcal{O}(1.24^N)$ for sequence length $N \in [27,37]$ . This scaling surpasses the best-known classical heuristic $\mathcal{O}(1.34^N)$ and improves upon the $\mathcal{O}(1.46^N)$ of the quantum approximate optimization algorithm, achieving superior performance with a $6\times$ reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at $N \gtrsim 47$ , beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.We introduce quantum-enhanced memetic tabu search (QE-MTS), a non-variational hybrid algorithm that achieves state-of-the-art scaling for the low-autocorrelation binary sequence (LABS) problem. By seeding the classical MTS with high-quality initial states from digitized counterdiabatic quantum optimization (DCQO), our method suppresses the empirical time-to-solution scaling to $\mathcal{O}(1.24^N)$ for sequence length $N \in [27,37]$. This scaling surpasses the best-known classical heuristic $\mathcal{O}(1.34^N)$ and improves upon the $\mathcal{O}(1.46^N)$ of the quantum approximate optimization algorithm, achieving superior performance with a $6\times$ reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at $N \gtrsim 47$, beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.

quant-pharXiv:2511.04553Quantum Machine IntelligenceNov 7, 20250 citations

Long-range interactions generated by random Lévy flights: Spin-flip and spin-exchange kinetic Ising model in two dimensions

Huang-Jian Xu, B. Bergersen, Zoltàn Ràcz

A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random L\'evy flights of dimension \ensuremath{\sigma}=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as ${\mathit{r}}^{\mathrm{\ensuremath{-}}3.5}$, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random L\'evy flights generating long-range interaction of the form ${\mathit{V}}_{\mathrm{eff}}$ (r)\ensuremath{\sim}${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{d}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ is valid not only in the spherical limit and in d=1 but also in d=2.A d=2 dimensional kinetic Ising model that evolves by a combination of spin flips and spin exchanges is investigated. The spin flips satisfy detailed balance for the equilibrium state of the Ising model at temperature T while the spin exchanges are random L\'evy flights of dimension \ensuremath{\sigma}=1.5. Our Monte Carlo (MC) simulations show that the steady state of this system displays a second-order phase transition as T is lowered. Comparing the critical fluctuations of the magnetization to those of an Ising model in which the interaction decays with distance as ${\mathit{r}}^{\mathrm{\ensuremath{-}}3.5}$, we find that, within the resolution of the MC data, the critical exponents and the scaling functions of the two systems coincide. We argue that this coincidence indicates that a recent conjecture about the random L\'evy flights generating long-range interaction of the form ${\mathit{V}}_{\mathrm{eff}}$(r)\ensuremath{\sim}${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{d}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ is valid not only in the spherical limit and in d=1 but also in d=2.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMar 1, 199310 citations

Quantum multiverse optimization algorithm for optimization problems

Gehad Ismail Sayed, Ashraf Darwish, Aboul Ella Hassanien

Neural Computing and ApplicationsNov 1, 201772 citations

\mathcal{O}(1.24^N)

for sequence length

N \in [27,37]

. This scaling surpasses the best-known classical heuristic

\mathcal{O}(1.34^N)

and improves upon the

\mathcal{O}(1.46^N)

of the quantum approximate optimization algorithm, achieving superior performance with a

6\times

reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at

N \gtrsim 47

, beyond which QE-MTS outperforms its classical counterpart. These results provide evidence that quantum enhancement can directly improve the scaling of classical optimization algorithms for the paradigmatic LABS problem.

{\mathit{V}}_{\mathrm{eff}}

(r)\ensuremath{\sim}${\mathit{r}}^{\mathrm{\ensuremath{-}}\mathit{d}\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\sigma}}}$ is valid not only in the spherical limit and in d=1 but also in d=2.