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arXiv:2511.04553 · Quantum Machine Intelligence

Scaling advantage with quantum-enhanced memetic tabu search for LABS

Alejandro Gomez Cadavid, Pranav Chandarana, Sebastián V. Romero, Jan Trautmann, Enrique Solano, Taylor Lee Patti, Narendra N. Hegade

quant-phcond-mat.stat-mechSubmitted Nov 6, 2025• Announced Nov 7, 2025• 0 citations
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Abstract

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.

Comments
9 pages, 7 figures

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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 O(1.24N)\mathcal{O}(1.24^N)O(1.24N) for sequence length N∈[27,37]N \in [27,37]N∈[27,37]. This scaling surpasses the best-known classical heuristic O(1.34N)\mathcal{O}(1.34^N)O(1.34N) and improves upon the O(1.46N)\mathcal{O}(1.46^N)O(1.46N) of the quantum approximate optimization algorithm, achieving superior performance with a 6×6\times6× reduction in circuit depth. A two-stage bootstrap analysis confirms the scaling advantage and projects a crossover point at N≳47N \gtrsim 47N≳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.
The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.
The low autocorrelation binary sequences (LABS) problem, often formulated as a spin-lattice energy-minimization problem, is a combinatorial optimization problem with a very rugged energy landscape. We demonstrate that iterative optimization of very small subsystems of n spins that are decoupled from the rest of the system achieves global optimization of LABS with a time-to-solution scaling that is competitive with heuristics that optimize the global system of N spins directly. Our isolated-subsystem heuristic with n = 4 achieves a time scaling of O(1.33^N ) on the interval N = [27, 60], while the current state-of-the-art classical and quantum scalings are respectively O(1.34^N ) and O(1.21^N ). Our results suggest that specialized optimization hardware with only small numbers of logical spins may be of practical relevance, and that quantum speedups demonstrated in the absence of decomposition may not provide a practical quantum advantage for large-scale problems that require decomposition.
We introduce hybrid sequential quantum computing (HSQC), a paradigm for combinatorial optimization that systematically integrates classical and quantum methods within a structured, stage-wise workflow. HSQC may involve an arbitrary sequence of classical and quantum processes, as long as the global result outperforms the standalone components. Our testbed begins with classical optimizers to explore the solution landscape, followed by quantum optimization to refine candidate solutions, and concludes with classical solvers to recover nearby or exact-optimal states. We demonstrate two instantiations: (i) a pipeline combining simulated annealing (SA), bias-field digitized counterdiabatic quantum optimization (BF-DCQO), and memetic tabu search (MTS); and (ii) a variant combining SA, BF-DCQO, and a second round of SA. This workflow design is motivated by the complementary strengths of each component. Classical heuristics efficiently find low-energy configurations, but often get trapped in local minima. BF-DCQO exploits quantum resources to tunnel through these barriers and improve solution quality. Due to decoherence and approximations, BF-DCQO may not always yield optimal results. Thus, the best quantum-enhanced state is used to continue with a final classical refinement stage. Applied to challenging higher-order unconstrained binary optimization (HUBO) problems on a 156-qubit heavy-hexagonal superconducting quantum processor, we show that HSQC consistently recovers ground-state solutions in just a few seconds. Compared to standalone classical solvers, HSQC achieves a speedup of up to 700 times over SA and up to 9 times over MTS in estimated runtimes. These results demonstrate that HSQC provides a flexible and scalable framework capable of delivering up to two orders of magnitude improvement at runtime quantum-advantage level on advanced commercial quantum processors.
We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground-state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground-state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3 × better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin glass on a heavy-hexagonal lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.
Quantum phase estimation (QPE) plays a pivotal role in many quantum algorithms, offering provable speedups in applications such as Shor's factoring algorithm. While faulttolerant quantum algorithms for combinatorial and Hamiltonian optimization often integrate QPE with variational protocols-like the quantum approximate optimization Ansatz or variational quantum eigensolver-these approaches typically rely on heuristic techniques requiring parameter optimization. In this work, we present the QPE-based quantum imaginary time evolution (QPEQITE) algorithm, designed for post-variational ground state estimation on fault-tolerant quantum computers. Unlike variational methods, QPE-QITE employs additional ancillae to project the quantum register into low-energy eigenstates, eliminating the need for parameter optimization. We demonstrate the capabilities of QPE-QITE by applying it to the low-autocorrelation binary sequences (LABS) problem, which is a higher order optimization problem that has been studied in the context of quantum scaling advantage. Scaling estimates for magic state requirements are provided to assess the feasibility of addressing these problems on near-term fault-tolerant devices, establishing a benchmark for quantum advantage. Moreover, we discuss potential implementations of QPE-QITE on existing quantum hardware as a precursor to fault tolerance.
Branch-and-bound algorithms effectively solve combinatorial optimization problems, relying on the relaxation of the objective function to obtain tight lower bounds. While this is straightforward for convex objective functions, higher-order formulations pose challenges due to their inherent non-convexity. In this work, we propose branch-and-bound digitized counterdiabatic quantum optimization (BB-DCQO), a quantum algorithm that addresses the relaxation difficulties in higher-order unconstrained binary optimization (HUBO) problems. By employing bias fields as approximate solutions to the relaxed problem, we iteratively enhance the quality of the results compared to the bare bias-field digitized counterdiabatic quantum optimization (BF-DCQO) algorithm. We refer to this enhanced method as BBB-DCQO. In order to benchmark it against simulated annealing (SA), we apply it on sparse HUBO instances with up to 156156156 qubits using tensor network simulations. To explore regimes that are less tractable for classical simulations, we experimentally apply BBB-DCQO to denser problems using up to 100 qubits on IBM quantum hardware. We compare our results with SA and a greedy-tuned quantum annealing baseline. In both simulations and experiments, BBB-DCQO consistently achieved higher-quality solutions with significantly reduced computational overhead, showcasing the effectiveness of integrating counterdiabatic quantum methods into branch-and-bound to address hard non-convex optimization tasks.