The low-autocorrelation binary sequence problem, known in the literature as LABS, asks for a binary string of length N whose autocorrelations, measured across all possible shifts of the sequence, are as small as possible. The objective function sums the squared autocorrelation values, and finding the string that minimizes this energy is exponentially hard in the worst case. The problem is not an academic curiosity: binary sequences with low autocorrelation are the backbone of pulse compression codes used in radar, spread-spectrum communications, and signal processing, a connection that dates back to foundational work in the 1960s and 1970s. Because the energy landscape of LABS is rugged and spin-glass-like, filled with metastable states that trap local search algorithms, it has become a standard proving ground for optimization heuristics and, more recently, for quantum algorithms.

The new method works in two stages. First, a quantum processor or quantum simulator runs digitized counterdiabatic quantum optimization, DCQO, a technique that approximates the shortcuts to adiabaticity that would, in principle, allow a quantum system to follow the instantaneous ground state of a slowly changing Hamiltonian. By digitizing the evolution into a sequence of quantum gates and incorporating approximate counterdiabatic terms, DCQO produces high-quality candidate solutions with circuits that are far shallower than those required by the quantum approximate optimization algorithm, QAOA. These quantum-generated bitstrings then serve as the initial population for a classical memetic tabu search, which combines a population-based evolutionary framework with tabu search, a local refinement method that uses short-term memory to avoid cycling and to encourage exploration of the search space.

The quantum stage is not trying to solve the problem on its own. Instead, it acts as a biased sampler, concentrating the initial population of the classical search in promising regions of the configuration space. This warm-starting philosophy, which has been explored theoretically in recent work on quantum-enhanced optimization, is here put to a rigorous empirical test. The researchers measured time-to-solution in objective-function evaluations, a hardware-agnostic metric that counts how many times the energy of a candidate sequence must be computed, and they benchmarked every system size using one hundred independent replicates, each comprising one hundred randomized seeds. This produced a robust distributional scaling analysis rather than a handful of cherry-picked successes.

The headline result is a scaling exponent of O(1.24^N) for sequence lengths N between 27 and 37. The best-known purely classical heuristic for LABS scales as O(1.34^N), while QAOA achieves O(1.46^N) on this problem, so the quantum-enhanced hybrid improves on both. The advantage over QAOA is compounded by a roughly sixfold reduction in circuit depth, since the counterdiabatic circuits used for warm-starting require substantially fewer entangling gates than comparable QAOA circuits. The authors verified the scaling advantage with a two-stage bootstrap analysis that accounts for variance both across replicates and across seeds, and this analysis projects a crossover point at N greater than roughly 47, beyond which QE-MTS is expected to outperform its purely classical counterpart in absolute runtime as well as in scaling exponent.

The technical details of the quantum stage reveal careful engineering. After trotterizing the digitized evolution, each term in the effective Hamiltonian becomes a generalized Pauli rotation. The two-body interactions decompose into blocks requiring two entangling RZZ gates and four single-qubit rotations, while the four-body interactions that make LABS particularly challenging decompose into blocks requiring ten entangling gates and twenty-eight single-qubit rotations. The first-order counterdiabatic coefficient is obtained analytically by minimizing a trace-based action, yielding a closed-form expression that depends on the structure of the interaction graph. The authors note that a single Trotter step of DCQO costs roughly the same as two layers of QAOA while retaining favorable performance in the low-depth regime, which is exactly where today’s noisy intermediate-scale quantum devices operate.

Because no quantum hardware with thirty-seven high-quality qubits was needed for the study, the team simulated the quantum circuits on classical hardware using CUDA-Q, NVIDIA’s hybrid quantum-classical programming framework with GPU-accelerated state-vector simulation. They tested three AWS GPU instances, including machines built on A100, H200, and B200 accelerators, with the largest GPUs providing enough memory to simulate systems up to thirty-seven qubits. For each sequence length, the DCQO circuits were executed with one hundred thousand measurement shots to generate the initial populations. The classical memetic tabu search component ran in single-threaded mode to ensure accurate counting of objective-function evaluations, and both the baseline and quantum-enhanced versions used identical parameters, including a population size of one hundred, a recombination probability of 0.9, a mutation rate of one over N, and a tournament size of two, so that the only difference between the two methods was the initialization.

The paper also probes the robustness of the result. An appendix describes an alternative initialization strategy in which the initial population is built from the lowest-energy bitstrings obtained across multiple independent DCQO runs, making the procedure more resilient to shot noise. With this setup, the best-performing quantum-enhanced seeds outperform the best classical seeds by up to two orders of magnitude for most sequence lengths, although three isolated system sizes showed no enhancement. The authors also quantify the gap between the two methods using a logarithmic ratio of time-to-solution distributions, showing that the gap narrows steadily with increasing problem size, consistent with the projected crossover. These analyses suggest that the scaling advantage is not an artifact of a particular parameter choice but a structural consequence of seeding the classical search with quantum-generated bias.

The significance of the work lies in its framing of how quantum computers may deliver practical value before fault tolerance arrives. Rather than attempting to run an entire optimization on a quantum device, the hybrid-sequential workflow assigns each paradigm the task it handles best: shallow quantum circuits explore the global structure of the energy landscape and produce biased initial states, while mature classical metaheuristics exploit those states with the full arsenal of local refinement, population diversity, and memory mechanisms. The LABS problem, with its spin-glass phenomenology and its roots in radar and communications engineering, serves as a demanding test case, and the measured improvement from 1.34 to 1.24 in the exponential base is substantial when compounded over large N. If the projected crossover near N equal to 47 holds on future hardware, quantum-enhanced warm starts could become a standard component of industrial optimization pipelines, from portfolio construction to code design, in the near-term era of quantum computing.

Subject of Research: Hybrid quantum-classical optimization of the low-autocorrelation binary sequence problem using quantum-enhanced memetic tabu search

Article Title: Scaling advantage with quantum-enhanced memetic tabu search for LABS

Article References: Scaling advantage with quantum-enhanced memetic tabu search for LABS. (n.d.). https://doi.org/10.1007/s42484-026-00433-1

Image Credits: AI Generated

DOI: 10.1007/s42484-026-00433-1

Keywords: quantum optimization, hybrid quantum-classical algorithms, memetic tabu search, counterdiabatic driving, low-autocorrelation binary sequences, runtime scaling, LABS problem, warm-starting, QAOA, spin-glass optimization, time-to-solution, DCQO