Quantum Computing Achieves up to 10% Improvement with Novel LOTUS Optimisation Schedules

Quantum Approximate Optimisation Algorithms (QAOA) hold immense promise for tackling complex optimisation problems, but their performance is often hampered by the challenges of optimising numerous parameters. Phuong-Nam Nguyen, from Viettel High Technology Industries Corporation, alongside colleagues, present a novel framework called LOTUS , Layer-Ordered Temporally Unified Schedules , to address this issue. LOTUS reimagines the optimisation process, transforming a chaotic, high-dimensional search into a more manageable, low-dimensional dynamical system through a Hybrid Fourier-Autoregressive mapping. This approach not only delivers consistently superior results, exceeding the performance of established optimisers such as L-BFGS-B and COBYLA, but also significantly reduces computational demands by requiring fewer optimisation iterations than conventional methods. The research represents a substantial step towards realising the full potential of QAOA for real-world applications.

The study pinpointed pathological behaviours within standard QAOA optimization landscapes, specifically discrete piecewise-constant transitions in parameter schedules and a tendency for parameters to swap roles between layers due to inherent permutation symmetry.

Experiments revealed these issues were amplified when scaling the number of qubits or increasing circuit depth, leading to unstable parameters and a performance gap compared to functionally-defined schedules. To overcome these challenges, scientists engineered a Hybrid Fourier-Autoregressive (HFA) mapping, replacing independent layer-wise angles with a unified parameterization. This innovative approach enforces global temporal coherence within the QAOA circuit while preserving local flexibility, effectively breaking the permutation symmetry that hinders traditional optimizers.

The team demonstrated that LOTUS achieves a dimensionality collapse, reducing optimization complexity to O(1) relative to circuit depth, a significant advancement for deep circuit training. This reduction enables the training of deeper circuits without the exponential performance degradation often experienced with classical optimizers. Rigorous benchmarking showcased LOTUS consistently outperforming standard optimizers, achieving up to a 27.2% improvement in expectation values when compared to L-BFGS-B and a 20.8% improvement over COBYLA.

Furthermore, the method drastically reduces computational costs, requiring over 90% fewer iterations than algorithms like Powell or SLSQP. This methodological innovation not only facilitates the training of deep circuits but also enables depth transferability, allowing schedules optimized at lower depths to serve as effective initializations for deeper circuits. The research team successfully transformed a traditionally high-dimensional and chaotic search space into a structured, low-dimensional dynamical system, achieving substantial gains in both solution quality and computational efficiency.

This was accomplished by replacing independent layer-wise parameters with a Hybrid Fourier-Autoregressive (HFA) mapping, enforcing global temporal coherence while preserving local flexibility within the algorithm. Experiments revealed that LOTUS consistently outperforms standard optimization methods across a range of test cases, achieving a remarkable 27.2% improvement in expectation values when compared to the L-BFGS-B optimizer. Furthermore, the team recorded over 26% improvement in expectation values compared with both TNC and SLSQP optimizers, solidifying LOTUS’s ability to identify superior configurations.

This breakthrough delivers a substantial advantage in finding optimal or near-optimal solutions for complex optimization problems. The efficiency of LOTUS is equally impressive, drastically reducing the computational burden associated with QAOA training. Tests prove that LOTUS requires 93.3% fewer iterations than the Powell method to reach convergence, representing a major step forward in scalability. Moreover, the framework demonstrates an iteration reduction exceeding 86% against both TNC and L-BFGS-B, highlighting its ability to rapidly refine parameters and achieve optimal performance.

This reduction in computational cost is critical for tackling larger and more complex problems that are currently intractable for conventional optimization techniques. Data shows that LOTUS achieves a dimensionality collapse, reducing the optimization complexity to O(1) relative to circuit depth, enabling the training of deep circuits without the exponential degradation often seen with classical optimizers. The work also facilitates depth transferability, allowing schedules optimized at lower depths to serve as effective initializations for deeper circuits. Ultimately, this research provides a robust pathway for scaling QAOA towards utility-scale quantum advantage, offering a superior balance between solution quality and computational efficiency.

LOTUS Framework Achieves Efficient Global Optimisation

This work introduces LOTUS, a novel framework which reformulates complex optimisation problems as a low-dimensional dynamical system, moving away from traditional chaotic search methods. By employing a Hybrid Fourier-Autoregressive mapping, LOTUS establishes global temporal coherence within optimisation schedules while retaining necessary local flexibility, demonstrably exceeding the performance of established optimisation techniques like L-BFGS-B and COBYLA on the MaxCut problem.

Furthermore, the method achieves substantial reductions in computational cost, requiring significantly fewer iterations than algorithms such as Powell or SLSQP. A key contribution of LOTUS lies in its ability to define parameters as continuous functions, enabling depth transferability. Optimisation at a given depth allows for the creation of continuous curves that can be readily adapted to deeper circuits, providing near-optimal initial conditions and reducing the computational burden of training at increased depths.

The authors acknowledge limitations inherent in applying the HFA ansatz exclusively to the MaxCut problem, and future research will investigate its efficacy across a wider range of NP-hard challenges, including MaxSAT, TSP, and QUBO. LOTUS reimagines the optimisation process, transforming a chaotic, high-dimensional search into a more manageable, low-dimensional dynamical system through a Hybrid Fourier-Autoregressive mapping. This approach not only delivers consistently superior results, but also significantly reduces computational demands by requiring fewer optimisation iterations than conventional methods. The research represents a substantial step towards realising the full potential of QAOA for real-world applications.