Ulich GmbH Team Integrates Reverse Annealing for Enhanced Combinatorial Optimisation

Lucas Joshua Menger of ulich GmbH and colleagues at Goethe University have shown that combining forward and reverse annealing consistently improves solution quality and efficiency across several problem types. Their systematic experimental study on a D-Wave Advantage system reveals that reverse annealing offers key benefits, particularly for larger and more complex problems where standard forward annealing struggles. These results highlight the potential of reverse annealing to unlock greater computational power from quantum annealing hardware as it develops towards tackling real-world applications.

Reverse annealing achieves substantial energy reduction in quantum optimisation

A reduction of 2x 10⁻²⁴ Joules in energy occurred through the implementation of reverse annealing, as demonstrated by scientists at ulich GmbH and Goethe University. This improvement unlocks the potential to solve optimisation problems of a scale and complexity previously considered computationally impossible, now making larger, more intricate problems tractable. Quantum annealing operates on the principle of adiabatic quantum computation, where a quantum system starts in a known ground state and is slowly evolved to represent the problem’s cost function. The system then ideally settles into the ground state of the cost function, representing the optimal solution. However, real quantum annealers are susceptible to noise and have limited coherence times, leading to errors. The energy landscape of complex optimisation problems often contains shallow energy gaps, making it difficult for the system to reliably find the true ground state. Reverse annealing aims to mitigate these issues by, after an initial forward annealing run, briefly reversing the annealing process before continuing forward. This ‘backtracking’ allows the system to escape local minima and explore a wider range of potential solutions. A systematic study on a D-Wave Advantage system revealed that combining forward and reverse approaches consistently delivers superior solution quality and efficiency across diverse problem types, including Max-Cut, Number Partitioning, and sparse clustering.

Specific points within the annealing schedule correlate with optimal reverse annealing parameters, corresponding to transitions between energy levels and the ‘freezing’ into potential solutions. The annealing schedule dictates how the quantum system evolves over time, controlling the strength of the problem Hamiltonian relative to the transverse field. Identifying the optimal reverse distance, the extent to which the annealing process is reversed, and pause duration, the time spent in the reversed direction, is crucial for maximising the benefits of this technique. The researchers found that these parameters link to specific points in the annealing schedule where the system undergoes significant energy transitions. These transitions represent the system ‘freezing’ into a particular configuration, and manipulating them with reverse annealing can guide the system towards better solutions. Benchmarking across Max-Cut, Number Partitioning, and sparse clustering demonstrated that the efficiency gains from reverse annealing were demonstrably greater than simply increasing the duration of standard forward annealing, especially for highly complex problems. Max-Cut, for example, seeks to divide a graph into two sets to minimise the number of edges connecting nodes in different sets. Number Partitioning aims to divide a set of integers into two subsets with equal sums. Sparse clustering involves identifying clusters within data where the connections between data points are limited. Precise control is vital for harnessing the power of reverse annealing, as a narrow range of reverse distance and pause duration parameters yielded the most significant improvements.

Optimising annealing parameters enhances solution quality on D-Wave systems

Quantum annealing, a technique for solving complex problems by finding the lowest energy state of a system, has been refined by researchers from ulich GmbH and Goethe University, proving particularly valuable as these systems tackle increasingly intricate challenges. The technique is applicable to a wide range of combinatorial optimisation problems, including logistics, finance, and machine learning. However, the performance of quantum annealers is heavily influenced by the specific parameters used during the annealing process. These parameters control the rate at which the system evolves, the strength of the applied fields, and the duration of various stages of the annealing schedule. While optimal parameters have been identified for this approach, the extent to which these apply to other quantum annealing architectures remains unclear, and the findings stem from experiments on a specific D-Wave Advantage system, limiting immediate generalisation to all quantum annealing platforms. Different quantum annealing platforms, such as those based on superconducting qubits or trapped ions, may exhibit different characteristics and require different parameter settings. This refinement strategy proves most beneficial when tackling complex problems where standard methods struggle, offering a pathway to enhance performance as quantum computers scale. Classical algorithms often become trapped in local optima when solving these problems, whereas quantum annealing, with its ability to explore multiple solutions simultaneously, can potentially overcome these limitations. Incorporating a ‘reverse’ step consistently enhances both the quality and speed of finding solutions, and this is most valuable when tackling problems that challenge standard optimisation techniques. The improvement in solution quality is measured by the reduction in the cost function value, while the speed improvement is reflected in the time taken to find a solution. Confirmation of the link between optimal parameters and key points within the annealing schedule, specifically where the system transitions between energy levels, also emerged from the investigation. Understanding these transitions is crucial for developing more effective annealing strategies and improving the overall performance of quantum annealers. Further research is needed to explore the applicability of these findings to other quantum annealing architectures and to investigate the potential for combining reverse annealing with other optimisation techniques.

The research demonstrated that combining forward and reverse annealing consistently improves the quality and efficiency of solutions for complex optimisation problems. This is significant because standard quantum annealing methods experience performance declines with increasing problem complexity, and reverse annealing offers a means of mitigating this. Researchers found the benefits of reverse annealing were greatest for larger, more challenging problems tested on a D-Wave Advantage system, including Max-Cut, Number Partitioning, and sparse clustering. The authors suggest further work is needed to determine if these findings apply to other quantum annealing hardware.