In this paper, we study the potential capability of quantum annealing in solving the phase unwrapping problem, an instance of hard computational problems. To solve the phase unwrapping problem using quantum annealing, we deploy the D-Wave Advantage machine which is currently the largest available quantum annealer. The structure of this machine, however, is not compatible with our problem graph structure. Consequently, the problem graph needs to be mapped into the target (Pegasus) graph, and this minor embedding significantly affects the quality of the results. Based on our experiment and also D-Wave's reports, the lower chain lengths can result in a better performance of quantum annealing. In this paper, we propose a new minor embedding algorithm that has the lowest possible chain length for minor embedding the graph of the phase unwrapping problem onto the Pegasus graph. The obtained results using this embedding strongly outperform the results of Auto-embedding provided by the D- Wave's minorminer tool both in the quality of the solution obtained and in the length of the chain.
In this paper, we study the potential capability of quantum annealing in solving the phase unwrapping problem, an instance of hard computational problems. To solve the phase unwrapping problem using quantum annealing, we deploy the D-Wave Advantage machine which is currently the largest available quantum annealer. The structure of this machine, however, is not compatible with our problem graph structure. Consequently, the problem graph needs to be mapped into the target (Pegasus) graph, and this minor embedding significantly affects the quality of the results. Based on our experiment and also D-Wave's reports, the lower chain lengths can result in a better performance of quantum annealing. In this paper, we propose a new minor embedding algorithm that has the lowest possible chain length for minor embedding the graph of the phase unwrapping problem onto the Pegasus graph. The obtained results using this embedding strongly outperform the results of Auto-embedding provided by the D- Wave's minorminer tool both in the quality of the solution obtained and in the length of the chain.
With the current progress of quantum computing, quantum annealing is being introduced as a powerful method to solve hard computational problems. In this paper, we study the potential capability of quantum annealing in solving the phase unwrapping problem, an instance of hard computational problems. To solve the phase unwrapping problem using quantum annealing, we deploy the D-Wave Advantage machine which is currently the largest available quantum annealer. The structure of this machine, however, is not compatible with our problem graph structure. Consequently, the problem graph needs to be mapped onto the target (Pegasus) graph, and this embedding significantly affects the quality of the results. Based on our experiment and also D-Wave's reports, the lower chain lengths can result in a better performance of quantum annealing. In this paper, we propose a new embedding algorithm that has the lowest possible chain length for embedding the graph of the phase unwrapping problem onto the Pegasus graph. The obtained results using this embedding strongly outperform the results of Auto-embedding provided by D-Wave. Besides the phase unwrapping problem, this embedding can be used to embed any subset of our problem graph to the Pegasus graph.
Quantum computers and algorithms are undergoing rapid development, offering promising solutions to complex computational problems. This study focuses on harnessing the potential of quantum annealing to address the challenging phase unwrapping problem. Specifically, we employed D-Wave’s quantum annealers, currently among the most powerful in existence. To effectively utilize these systems, it is crucial to embed the problem onto their underlying structure, the Pegasus graph in the case of the D-Wave Advantage system. A shorter chain-length in the embedding process generally correlates with improved results. In the course of this thesis, we devised an algorithm for efficiently embedding the phase unwrapping problem onto the D-Wave Advantage system. Our approach yielded promising results when compared to D-Wave’s automatic embeddings. Notably, our introduced embedding boasts the minimum chain-length and utilizes the native structure of the target graph. Additionally, we leveraged D-Wave’s hybrid workflow, combining classical and quantum computing capabilities, to tackle larger image problems. Refinements to the hybrid method were implemented, resulting in enhanced performance. Experimental evaluations were conducted on actual quantum annealers, demonstrating that our refined algorithms outperform those provided by D-Wave.
This study addresses the minor-embedding problem, which involves mapping the variables of an Ising model onto a quantum annealing processor. The primary motivation stems from the observed performance disparity of quantum annealers when solving problems suited to the processor's architecture versus those with non-hardware-native topologies. Our research has two main objectives: i) to analyze the impact of embedding quality on the performance of D-Wave Systems quantum annealers, and ii) to evaluate the quality of the embeddings generated by Minorminer, the standard minor-embedding technique in the quantum annealing literature, provided by D-Wave. Regarding the first objective, our experiments reveal a clear correlation between the average chain length of embeddings and the relative errors of the solutions sampled. This underscores the critical influence of embedding quality on quantum annealing performance. For the second objective, we evaluate Minorminer's embedding capabilities, the quality and robustness of its embeddings, and its execution-time performance on Erdös-Rényi graphs. We also compare its performance with Clique Embedding, another algorithm developed by D-Wave, which is deterministic and designed to embed fully connected Ising models into quantum annealing processors, serving as a worst-case scenario. The results demonstrate that there is significant room for improvement for Minorminer, suggesting that more effective embedding strategies could lead to meaningful gains in quantum annealing performance.
Quantum annealing is a quantum algorithm for computing solutions to combinatorial optimization problems. This study proposes a method for minor embedding optimization problems onto sparse quantum annealing hardware graphs called 4-clique network minor embedding. This method is in contrast to the standard minor embedding technique of using a path of linearly connected qubits in order to represent a logical variable state. The 4-clique minor embedding is possible on Pegasus graph connectivity, which is the native hardware graph for some of the current D-Wave quantum annealers. The Pegasus hardware graph contains many cliques of size 4, making it possible to form a graph composed entirely of paths of connected 4-cliques on which a problem can be minor-embedded. The 4-clique chains come at the cost of additional qubit usage on the hardware graph, but they allow for stronger coupling within each chain, thereby increasing chain integrity, reducing chain breaks, and allow for greater usage of the available energy scale for programming logical problem coefficients on current quantum annealers. The 4-clique minor embedding technique is compared with the standard linear path minor embedding with experiments on two D-Wave quantum annealing processors with Pegasus hardware graphs. We show proof-of-concept experiments where the 4-clique minor embeddings can use weak chain strengths while successfully carrying out the computation of minimizing random all-to-all spin glass problem instances. Published by the American Physical Society 2024
Minor embedding is essential for mapping largescale combinatorial problems onto quantum annealers, particularly in quantum machine learning and optimization. This work presents an optimized, universal minor-embedding framework that efficiently accommodates complete bipartite graphs onto the hardware topology of quantum annealers. By leveraging the inherent topographical periodicity of the physical quantum adiabatic annealer processor, our method systematically reduces qubit chain lengths, resulting in enhanced stability, computational efficiency, and scalability of quantum annealing. We benchmark our embedding framework against Minorminer, the default heuristic embedding algorithm, for the Pegasus topology, demonstrating that our approach significantly improves embedding quality. Our empirical results show a 99.98% reduction in embedding time for a 120 x 120 complete bipartite graphs. Additionally, our method eliminates long qubit chains, which primarily cause decoherence and computational errors in quantum annealing. These findings advance the scalability of quantum embeddings, particularly for quantum generative models, anomaly detection, and large-scale optimization tasks. Our results establish a foundation for integrating efficient quantum-classical hybrid solutions, paving the way for practical applications in quantum-enhanced machine learning and optimization.
The qubits in a D-wave quantum annealer (D-wave QA) are designed on a Pegasus graph that is different from the structure of a combinatorial optimization problem. This situation requires embedding with the chains connected by ferromagnetic coupling Jc between the qubits. Weak and strong Jc values induce chain breaking and enforcement of chain energy, which reduce the accuracy of quantum annealing (QA) measurements, respectively. In addition, we confirmed that even though the D-wave Ocean package provides a default coupling Jcdefault, it is not an optimal coupling Jcoptimal that maximizes the possible correct rate of QA measurements. In this paper, we present an algorithm how Jcoptimal with the maximum probability p for observing the possible lowest energy is determined. Finally, we confirm that the extracted Jcoptimal shows much better p than Jcdefault in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems. The open code is available in https://github.com/HunpyoLee/OptimizeChainStrength.