Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking
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arXiv
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| Format: | Preprint |
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2024
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| author | Pelofske, Elijah Hahn, Georg Djidjev, Hristo |
| author_facet | Pelofske, Elijah Hahn, Georg Djidjev, Hristo |
| contents | Posiform planting is a method for constructing QUBO problems with a single unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random discrete coefficient spin-glass Ising models, whose global minimum energy is computed classically using classical binary integer programming optimization software, with posiform-planted QUBOs. The single unique ground-state solution of the resulting QUBO problem is the concatenation of (exactly one of) the ground-states of each of the smaller problems. We apply these modified posiform planted QUBOs to the task of benchmarking programmable D-Wave quantum annealers. The proposed method enables generating binary variable combinatorial optimization problems that cover the entire quantum annealing processor hardware graph, have a unique solution, are entirely hardware-graph-native, and can have tunable computational hardness. We benchmark the capabilities of three D-Wave superconducting qubit quantum annealing processors, having from 563 up to 5627 qubits, to sample the optimal unique planted solution of problems generated by our proposed method and compare them against simulated annealing and Gurobi. We find that the D-Wave QPU ground-state sampling success rate does not change with respect to the size of the random QUBOs we employ. Surprisingly, we find that some of these classes of QUBOs are solved at very high success rates at short annealing times compared to longer annealing times for the Zephyr connectivity graph QPUs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2411_03626 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking Pelofske, Elijah Hahn, Georg Djidjev, Hristo Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Optimization and Control Posiform planting is a method for constructing QUBO problems with a single unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random discrete coefficient spin-glass Ising models, whose global minimum energy is computed classically using classical binary integer programming optimization software, with posiform-planted QUBOs. The single unique ground-state solution of the resulting QUBO problem is the concatenation of (exactly one of) the ground-states of each of the smaller problems. We apply these modified posiform planted QUBOs to the task of benchmarking programmable D-Wave quantum annealers. The proposed method enables generating binary variable combinatorial optimization problems that cover the entire quantum annealing processor hardware graph, have a unique solution, are entirely hardware-graph-native, and can have tunable computational hardness. We benchmark the capabilities of three D-Wave superconducting qubit quantum annealing processors, having from 563 up to 5627 qubits, to sample the optimal unique planted solution of problems generated by our proposed method and compare them against simulated annealing and Gurobi. We find that the D-Wave QPU ground-state sampling success rate does not change with respect to the size of the random QUBOs we employ. Surprisingly, we find that some of these classes of QUBOs are solved at very high success rates at short annealing times compared to longer annealing times for the Zephyr connectivity graph QPUs. |
| title | Increasing the Hardness of Posiform Planting Using Random QUBOs for Programmable Quantum Annealer Benchmarking |
| topic | Quantum Physics Disordered Systems and Neural Networks Statistical Mechanics Optimization and Control |
| url | https://arxiv.org/abs/2411.03626 |