Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking
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Abstract
Posiform planting is a method for constructing QUBO instances with a 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 Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.