aiqbench analysis
This paper maps MAX-k-CUT on hypergraphs onto Ising Hamiltonians with pairwise interactions, then runs QAOA simulations (p=2 to p=15) on IBM's Qiskit AerSimulator for two example hypergraph families. The results come from classical simulation of small instances, not hardware, so they say little yet about whether the approach scales or beats classical solvers. The useful takeaway for quantum readers is the reduction technique, which could make higher-order combinatorial problems easier to encode for near-term variational algorithms.
Solving the MAX-$k$-CUT problem for hypergraphs with quantum computing
arXiv:2610.41678v1 Announce Type: new Abstract: We investigate the MAX-$k$-CUT problem on hypergraphs by considering their representation as spin systems with Ising interactions. The corresponding cost Hamiltonian for MAX-$k$-CUT problem on hypergraphs is reduced to an Ising Hamiltonian with pairwise interactions. This reduction simplifies the solution of the MAX-$k$-CUT problem using quantum computing. As illustrative examples, a 3-uniform tight-star hypergraph and a sunflower hypergraph are considered. The corresponding Hamiltonians are constructed, and quantum protocols for the MAX-$k$-CUT problems are presented. The MAX-3-CUT and MAX-4-CUT instances are investigated for these hypergraphs by varying the number of Quantum Approximate Optimization Algorithm (QAOA) layers from (p=2) to (p=15) with quantum computing on IBM's Qiskit AerSimulator.
Abstract:We investigate the MAX-$k$-CUT problem on hypergraphs by considering their representation as spin systems with Ising interactions. The corresponding cost Hamiltonian for MAX-$k$-CUT problem on hypergraphs is reduced to an Ising Hamiltonian with pairwise interactions. This reduction simplifies the solution of the MAX-$k$-CUT problem using quantum computing. As illustrative examples, a 3-uniform tight-star hypergraph and a sunflower hypergraph are considered. The corresponding Hamiltonians are constructed, and quantum protocols for the MAX-$k$-CUT problems are presented. The MAX-3-CUT and MAX-4-CUT instances are investigated for these hypergraphs by varying the number of Quantum Approximate Optimization Algorithm (QAOA) layers from (p=2) to (p=15) with quantum computing on IBM's Qiskit AerSimulator.
arXiv:2610.41678 [quant-ph]
(or arXiv:2610.41678v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.41678 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 197 words
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