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Quantum Optimization
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We present a quantum algorithm for combinatorial optimization using the cost structure of the search states. Its behavior is illustrated for overconstrained satisfiability and asymmetric traveling salesman problems. Simulations with randomly generated problem instances show each step of the algorithm shifts amplitude preferentially towards lower cost states, thereby concentrating amplitudes into low-cost states, on average. These results are compared with conventional heuristics for these problems.
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Quantum Approximate Optimization of Integer Graph Problems and Surpassing Semidefinite Programming for Max-k-Cut
QAOA on qudit-encoded integer graph problems outperforms the Frieze-Jerrum SDP for Max-k-Cut at p≤4 in regimes k=3 d≤10 and k=4 d≤40, while a new degree-of-saturation heuristic beats both on GSet but may be overtaken ...
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