Table 1 Approximate optima for max-XORSAT

From: Optimization by decoded quantum interferometry

Algorithm

Fraction satisfied

Tailored heuristic (7 min  × 1 core)

0.880

Long anneal (73 h × 5 cores)

0.832

DQI + BP

≥0.831

Prange’s algorithm

0.812

Short anneal (8 s × 1 core)

0.764

Greedy algorithm

0.666

AdvRand

0.554

  1. Here we compare DQI, using a standard belief-propagation decoder, against classical algorithms for a randomly generated max-XORSAT instance with irregular degree distribution specified in Supplementary Information section 9. We consider an example instance with 31,216 variables and 50,000 constraints. The classical algorithms above are defined in Supplementary Information section 8. For simulated annealing, the satisfaction fraction grows with the runtime, so we report two numbers. The first is the optimum reachable by limiting simulated annealing to the same runtime used by belief propagation to solve the problem to which the max-XORSAT instance is reduced by DQI (8 s × 1 core), and the second is for the shortest anneal that matched the satisfaction fraction achieved by DQI + BP (73 h × 5 cores).
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