Fig. 6: Demonstration of hybrid computation in the chemical array.
a Flow chart describing hybrid electronic–chemical logic for solving quadratic optimization problems using a chemical array where Econv represents the converged energy. b Chemical states (CS) lookup table used for chemical decision-making based on probabilistic outcomes (light blue: \({{{{{{\rm{CS}}}}}}}_{{i}}^{{t}}=0\) and dark blue \({{{{{{\rm{CS}}}}}}}_{{i}}^{{t}}=1\)). c Left: Mapping a 4-number partition problem on a chemical array with isolated spins with all couplings defined by neighbouring auxiliary cells. Right: Efficient mapping of 4-number partition problem on the chemical array. (Blue: principal cells, Red: auxiliary cells for spin variables). d and e Energy minimization of four-number partitioning solved using a hybrid probabilistic algorithm using two different approaches. f Pictorial representation of chemical states from an experiment on energy minimization for a 4-number partition problem (light blue: \({{{{{{\rm{CS}}}}}}}_{{i}}^{{t}}=0\), dark blue: \({{{{{{\rm{CS}}}}}}}_{{i}}^{{t}}=0\)), see Supplementary Video 6. g The distribution of initial configurations (\({{{{{{\mathscr{D}}}}}}}_{{\rm {{conf}}}}\)) over the success probability (\({{{{{{\mathscr{P}}}}}}}_{{{\rm {success}}}}\)) of solving an 8-number partition problem (\(S=\{1,\, 3,\, 4,\, 9,\, 3,\, 5,\, 3,\, 6\}\)) in pure deterministic, random and hybrid approaches. h Success probabilities of deterministic (index = 1.0), random (index = 0.5) and hybrid approach (index = 0.99/0.95) vs. initial configuration indices for the 8-number partition problem. The deterministic index with a value of 1.0 corresponds to a pure deterministic algorithm, 0.99/0.95 as our tuneable hybrid approach and 0.5 as a random algorithm.
