Equation 5 · Variational Evolution: How Quantum Computers Learn Their Answers
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The same architecture, aimed at combinatorial optimization rather than chemistry, produced the quantum approximate optimization algorithm (QAOA) later that same year. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann proposed a circuit built from alternating problem and mixing unitaries, controlled by a small number of classical parameters, whose measured output approximates the solution to a combinatorial problem such as MaxCut [ 2 ] . For MaxCut on 3-regular graphs at the shallowest depth ( p=1 ), they proved the algorithm returns a cut at least 0.6924 times the size of the true optimum — a specific, checkable guarantee rather than a promise of “quantum speedup” in the abstract, and one…
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The same architecture, aimed at combinatorial optimization rather than chemistry, produced the quantum approximate optimization algorithm (QAOA) later that same year. Edward Farhi, Jeffrey Goldstone, and Sam Gutmann proposed a circuit built from alternating problem and mixing unitaries, controlled by a small number of classical parameters, whose measured output approximates the solution to a combinatorial problem such as MaxCut [ 2 ] . For MaxCut on 3-regular graphs at the shallowest depth ( p=1 ), they proved the algorithm returns a cut at least 0.6924 times the size of the true optimum — a specific, checkable guarantee rather than a promise of “quantum speedup” in the abstract, and one that improves as the depth parameter p is increased [ 2 ] .
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