Better-than-classical circuits for OR and AND/OR found using genetic programming
Howard Barnum, Herbert Jacob Bernstein, Lee C. Spector · arXiv (Cornell University) · 1999
We present a quantum circuit evolved using genetic programming. From it we derive the first better-than-classical one-query bounded-error circuit for OR of one-bit black-box functions. The larger evolved circuit calculates, with error probability lower than any possible classical one-query algorithm, the property defined by a depth-two binary AND/OR tree with the four possible function input values as leaves. We analyze it as a kind of recursive application of the OR circuit. Since the OR and AND/OR trees have fan-in 2, these circuits may be useful in investigating the uniform binary AND/OR tree in the large-N asymptotic regime, a problem whose classical query complexity is completely understood and which has applications in game tree evaluation, logic programming, theorem-proving, and many other areas.