Understanding and controlling quantum interference QI in single molecules is fundamental to the development of QI based single molecule electronics. Over the past decade, simple rules such as counting rules, curly arrow rules, circuit rules and more recently magic ratio rules have been developed to predict QI patterns in polycyclic aromatic hydrocarbons. These rules have been successful in explaining observed electronic transport properties of molecular junctions and provide helpful design tools for predicting properties of molecules before their synthesis. Curly arrow rules are widely used by chemists, material scientists and physicists to predict destructive QI. Here we examine the validity of curly arrow rules in fully conjugated anthracene and dihydroxyanthracene, cross‐conjugated anthraquinone and broken conjugated dihydroanthracene attached to graphene or gold electrodes through pi‐pi stacking or thiol and Au‐C anchors. For the first time, we demonstrate that curly arrow rules break down in molecular junctions formed by cross‐conjugated anthraquinone. In contrast with the destructive QI predicted by curly arrow rules for a meta connected anthraquinone core, we demonstrate that QI is constructive. This behavior is independent of the choice of electrode material or anchor groups. This is significant, because by changing the redox state of meta connected dihydroxyanthracene to form meta connected anthraquinone, the conductance of the junction increases by couple of orders of magnitude due to the cross over form constructive to destructive QI. This opens new avenues for realization of quantum interference based single molecule switches.