On the design of molecular excitonic circuits for quantum computing: the universal quantum gates
This manuscript presents a strategy for controlling the transformation of excitonic states through the design of circuits made up of coupled organic dye molecules. Specifically, we show how unitary transformation matrices can be mapped to the Hamiltonians of physical systems of dye molecules with specified geometric and chemical properties. The evolution of these systems over specific times encode the action of the unitary transformation. We identify the bounds on complexity of the transformations that can be represented by these circuits. We formalize this strategy and apply it to identify the excitonic circuits of the four universal quantum logic gates: NOT, Hadamard, $\pi/8$ and CNOT. We discuss the properties of these circuits and how their performance is expected to be influenced by the presence of environmental noise. We quantify the bounds on the spectroscopic properties of organic dye circuits under which single-qubit unitary transformations are possible.