Design of molecular excitonic circuits for quantum computing: Theory and application to simple quantum algorithms.

Excitonic circuits made of organic dye molecules are known to be highly sensitive to environmental noise, however, they can also be strongly coupled so as to enable rapid transfer and evolution of phase information. Designing potential quantum computing platforms based on these systems requires a detailed description of their strengths and limitations.

Here, we present a strategy for controlling the dynamics of excitons by constructing circuits of strongly coupled molecular dyes. The programmable state of the exciton can then be exploited to encode the unitary transformation matrix representing a quantum logic gate, or a sequence of transformations representing a quantum algorithm. By studying the evolution of the excitonic circuit under open system conditions, we can assess the effect of the environmental fluctuations on the fidelity of the quantum computation. Specifically, we begin by designing a general method to map a set of universal quantum gates: NOT, Hadamard, π/8 and CNOT. Then, we extend this method to map the 2-qubit Deutsch-Jozsa algorithm - one of the simplest algorithms for which a quantum computer can outperform a classical one. For the latter, we propose and compare the performance of two different strategies: A higher fidelity approach where the entire algorithm is “hard-coded” into a single circuit, and a modular strategy, whereby the algorithm is implemented as a sequence of unitary gate operations. We observe that the fidelity of the encoded quantum operation depends entirely on the chemical and geometrical properties specified for the dyes in the circuit, and that these characteristics can be engineered to reduce the effect of the bath to maintain the integrity of the information encoded.