Variational Quantum Eigensolver Models of Molecular Quantum Dot Cellular Automata

Abstract: Molecular quantum-dot Cellular Automata (QCA) may provide low-power, high-speed computational hardware for processing classical information. Simulation and modeling play an important role in the design of QCA circuits because fully-coherent models of QCA scale exponentially with the number of devices, and such models are severely limited in size. For larger circuits, approximations become necessary. In the era of fault-tolerant quantum computation, however, it may become possible to model large QCA circuits without such limitations. Presently, this work explores the use of the noisy-intermediate scale quantum (NISQ) variational quantum eigensolver (VQE) method for estimating the ground state of QCA circuits. This is relevant because the computational result of a QCA calculation is encoded in the circuit's ground state. In this study, VQE is used to model logic circuits, including binary wires, inverters, and majority gates. VQE models are performed ideal simulators, noisy simulators, and actual quantum hardware. This study demonstrates that VQE may indeed be used to model molecular QCA circuits. It is observed that using modern NISQ hardware, results are still quite sensitive to noise, so measures should be taken to minimize noise. These include simplifying the ansatz circuit whenever possible, and using low-noise hardware.